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Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields
Energy xxx (2015) 1e11
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Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields Seyfolah Saedodin, Mohammad Sadegh Motaghedi Barforoush* Faculty of Mechanical Engineering, Semnan University, 35131-19111 Semnan, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 March 2015 Received in revised form 18 May 2015 Accepted 22 July 2015 Available online xxx
The energy crisis has led humankind to drastically think about optimization of facilities which are in closed connection with energy resources. Therefore, optimization of thermal systems from heat transfer point of view, to decrease heat losses and therefore energy consumption, is an explicit goal in the field of thermal sciences. This work is about conjugate radiation and convection heat transfer in a cylindrical enclosure using two radiation shields, to decrease heat loss. The experimental study applies three different materials, namely aluminum, copper and steel, as radiation shields. Numerical investigation is performed and validated against experimental data, using three-dimensional finite volume method. Different positions for radiation shields within the enclosure are considered. Both experimental and modeling studies adopt two different enclosure pressures, i.e., 0.2 and 1.0 atm. The inner cylinder is assumed to have two different temperatures, i.e., 473 K and 673 K. Seventy six different experiments are carried out to capture the best heat reduction with different radiation shield materials, inner cylinder temperatures, enclosure pressures and radii for radiation shields. Results show that both enclosure pressure and radiation shield emissivity are responsible for reduction of the total heat loss from the inner cylinder. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Experimental measurement Radiation Natural convection Radiation shields Numerical simulation
1. Introduction The growth rate of energy demand for both domestic and industrial facilities around the world is a side effect of modern life style. The dramatic increase in the energy consumption has brought humankind a new problematic issue which is known as energy crisis. Two important heat transfer modes which can lead to severe energy losses are convection and radiation. To reduce heat loss by these two modes and finally reduce energy consumption within a system, many studies have been conducted in various thermal systems by considering conjugate convection and radiation heat transfers [1e4]. The combined convection and radiation heat transfer modes are important in many industries. The significant interest in such problems originates from their importance in many engineering applications such as nuclear reactors [5,6], process industry [7,8], radiative cooling systems [9], heat exchangers [10e13], thermal
* Corresponding author. E-mail address: [email protected] (M.S. Motaghedi Barforoush).
energy storage systems [14], cooling of electronic components [15,16], thermal processing of moving plates [17], and even for buildings heating where the radiation and natural convection have considerable effect at the room temperature [18e22]. From the modeling point of view, two categories can be assumed to classify the above mentioned problems. The first category simplifies the convection and radiation effects, which have been set on the available boundary conditions, into the energy mathematical equation. These simplifications vastly lessen the complexity of the governing energy equation of the problem. By further assuming that the heat merely transferred through a specific direction, due to the dimensions of the system, the problem is reduced into a linear or nonlinear ordinary differential equation [9e12,17]. Although this method is cheap and available from the computational point of view, it mainly used to calculate the temperature of solid medium and may lack from the precision point of view. To overcome this weakness, another procedure has to be used. This approach is to tackle the partial differential equations of the system. If the system consists of fluid/gas materials, continuity, momentum and energy equations together by assuming the effects of convection and radiation should be solved [5,7,8,14e16,18e20]. Therefore,
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Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
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Nomenclature a g Gr I k Lc n p q00 R !0 s ! s T V
absorption coefficient gravitational acceleration, m/s Grashof number radiation intensity, W/sr thermal conductivity, W/mK characteristic length, m refractive index pressure, atm heat flux loss radius, m scattering direction vector, m direction vector, m temperature, K velocity, m/s
Greek letter volume expansion coefficient, 1/K ε emissivity F scattering phase function m dynamic viscosity, Pa-s
b
computational fluid dynamics should be employed to solve the coupled equations of these systems. Although this approach is costly and more challenging compared to the previous method, it has the advantage that has the ability to address the temperature field within both fluid and solid materials. The effect of radiation on the temperature and flow fields has been neglected in enclosures [23,24]. Despite numerous studies for natural convection, small amount of investigations have concentrated on the radiation transfer. The effect of radiation on the temperature and flow fields has been unfairly neglected for the analysis of heat transfer in enclosures which are filled with fluids [23,25] and nanofluids [26,27]. A conscientious investigation within the literature regarding heat transfer in convective-radiative environments reveals that the radiation effects play a significant role in these systems. Temperature distribution within these systems can greatly change by introducing the effects of radiation. In two different studies, Kuznetsov and Sheremet [28], and Martyushev and Sheremet [29] investigated the effect of Grashof number, transient factor, optical thickness and the solid wall thermal conductivity on the local thermo-hydrodynamic characteristics and on the integral parameters in an enclosure having finite thickness heat-conducting walls with local heating at the bottom of the cavity. Regarding thermo-hydrodynamic specifications of the system streamlines and temperature distribution were plotted and about integral parameters the average Nusselt number on the heat source surface was calculated. A conjugate study about turbulent natural convection and surface radiation in rectangular enclosures with various aspect ratios using a finite volume method was performed by Sharma et al. [30]. The analyzed geometry which is typically seen in liquid metal fast breeder reactor subsystems is heated from the bottom and cooled from other walls. A formula was proposed to calculate mean convection Nusselt number in terms of Rayleigh number and aspect ratio, which is an important design parameter for these systems. Special attention was paid to study the effectiveness in the horizontal fin arrays by Rao et al. [31]. It was assumed that both natural convection and radiation are participating in heat transfer mechanism. The effectiveness was calculated by considering different values for number of fins, fins height
n r s ss 0 U z
kinematic viscosity, m2/s density, kg/m3 StefaneBoltzmann's constant, W/m2K4 scattering coefficient solid angle, sr volume viscosity coefficient, Pa-s
Subscripts Al aluminum con convection Cu copper enc enclosure f fluid in inner cylinder inc incident out outer cylinder sh1 first shield sh2 second shield rad radiation St steel tot total w wall
and surface emissivity parameter. In another interesting study, Rabhi et al. [32] numerically studied the effects of surface radiation, and number of partitions on the heat transfer and flow structures in a rectangular enclosure. The enclosure had an inclination of 45 with respect to the horizontal plane. It was found that the value of total heat transfer is considerably increased under thermal radiation heat flux and reduced significantly with increasing the number gue and Bilgen [33] have numerically invesof partitions. Nouane tigated conjugate conduction, convection and radiation heat transfer in solar chimney systems. By adopting a control volume code ANSYS FLUENT, a study was performed on radiation interchanges between surfaces on the transition from steady, symmetric flows about the cavity centerline to complex periodic flow by Sun et al. [34]. Premachandran and Balaji [35] considered conjugate convection and radiation from vertical channels with four discrete protruding heat sources mounted on the right side wall of the channel. The effects of buoyancy and radiation heat transfer on flow and heat transfer characteristics of the thermal system have been analyzed. More recently, Saravanan and Sivaraj [36] have opted in favor of a numerical simulation of an air filled cavity with a centrally placed thin heated plate. Both convection and radiation modes have been considered. It was assumed that vertical walls of the cavity are cooled while the horizontal ones are insulated. A comparison between the experimental data and numerical simulation has been performed by Montiel-Gonzalez et al. [37]. They used SIMPLEC algorithm for the numerical approach and found that for most probed temperatures the deviation between the two methods is less than ten percent. De Faoite et al. [38] have opted in favor of inverse heat flux estimation on a plasma discharge tube using thermocouple data and a radiation boundary condition. Apart from direct approaches, inverse methods have been employed to find various characteristics of convective-radiative systems. Moghadassian and Kowsary [39] interestingly investigated the impact of heaters in a 2D enclosure to produce the desired temperature and heat flux distributions. The LevenbergeMarquardt algorithm was chosen to perform the iterative search procedure.
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
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It is well-known that the convection heat transfer needs a fluid to take place within the vicinity of a solidefluid interface. Therefore, it has been mentioned within the literature that considerably low air pressure in an enclosure can result a negligible heat transfer with convection mechanism from a solid surface [40]. Hence, radiation mode can be dominant if the system is considered from the heat transfer point of view. By controlling thermal radiation in this situation, due to the absence of the convection mode, a thermally insulating structure can be obtained [41]. By assuming highvacuum condition and applying radiation shields between the main hot and cold surfaces, heat transfer can be reduced. This approach has been used in recently theoretical published articles [42,43]. The concept of net radiation has been used. This concept provides an easy way for solving a variety of situations. Although this method is straightforward and without much complexities, it cannot be used when low-vacuum is presented. Using multilayer composite materials as a radiation shield have been discussed in an interesting patent by Bowers et al. [44]. A multilayer material with non-interlayer-contact spacer for space cryogenic missions has been developed and discussed by Miyakita et al. [45]. They also modeled temperature filed within different layers of the developed blanket. A good agreement between the measured temperature and the numerical results for the outermost layer was seen. If number of radiation shield exceeds a certain amount, it is possible to increase the heat transfer between the two main surfaces. This point has been mentioned in an article by Augusto [46]. Therefore, for multiple radiation shields an optimization procedure could be useful to find an optimum number of radiation shields and consequently the minimum heat transfer between the two surfaces. The main aim of this work is devoted to present experimental and numerical studies, to reduce conjugate radiation and natural convection heat transfer loss by inserting two radiation shields between two finite concentric cylinders at different enclosure pressures. For this purpose two radial radiation shields are inserted between two cylindrical surfaces. Three different radial positions between two cylinders have been considered. Three different materials, namely aluminum, copper, and steel, for radiation shields are used. Due to the direct effect of emissivity on the radiation, temperature dependent emissivity was considered for all materials. In the numerical modeling, a conjugate analysis is carried out in which the mass, momentum and energy balance equations in the enclosure are solved together. Furthermore, it was assumed that the density of the air is a function of temperature, and pressure follows the ideal gas law. The rest of this study has been divided into four sections. Section 2 illustrates the experimental procedure. Section 3 gives information regarding the numerical modeling and solution of involved equations. Section 4 provides graphs and tables about temperature and heat flux within studied structures. This section discusses the heat transfer reduction with application of radiation shields from both experimental and numerical points of view. Finally, Section 5 gives conclusion. It should be noted here that by considering previous studies about radiation heat loss reduction by radiation shields such as Ref. [46], it is seen that in most cases multiple shields have been used to maximize the heat reduction between main surfaces. Furthermore, in our recently published work [47], we have investigated the heat loss reduction between two concentric cylinders using one radiation shield. To extend our previous work [47] and at the same time make use of multiple radiation shields to minimize heat loss from two finite concentric cylinders, two radiation shields have been applied in this work. Further analyses to characterize the effect of radiation shield number on the heat loss reduction and the financial aspects of this research are under investigation.
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2. Experimental setup Fig. 1 shows the schematic of the experimental setup. The main parts of the system are a cylindrical enclosure, temperature sensors, resistance heating wire, vacuum pump, vacuum gage, and DAS (data acquisition system). The enclosure has two concentric cylinders which the inner one is heated with electrical heaters. It is filled with air during the experiments using two different pressures, i.e., 1 and 0.2 atm. Two cylindrical shields are inserted between the two main cylinders of the enclosure during experiments. Each cylindrical shield which is used as radiation shield has 2 mm thickness. Inner and outer cylinders' material together with the upper and lower bases of the cylindrical enclosure is steel. Three different materials, namely aluminum, copper and steel are used for radiation shields. Fig. 2 shows the main cylindrical enclosure and the used radiation shields. Experiments are carried out by changing the inner cylinder temperature, radiation shield materials and/or diameters, and enclosure air pressure. Using different inputs for power sources and fixing the temperature of the inner cylinder, the temperature of the radiation shields and the outer cylinder can be measured with K-type thermocouples. At different experiments the inner cylinder temperatures were measured in the range of 473e673 K and the thermocouple signals were sent to a data acquisition system. The heating was supplied by a resistance heating wire controlled by changing the electrical current of resistance wire to maintain a constant temperature. This electrical heating system that is used extensively in industrial applications is capable of withstanding severe temperatures which are applied in our experiments. Thermocouples are mounted at the central location of each cylinder. The upper and lower base sides of the structure were insulated, although in high temperatures it was not totally effective. A ceramic fiber material which has a recommended operating temperature more than 1000 K is suggested as the insulator. This material has high stability at elevated temperatures and low thermal shrinkage to less than 1% after more than 100 h. The low thermal conductivity of this material which is about 1 W/m.K offers an acceptable insulation of the base sides. The insulation of the base sides and the high aspect ratio of height to radius of the cylindrical system would allow us to assume negligible heat transfer from the bottom and top surfaces of the structure. The system operates in a room with ambient temperature of 303 K. By changing different parameters and specifications of the system, it has been tried to obtain an optimum condition. The optimum condition is considered as the situation which less heat is transferred through the inner cylinder to the outer one, using specific radiation shields in specific radius. The amount of heat loss was measured by multiplying the electrical current of resistance wire by its voltage. 3. Numerical modeling To construct the numerical analysis a three-dimensional model of two finite concentric cylinders with two different positions for radiation shields are prepared. For solving the continuity, momentum and energy equations, FLUENT 6.3.26 unsteady solver has been used and SIMPLE algorithm imposed for decoupling pressure and velocity fields. A time step of 0.5 s has been used. The simulation is continued to reach a steady value for the temperature of the radiation shield and its neighbor fluid flow. Obtaining this condition shows that the steady state is achieved. It is curios to note that using steady solver directly, the convergence of the velocity field cannot be ensured, and therefore we are urged to employ the unsteady solver. In another word, in natural convection problems in the enclosures, the solution will depend on the mass inside the domain. To obtain the enclosed mass the density of fluid should be
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
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Fig. 1. Schematic of the experimental setup (left), and cylindrical enclosure cross section with radiation shields (right).
Fig. 2. Experimental facilities, (a) cylindrical enclosure, (b) radiation shields.
known. When the temperature gradients in the domain are small, the Boussinesq model is suitable and steady state solver can be used. However, for large temperature differences the ideal gas model is employed. In this approach, the initial density will be computed from the initial pressure and temperature. Therefore, the initial mass is known and by solving the governing equations over time, the mass will be properly conserved [48]. Since the latter approach has been used in this work, the transient solution is adopted. As mentioned in Section 2, the upper and lower surfaces are assumed isolated. The differential equation of the continuity for a compressible fluid can be written as follows:
! vr þ V: r V ¼ 0 vt
(1)
Also momentum equation is presented in its deferential form as [49]:
! ! v rV ! ! ! ! þ V :V r V ¼ r g Vp þ mV2 V þ lV V: V vt
(2)
! where V is the velocity vector in (r,q,z) directions, p indicates the pressure, r refers to the density, m is the dynamic viscosity, and l stands for the second coefficient of viscosity. It was assumed that the enclosed air is isotropic and treated as an ideal gas, hence, the equation of state is valid for correlating the pressure, temperature and density to each other. According to the Stokes assumption the second coefficient of viscosity for the compressible enclosed air assumed as l ¼ 2=3m. DO (discrete ordinate) model is selected for radiation modeling, which solves the RTE (radiation transfer equation) for a finite number of discrete solid angles, each associated with a ! vector direction s fixed in the global system. The DO model ! ! which considers RTE at position r in the direction s as follows [48]:
4
sT ! !! ! ! V:ðIð r ; s Þ s Þ ¼ ða þ ss ÞIð r ; s Þ þ an2 p Z4p ! !0 ! !0 ss þ I r ; s F s ; s dU0 4p
(3)
0
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
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!0
! where, I is the radiation intensity, s is the direction vector, s indicates the scattering direction vector, a is the absorption coefficient, ss refers to the scattering coefficient, F is the scattering phase function which indicates the angular distribution of radiation 0 intensity scattered by a particle, U is the solid angle and n expresses the refractive index. In the present work, it was assumed that there are no aerosols, moisture and carbon dioxide molecules or other particles in the air. Hence, the scattering was neglected. The time step for RTE equation is set 5 times of flow time step (i.e. 2.5 s). Each octant of the angular space 4p at any spatial location is discretized into 2 2 solid angles in polar and azimuthal directions (q,f). The flow regime in natural convection is governed by the Grashof number in an enclosure, which represents the ratio of the buoyancy force to the viscous force acting on the fluid [50].
Gr ¼
gbðTh Tc ÞL3c n2
(4)
where, g is the gravitational acceleration, b indicates the coefficient of volume expansion, Th and Tc are the temperature of hot and cold surfaces, Lc is the characteristic length of the geometry (the distance between the hot and cold surfaces), and n is the kinematic viscosity of the fluid. In the current work, it is assumed that the emissivity of the walls material is a function of temperature and other thermo-physical properties are independent of temperature. The fluid is viscous, heat-conducting, Newtonian, and the ideal gas low is valid for correlating the pressure, temperature and density to each other. Also, it is assumed that the flow is laminar, which is conducted from comparing the Grashof number to its critical value (about 109) [50,51]. The temperature-dependent emissivity of wall's material extracted from trustworthy reference (Fig. 3) [51]. From this plot the best curve has been fitted and following relationships are achieved. The best formulas regarding emissivity versus temperature for aluminum, copper and steel are:
εðTÞal ¼ 4 1011 T 3 2 108 T 2 0:0004T þ 0:943
(5)
εðTÞcu ¼ 0:0002T 0:0035
(6)
εðTÞs ¼ 3 1011 T 3 þ 2 107 T 2 þ 8 105 T þ 0:0794 (7) Fig. 4 shows thermal boundary conditions for this problem. As it
Fig. 3. Temperature-dependent emissivity of aluminum, steel and copper [51].
5
was seen from this figure, in defining the boundary conditions for the above described governing equations, it is assumed that the inner cylinder has a constant temperature, while outer one has free convection with the ambient air. In addition, the top and bottom walls are both assumed to be perfectly insulated. In addition, the no-slip boundary condition imposes on all solid walls. The ambient temperature was assumed as initial temperature of the enclosure and the initial pressure was set equal to 0.2 atm and 1.0 atm, according to different experiments. To have less time consuming computations, only inside of enclosure was modeled, and available correlation was used to estimate the convective heat coefficient on the external side of the enclosure. In the laminar free convection problems around a vertical cylinder, Sparrow and Gregg [52] concluded that the vertical flat plate solution is acceptable for air when
D ðGrD PrÞ1=4 > 38 L
(8)
This means that the diameter of the cylinder is sufficiently large so that the curvature effects are negligible. The dimensions and operating conditions of this work satisfy the above inequality. Hence, for calculating the convection coefficient of the outer cylinder with the periphery air, Churchill and Chu [53] correlation for vertical plate was used:
0:670Ra1=4 Nu ¼ 0:68 þ h i4=9 1 þ ð0:492=PrÞ9=16
for RaL < 109
(9)
4. Results and discussions Both numerical and experimental analyses with two radiation shields between two main cylinders with three different positions along with previously mentioned different materials are examined. The geometrical characteristics of main cylinders by referring to Fig. 5 are reported in Table 1. The numerical analyses have been extended to mesh-independency calculations. The analyses were performed with different mesh numbers and finally a structured mesh of 228,000, 204,000, and 204,000 cells were chosen for Cases 1 to 3, respectively. These numbers of meshes are the least ones which the numerical simulations can be done with negligible inaccuracy. Validation of the numerical model is made by a comparison to the experimental data. Fig. 6 shows both numerical and experimental data for the temperature of the first radiation shield, i.e., aluminum, and the second radiation shield, i.e., copper, for all three cases. The symbol of AleCu in this figure means that the first shield which is near to the hotter inner cylinder is aluminum and the next one which is near to the outer cylinder is copper. The comparison shows a good agreement with experimental data. Nevertheless, a slight deviation is shown in Fig. 6. This small difference may arise from the adiabatic walls assumption for the top and down annular plates in the numerical procedure, which is not compatible very well with the experiments. For the other combinations of radiation shields similar agreements between simulations and experimental data have been seen, which are not repeated here. Temperature distributions along with isothermal surfaces at different pressures for case 1 to 3 with aluminum shield as the first and copper shield as the second layer are depicted in Fig. 7. As it can be seen from this figure, at low pressures the air temperature is relatively high, which arises from the low heat capacity (mcp) of enclosed air. The hotter air moves towards the top of the enclosure, because of its lower density, and yields to non-uniform temperature distribution at the radiation shields walls.
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
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Fig. 4. Boundary conditions of the problem.
2 np2 np1 !2 !2 !2 2 mp2 rp1 ideal gas mp2 P1 2 Grp1 P ¼ ¼ 0 f 1 mp1 rp2 mp1 P2 Grp2 P2
Grp1 ¼ Grp2
(11)
Fig. 5. Top view configurations of main cylinders and radiation shields.
Considering the ideal gas conditions (P ¼ rRT) the air volume expansion coefficient b, is equivalent to inverse of temperature:
b¼
1 T
(10)
Hence, for ideal gases with specific temperatures, reducing the enclosure pressure has no effect on the volume expansion coefficient. Therefore, the Gr number ratio for different pressures is evaluated as follows:
Hence, Gr number ratio is proportional to the square of pressure ratios. When the pressure descends from 1.0 atm to 0.2 atm, Gr number reduces by the ratio of 25, indicating the lower buoyancy force with respect to the viscous force at lower pressures and yields to low fluctuation for the flow field. Fig. 7 clearly illustrates this fact by comparing the isothermal surfaces of two enclosure pressures. The total heat loss from inner cylinder to the fluid is computed as [48]:
00 00 qtot ¼ hf Tw Tf þ qrad
(12)
where, Tw is the inner cylinder wall temperature, Tf is the local fluid 00 temperature, qrad is the radiation heat loss, and hf is the local heat transfer coefficient. The first term in the Eq. (12) is the convection heat loss and in the laminar flows it is computed using Fourier's law as follows:
Table 1 Main geometrical characteristics of concentric finite cylinders and radiation shields.
Case 1 Case 2 Case 3
Inner cylinder diameter (D1)
Outer cylinder diameter (D5)
Cylinders length (L)
First radiation shield diameter
Second radiation shield diameter
16 cm 16 cm 16 cm
50 cm 50 cm 50 cm
60 cm 60 cm 60 cm
26 cm 26 cm 34 cm
34 cm 42 cm 42 cm
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
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7
Fig. 6. The comparison between numerical and experimental results for AleCu radiation shields for Case 1 to 3.
hf Tw Tf
vT ¼ kf vr wall
(13)
where, kf is the fluid thermal conductivity and r is the radial coordinate normal to the cylinder wall. The second term in the Eq. (12) is radiation heat loss, and it is calculated using the following equation:
00
Z
qrad ¼ ð1 εw Þ$
!! 4 Iinc s : n dU þ n2 εw sTw
(14)
!! s : n >0 ! where, Iinc is the incident radiation intensity, s is the direction vector, n expresses the refractive index of medium next to the wall, εw is the wall emissivity, and s is the StefaneBoltzmann's constant.
The amount of total heat losses without radiation shields has been tabulated within Table 2. A comparison between the reported values by this table and the amount of total heat losses using radiation shields, i.e., Tables 3e5, confirms that radiation shields greatly contribute to lessen the heat loss within the cylindrical enclosure. Effects of locating the radiation shields with different conditions are detailed in Tables 3e5. Table 3 reports the effect of aluminum, copper and steel shields on the heat loss reduction from inner cylinder at two different temperatures for Case 1. Radiation shields' temperatures, radiation and convection heat losses from the inner cylinder are presented in this table. As can be seen, the temperature of the first shield increases when the pressure decreases. Therefore, the enclosure pressure modifies the flow fields, and reduces the first shield temperature by increasing the convection heat losses. On the other hand, with increasing the first shield temperature along with pressure reduction, the radiation heat losses are slightly
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
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Fig. 7. Temperature distribution and iso-surfaces for Case 1 to 3 at different pressures.
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
S. Saedodin, M.S. Motaghedi Barforoush / Energy xxx (2015) 1e11 Table 2 Total heat transfer loss through the cylinder enclosure without radiation shield. 00
Original case
Tin [K]
Penc [atm]
qtot [w/m2]
Without shield
473.15
1.0 0.2 1.0 0.2
993.5735 578.9321 3021.835 2174.176
673.15
9
significant. Comparing the results of this table indicates that using the copper as the first shield with lower emissivity comparing to steel and aluminum better decreases the total heat transfer loss by alleviating the amount of radiation loss. Hence, when the copper shield is used in the first layer and the steel shield is located at the second layer the minimum heat transfer loss is achieved. The same behavior of reduction in the heat losses at various
Table 3 Heat loss reduction at different enclosure pressures and inner cylinder temperatures in Case 1. 00
00
00
Case 1
Tin [K]
Penc [atm]
qtot [w/m2]
qrad [w/m2]
qcon [w/m2]
Tsh1 [K]
Tsh2 [K]
AleCu
473.15
1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2
396.5734 229.9469 1307.107 937.3605 422.5654 261.6159 1452.711 1107.082 362.3963 201.674 1102.047 786.2101 349.1902 185.5182 1032.969 696.4203 394.9779 237.0998 1287.275 981.7267 361.3965 194.6464 1100.284 745.0569
198.8161 170.4714 1078.092 875.3813 209.4459 190.9324 1187.114 1027.877 110.2451 107.9862 713.5259 668.0712 107.3371 101.6668 680.3275 601.8067 147.2163 144.6958 919.7992 864.5757 137.5726 123.7006 809.6854 672.0205
197.7573 59.4755 229.015 61.9792 213.1195 70.6835 265.597 79.205 252.1512 93.6878 388.5211 118.1389 241.8531 83.8514 352.6415 94.6136 247.7616 92.404 367.4758 117.151 223.8239 70.9458 290.5986 73.0364
412.3034 419.3417 583.3635 599.8065 408.2677 411.437 571.7998 584.0599 400.8778 397.7585 542.2319 549.9031 403.7475 404.2562 552.5386 568.8359 401.1309 397.8523 545.4039 550.9116 407.5154 412.2043 567.9555 587.9086
358.7117 360.5854 469.9551 491.2754 358.5709 361.506 472.4442 495.2074 347.0186 338.9377 427.657 426.0544 350.2428 345.272 435.884 441.6292 349.8253 344.7159 440.412 446.6236 353.6019 351.9884 449.4905 462.52
673.15 AleSt
473.15 673.15
CueAl
473.15 673.15
CueSt
473.15 673.15
SteAl
473.15 673.15
SteCu
473.15 673.15
Table 4 Heat loss reduction at different enclosure pressures and inner cylinder temperatures for Case 2. 00
00
00
Case 2
Tin [K]
Penc [atm]
qtot [w/m2]
qrad [w/m2]
qcon [w/m2]
Tsh1 [K]
Tsh2 [K]
AleCu
473.15
1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2
417.8251 251.9402 1373.349 1042.663 444.2729 282.6831 1519.305 1205.347 377.8359 208.9802 1122.551 809.8032 364.867 195.0259 1056.824 735.1973 409.949 244.9875 1307.837 1010.148 376.3656 201.3687 1134.054 807.2021
209.8266 185.8119 1136.237 971.1304 220.099 204.8305 1243.796 1115.661 113.3113 110.9212 726.8194 685.2079 110.8545 105.9412 698.1395 631.9539 151.3809 148.5261 936.3123 886.9631 142.7667 134.6752 838.5148 725.0999
207.9985 66.1283 237.112 71.5326 224.1739 77.8526 275.509 89.686 264.5246 98.059 395.7316 124.5953 254.0125 89.0847 358.6845 103.2434 258.5681 96.4614 371.5247 123.1849 233.5989 66.6935 295.5392 82.1022
385.08 405.211 540.0067 578.8179 382.2583 398.2309 532.2805 564.7611 371.3587 383.6279 487.953 525.1131 374.187 389.3623 498.1909 542.2836 373.4127 385.2159 498.1085 530.2628 379.0213 392.0936 517.0708 562.9022
325.6722 342.4008 388.009 440.5428 326.6785 344.1147 392.894 446.437 319.6078 326.9337 362.3113 391.1952 320.5641 330.1716 364.4581 398.441 321.8845 331.9597 372.6505 409.3558 322.5032 330.6328 372.448 414.2155
673.15 AleSt
473.15 673.15
CueAl
473.15 673.15
CueSt
473.15 673.15
SteAl
473.15 673.15
SteCu
473.15 673.15
reduced because of decreasing the temperature difference between the inner cylinder and the first shield. In lower pressures, the power of electromagnetic radiation waves to travel through the vacuum medium makes thermal radiation the main mode of heat transfer and its contribution to the total heat transfer rate becomes
temperatures and pressures have been achieved for Cases 2 and 3 and results are reported in Tables 4 and 5, respectively. Comparing the results of these tables to Table 3 indicates that the heat transfer losses in Case 1 are much less than Cases 2 and 3. Hence, locating the radiation shield closer to the hotter surface has the maximum
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S. Saedodin, M.S. Motaghedi Barforoush / Energy xxx (2015) 1e11
Table 5 Heat loss reduction at different enclosure pressures and inner cylinder temperatures for Case 3. 00
00
00
Case 3
Tin [K]
Penc [atm]
qtot [w/m2]
qrad [w/m2]
qcon [w/m2]
Tsh1 [K]
Tsh2 [K]
AleCu
473.15
1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2
444.0579 262.8758 1425.074 1066.651 471.4276 294.62 1574.529 1236.465 421.6281 236.4019 1258.222 921.5991 404.4398 219.3997 1174.172 826.0812 453.8656 272.5266 1443.526 1120.452 419.8839 228.6463 1230.227 874.3762
209.1243 185.5805 1154.508 980.4564 218.9335 204.5564 1259.356 1127.829 130.8206 128.1522 831.8172 780.1287 127.4313 121.4852 792.2551 709.9549 165.372 163.3278 1029.087 975.1588 152.3533 142.3886 909.7609 779.5037
234.9336 77.2953 270.566 86.1946 252.4941 90.0636 315.173 108.636 290.8075 108.2497 426.4048 141.4704 277.0085 97.9145 381.9169 116.1263 288.4936 109.1988 414.439 145.2932 267.5306 86.2577 320.4661 94.8725
384.0189 404.4431 533.6197 576.21 381.4832 397.7226 526.7566 562.2176 371.4208 383.4179 486.9471 524.5009 374.6093 389.6682 497.8376 542.8329 373.0345 384.3096 495.4409 528.1301 386.2597 397.3663 514.6194 562.4971
362.3618 360.6566 480.6047 489.1952 361.7086 361.1475 480.6359 492.5062 351.745 342.1176 440.9426 433.7897 354.8558 347.2532 449.4638 445.9893 354.1431 347.3705 452.0475 452.3701 351.1204 353.2953 462.867 464.4673
673.15 AleSt
473.15 673.15
CueAl
473.15 673.15
CueSt
473.15 673.15
SteAl
473.15 673.15
SteCu
473.15 673.15
heat loss reduction. This fact has been pointed out in previous theoretical studies by Saedodin et al. [42] and Torabi et al. [43] for the application of radiation shields between two surfaces, when completely vacuum condition is considered. With the increasing of the distance between cylinders Gr number (Eq. (4)) will increase and thus will magnify the heat transfer. This phenomenon is clearly visible by comparing the results of Tables 3e5. As in the first Case, the distance between the first shield and the inner cylinder is equal to 8 cm and second shield is located 8 cm far from the first shield, the convective losses reach their minimum value. Therefore, it is inferred that the enclosure pressure affects the convection heat losses, and the shield emissivity impacts on the radiation heat losses. Therefore, the both heat loss mechanisms will be responsible for reducing the total heat loss from the inner cylinder. Another point is that, Tables 3 and 5 express the heat loss increment with increasing the distance between the inner cylinder and radiation shields. It was found that for Cu-St radiation shields by setting the inner cylinder wall's temperature at 673.15 K and fixing enclosure pressure at 1.0 atm, heat losses ascend from 1032.969 to 1174.172 (W/m2) from Case 1 to Case 3, addressing 13.67% of growth. 5. Conclusions This work presents a numerical and experimental study about the cylindrical radiation shields with temperature-dependent emissivity between two finite concentric cylinders, and discusses effects of various parameters on the heat transfer and flow field. Two different pressures have been assumed for the enclosure and three different materials, namely aluminum, copper and steel, have been used as radiation shields. Results showed that radiation shields vastly decrease the total amount of heat transfer through the cylindrical enclosure. According to the results, radiation heat losses ascend with emissivity of radiation shields. Also, the convection contribution decreases the temperatures of the radiation shields, addressing the increase of the radiation loss from inner cylinder. The total heat losses for each case decreases by reducing the enclosure pressure, because of weakening both convection and radiation effects. Obtained results for copper deduce that the copper is more appropriate to be used as a radiation shield compared
with aluminum and steel because of its lower emissivity. It was found that using radiation shields between the two main surfaces vastly reduces the heat transfer between them. Also, it was indicated that the total heat losses is more reduced when the radiation shields are positioned near the hotter inner cylinder. As an example, for Cu-St radiation shields and inner cylinder temperature of 673.15 K and the enclosure pressure of 1 atm, the total heat losses for Cases 1 to 3 are found to be 1032.969, 1056.824, 1174.172 [w/m2] which is 40.63%, 43.73% and 34.1% lower than Al-St shields, respectively. References [1] Bouchair A. Steady state theoretical model of fired clay hollow bricks for enhanced external wall thermal insulation. Build Environ 2008;43:1603e18. Martin K, Urresti A, García-Romero A, Sala JM. [2] Diarce G, Campos-Celador A, A comparative study of the CFD modeling of a ventilated active façade including phase change materials. Appl Energy 2014;126:307e17. rez Sierra JL, Pen ~ uelas Sa nchez I. Non-linear [3] Del Coz Díaz JJ, García Nieto PJ, Sua thermal optimization and design improvement of a new internal light concrete multi-holed brick walls by FEM. Appl Therm Eng 2008;28:1090e100. [4] Hemmer C, Polidori G, Popa C. Case studies in thermal engineering temperature optimization of an electric heater by emissivity variation of heating elements. Case Stud Therm Eng 2014;4:187e92. [5] Senve V, Narasimham GSVL. Effective thermal conductivity of a heat generating rod bundle dissipating heat by natural convection and radiation. Nucl Eng Des 2011;241:4331e40. [6] Tsuji N, Nakano M, Takada E, Tokuhara K, Ohashi K, Okamoto F, et al. Study of the applicability of CFD calculation for HTTR reactor. Nucl Eng Des 2014;271: 564e8. [7] Malik AH, Alvi MS, Khushnood S, Mahfouz FM, Ghauri MKK, Shah A. Experimental study of conjugate heat transfer within a bottom heated vertical concentric cylindrical enclosure. Int J Heat Mass Transf 2012;55:1154e63. [8] Malik AH, Shah A, Khushnood S. CFD analysis of heat transfer within a bottom heated vertical concentric cylindrical enclosure. J Phys Conf Ser 2013;439: 012004. [9] Al-Nimr MA, Kodah Z, Nassar B. A theoretical and experimental investigation of a radiative cooling system. Sol Energy 1998;63:367e73. [10] Torabi M, Aziz A, Zhang K. A comparative study of longitudinal fins of rectangular, trapezoidal and concave parabolic profiles with multiple nonlinearities. Energy 2013;51:243e56. [11] Torabi M, Zhang QB. Analytical solution for evaluating the thermal performance and efficiency of convectiveeradiative straight fins with various profiles and considering all non-linearities. Energy Convers Manage 2013;66: 199e210. [12] Hatami M, Ganji DD. Thermal performance of circular convectiveeradiative porous fins with different section shapes and materials. Energy Convers Manage 2013;76:185e93.
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
S. Saedodin, M.S. Motaghedi Barforoush / Energy xxx (2015) 1e11 [13] Abdesslem J, Khalifa S, Abdelaziz N, Abdallah M. Radiative properties effects on unsteady natural convection inside a saturated porous medium. Application for porous heat exchangers. Energy 2013;61:224e33. F, Zhao CY, Baeyens J, Degre ve J, Zhang HL. Circulating fluidized bed heat [14] Pitie recovery/storage and its potential to use coated phase-change-material (PCM) particles. Appl Energy 2013;109:505e13. [15] Sawant SM, Gururaja Rao C. Conjugate mixed convection with surface radiation from a vertical electronic board with multiple discrete heat sources. Heat Mass Transf 2008;44:1485e95. [16] Baïri A. Transient thermal characteristics of airborne electronic equipment with discrete hot bands in square cavities. Appl Energy 2008;85:951e67. [17] Saedodin S, Barforoush MSM. Comprehensive analytical study for convectiveeradiative continuously moving plates with multiple non-linearities. Energy Convers Manage 2014;81:160e8. [18] Wang Y, Meng X, Yang X, Liu J. Influence of convection and radiation on the thermal environment in an industrial building with buoyancy-driven natural ventilation. Energy Build 2014;75:394e401. [19] Rahimi M, Sabernaeemi A. Experimental study of radiation and free convection in an enclosure with under-floor heating system. Energy Convers Manage 2011;52:2752e7. [20] Rahimi M, Sabernaeemi A. Experimental study of radiation and free convection in an enclosure with a radiant ceiling heating system. Energy Build 2010;42:2077e82. [21] Slimi K, Mhimid A, Ben Salah M, Ben Nasrallah S, Mohamad AA, Storesletten L. Anisotropy effects on heat and fluid flow by unsteady natural convection and radiation in saturated porous media. Numer Heat Transf Part A Appl 2005;48: 763e90. [22] Slimi K. A two-temperature model for predicting heat and fluid flow by natural convection and radiation within a saturated porous vertical channel. J Porous Media 2009;12:43e63. [23] Kuznetsov GV, Sheremet MA. Numerical simulation of turbulent natural convection in a rectangular enclosure having finite thickness walls. Int J Heat Mass Transf 2010;53:163e77. [24] Rashidi I, Mahian O, Lorenzini G, Biserni C, Wongwises S. Natural convection of Al2O3/water nanofluid in a square cavity: effects of heterogeneous heating. Int J Heat Mass Transf 2014;74:391e402. [25] Saha SC, Gu YT. Natural convection in a triangular enclosure heated from below and non-uniformly cooled from top. Int J Heat Mass Transf 2015;80: 529e38. [26] Ahmed M, Eslamian M. Natural convection in a differentially-heated square enclosure filled with a nanofluid: significance of the thermophoresis force and slip/drift velocity. Int Commun Heat Mass Transf 2014;58:1e11. € [27] Rahman MM, Oztop HF, Mekhilef S, Saidur R, Al-Salem K. Unsteady natural convection in Al2O3-water nanoliquid filled in isosceles triangular enclosure with sinusoidal thermal boundary condition on bottom wall. Superlattices Microstruct 2014;67:181e96. [28] Kuznetsov GV, Sheremet MA. Conjugate natural convection with radiation in an enclosure. Int J Heat Mass Transf 2009;52:2215e23. [29] Martyushev SG, Sheremet MA. Conjugate natural convection combined with surface thermal radiation in a three-dimensional enclosure with a heat source. Int J Heat Mass Transf 2014;73:340e53. [30] Sharma AK, Velusamy K, Balaji C, Venkateshan SP. Conjugate turbulent natural convection with surface radiation in air filled rectangular enclosures. Int J Heat Mass Transf 2007;50:625e39. [31] Rao VD, Naidu SV, Rao BG, Sharma KV. Heat transfer from a horizontal fin array by natural convection and radiationda conjugate analysis. Int J Heat Mass Transf 2006;49:3379e91.
11
[32] Rabhi M, Bouali H, Mezrhab A. Radiationenatural convection heat transfer in inclined rectangular enclosures with multiple partitions. Energy Convers Manage 2008;49:1228e36. gue HF, Bilgen E. Heat transfer by convection, conduction and radia[33] Nouane tion in solar chimney systems for ventilation of dwellings. Int J Heat Fluid Flow 2009;30:150e7. nier E, Lauriat G. Effect of surface radiation on the breakdown of [34] Sun H, Che steady natural convection flows in a square, air-filled cavity containing a centered inner body. Appl Therm Eng 2011;31:1252e62. [35] Premachandran B, Balaji C. Conjugate mixed convection with surface radiation from a vertical channel with protruding heat sources. Numer Heat Transf Part A Appl 2011;60:171e96. [36] Saravanan S, Sivaraj C. Coupled thermal radiation and natural convection heat transfer in a cavity with a heated plate inside. Int J Heat Fluid Flow 2013;40:54e64. n-Vidales HI, Bautista-Orozco A, [37] Montiel-Gonz alez M, Hinojosa JF, Villafa Estrada CA. Theoretical and experimental study of natural convection with surface thermal radiation in a side open cavity. Appl Therm Eng 2014:1e11. [38] De Faoite D, Browne DJ, Del Valle Gamboa JI, Stanton KT. Inverse estimate of heat flux on a plasma discharge tube to steady-state conditions using thermocouple data and a radiation boundary condition. Int J Heat Mass Transf 2014;77:564e76. [39] Moghadassian B, Kowsary F. Inverse boundary design problem of natural convectioneradiation in a square enclosure. Int J Therm Sci 2014;75:116e26. [40] Thevenet J, Siroux M, Desmet B. Measurements of brake disc surface temperature and emissivity by two-color pyrometry. Appl Therm Eng 2010;30: 753e9. [41] Akamine S, Fujita M. Controlling heat radiation for development of hightemperature insulating materials. J Eur Ceram Soc 2014:3e8. [42] Saedodin S, Motaghedi Barforoush MS, Torabi M. Reducing heat transfer between two concentric semi-cylinders using radiation shields with temperature-dependent emissivity. Front Heat Mass Transf 2012;2:2e5. [43] Torabi M, Aziz A, Saedodin S. Application of hemisphere radiation shields with temperature-dependent emissivity for reducing heat transfer between two concentric hemispheres. Thermophys Aeromech 2013;19:481e8. [44] Bowers JA, Hyde RA, Ishikawa MY, Jung EKY, Kare JT, Leuthardt EC, et al. Multilayer insulation composite material including bandgap material, storage container using same, and related methods. U.S. Patent US 8,703,259 B2. 2014. [45] Miyakita T, Hatakenaka R, Sugita H, Saitoh M, Hirai T. Development of a new multi-layer insulation blanket with non-interlayer-contact spacer for space cryogenic mission. Cryogenics (Guildf) NovembereDecember 2014;64:112e20. [46] Augusto PA, Castelo-Grande T, Augusto P, Barbosa D. Optimization of refrigerated shields using multilayer thermal insulation: cryostats design e analytical solution. Cryogenics (Guildf) 2006;46:449e57. [47] Barforoush MSM, Saedodin S. Heat transfer reduction between two finite concentric cylinders using radiation shields; experimental and numerical studies. Int Commun Heat Mass Transf 2015;65:94e102. [48] FLUENT. User's guide 6.3. USA: Fluent Inc; 2005. [49] Lai M, Krempl E, Ruben D. Introduction to continuum mechanics. 4th ed. ButterwortheHeinemann; 2010. [50] Bejan A. Convection heat transfer. 4th ed. John Wiley & Sons, Inc; 2013. [51] Bergman TL, Lavine AS, Incropera FP, DeWitt DP. Introduction to heat transfer. 6th ed. John Wiley and Sons, Inc; 2011. [52] Sparrow EM, Gregg JL. Laminar free convection heat transfer from the outer surface of a vertical circular cylinder. Trans ASME 1956;78:183e9. [53] Churchill SW, Chu HHS. Correlating equations for laminar and turbulent free convection from a horizontal cylinder. Int J Heat Mass Transf 1975;18: 1049e53.
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Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields Seyfolah Saedodin, Mohammad Sadegh Motaghedi Barforoush* Faculty of Mechanical Engineering, Semnan University, 35131-19111 Semnan, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 March 2015 Received in revised form 18 May 2015 Accepted 22 July 2015 Available online xxx
The energy crisis has led humankind to drastically think about optimization of facilities which are in closed connection with energy resources. Therefore, optimization of thermal systems from heat transfer point of view, to decrease heat losses and therefore energy consumption, is an explicit goal in the field of thermal sciences. This work is about conjugate radiation and convection heat transfer in a cylindrical enclosure using two radiation shields, to decrease heat loss. The experimental study applies three different materials, namely aluminum, copper and steel, as radiation shields. Numerical investigation is performed and validated against experimental data, using three-dimensional finite volume method. Different positions for radiation shields within the enclosure are considered. Both experimental and modeling studies adopt two different enclosure pressures, i.e., 0.2 and 1.0 atm. The inner cylinder is assumed to have two different temperatures, i.e., 473 K and 673 K. Seventy six different experiments are carried out to capture the best heat reduction with different radiation shield materials, inner cylinder temperatures, enclosure pressures and radii for radiation shields. Results show that both enclosure pressure and radiation shield emissivity are responsible for reduction of the total heat loss from the inner cylinder. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Experimental measurement Radiation Natural convection Radiation shields Numerical simulation
1. Introduction The growth rate of energy demand for both domestic and industrial facilities around the world is a side effect of modern life style. The dramatic increase in the energy consumption has brought humankind a new problematic issue which is known as energy crisis. Two important heat transfer modes which can lead to severe energy losses are convection and radiation. To reduce heat loss by these two modes and finally reduce energy consumption within a system, many studies have been conducted in various thermal systems by considering conjugate convection and radiation heat transfers [1e4]. The combined convection and radiation heat transfer modes are important in many industries. The significant interest in such problems originates from their importance in many engineering applications such as nuclear reactors [5,6], process industry [7,8], radiative cooling systems [9], heat exchangers [10e13], thermal
* Corresponding author. E-mail address: [email protected] (M.S. Motaghedi Barforoush).
energy storage systems [14], cooling of electronic components [15,16], thermal processing of moving plates [17], and even for buildings heating where the radiation and natural convection have considerable effect at the room temperature [18e22]. From the modeling point of view, two categories can be assumed to classify the above mentioned problems. The first category simplifies the convection and radiation effects, which have been set on the available boundary conditions, into the energy mathematical equation. These simplifications vastly lessen the complexity of the governing energy equation of the problem. By further assuming that the heat merely transferred through a specific direction, due to the dimensions of the system, the problem is reduced into a linear or nonlinear ordinary differential equation [9e12,17]. Although this method is cheap and available from the computational point of view, it mainly used to calculate the temperature of solid medium and may lack from the precision point of view. To overcome this weakness, another procedure has to be used. This approach is to tackle the partial differential equations of the system. If the system consists of fluid/gas materials, continuity, momentum and energy equations together by assuming the effects of convection and radiation should be solved [5,7,8,14e16,18e20]. Therefore,
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S. Saedodin, M.S. Motaghedi Barforoush / Energy xxx (2015) 1e11
Nomenclature a g Gr I k Lc n p q00 R !0 s ! s T V
absorption coefficient gravitational acceleration, m/s Grashof number radiation intensity, W/sr thermal conductivity, W/mK characteristic length, m refractive index pressure, atm heat flux loss radius, m scattering direction vector, m direction vector, m temperature, K velocity, m/s
Greek letter volume expansion coefficient, 1/K ε emissivity F scattering phase function m dynamic viscosity, Pa-s
b
computational fluid dynamics should be employed to solve the coupled equations of these systems. Although this approach is costly and more challenging compared to the previous method, it has the advantage that has the ability to address the temperature field within both fluid and solid materials. The effect of radiation on the temperature and flow fields has been neglected in enclosures [23,24]. Despite numerous studies for natural convection, small amount of investigations have concentrated on the radiation transfer. The effect of radiation on the temperature and flow fields has been unfairly neglected for the analysis of heat transfer in enclosures which are filled with fluids [23,25] and nanofluids [26,27]. A conscientious investigation within the literature regarding heat transfer in convective-radiative environments reveals that the radiation effects play a significant role in these systems. Temperature distribution within these systems can greatly change by introducing the effects of radiation. In two different studies, Kuznetsov and Sheremet [28], and Martyushev and Sheremet [29] investigated the effect of Grashof number, transient factor, optical thickness and the solid wall thermal conductivity on the local thermo-hydrodynamic characteristics and on the integral parameters in an enclosure having finite thickness heat-conducting walls with local heating at the bottom of the cavity. Regarding thermo-hydrodynamic specifications of the system streamlines and temperature distribution were plotted and about integral parameters the average Nusselt number on the heat source surface was calculated. A conjugate study about turbulent natural convection and surface radiation in rectangular enclosures with various aspect ratios using a finite volume method was performed by Sharma et al. [30]. The analyzed geometry which is typically seen in liquid metal fast breeder reactor subsystems is heated from the bottom and cooled from other walls. A formula was proposed to calculate mean convection Nusselt number in terms of Rayleigh number and aspect ratio, which is an important design parameter for these systems. Special attention was paid to study the effectiveness in the horizontal fin arrays by Rao et al. [31]. It was assumed that both natural convection and radiation are participating in heat transfer mechanism. The effectiveness was calculated by considering different values for number of fins, fins height
n r s ss 0 U z
kinematic viscosity, m2/s density, kg/m3 StefaneBoltzmann's constant, W/m2K4 scattering coefficient solid angle, sr volume viscosity coefficient, Pa-s
Subscripts Al aluminum con convection Cu copper enc enclosure f fluid in inner cylinder inc incident out outer cylinder sh1 first shield sh2 second shield rad radiation St steel tot total w wall
and surface emissivity parameter. In another interesting study, Rabhi et al. [32] numerically studied the effects of surface radiation, and number of partitions on the heat transfer and flow structures in a rectangular enclosure. The enclosure had an inclination of 45 with respect to the horizontal plane. It was found that the value of total heat transfer is considerably increased under thermal radiation heat flux and reduced significantly with increasing the number gue and Bilgen [33] have numerically invesof partitions. Nouane tigated conjugate conduction, convection and radiation heat transfer in solar chimney systems. By adopting a control volume code ANSYS FLUENT, a study was performed on radiation interchanges between surfaces on the transition from steady, symmetric flows about the cavity centerline to complex periodic flow by Sun et al. [34]. Premachandran and Balaji [35] considered conjugate convection and radiation from vertical channels with four discrete protruding heat sources mounted on the right side wall of the channel. The effects of buoyancy and radiation heat transfer on flow and heat transfer characteristics of the thermal system have been analyzed. More recently, Saravanan and Sivaraj [36] have opted in favor of a numerical simulation of an air filled cavity with a centrally placed thin heated plate. Both convection and radiation modes have been considered. It was assumed that vertical walls of the cavity are cooled while the horizontal ones are insulated. A comparison between the experimental data and numerical simulation has been performed by Montiel-Gonzalez et al. [37]. They used SIMPLEC algorithm for the numerical approach and found that for most probed temperatures the deviation between the two methods is less than ten percent. De Faoite et al. [38] have opted in favor of inverse heat flux estimation on a plasma discharge tube using thermocouple data and a radiation boundary condition. Apart from direct approaches, inverse methods have been employed to find various characteristics of convective-radiative systems. Moghadassian and Kowsary [39] interestingly investigated the impact of heaters in a 2D enclosure to produce the desired temperature and heat flux distributions. The LevenbergeMarquardt algorithm was chosen to perform the iterative search procedure.
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
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It is well-known that the convection heat transfer needs a fluid to take place within the vicinity of a solidefluid interface. Therefore, it has been mentioned within the literature that considerably low air pressure in an enclosure can result a negligible heat transfer with convection mechanism from a solid surface [40]. Hence, radiation mode can be dominant if the system is considered from the heat transfer point of view. By controlling thermal radiation in this situation, due to the absence of the convection mode, a thermally insulating structure can be obtained [41]. By assuming highvacuum condition and applying radiation shields between the main hot and cold surfaces, heat transfer can be reduced. This approach has been used in recently theoretical published articles [42,43]. The concept of net radiation has been used. This concept provides an easy way for solving a variety of situations. Although this method is straightforward and without much complexities, it cannot be used when low-vacuum is presented. Using multilayer composite materials as a radiation shield have been discussed in an interesting patent by Bowers et al. [44]. A multilayer material with non-interlayer-contact spacer for space cryogenic missions has been developed and discussed by Miyakita et al. [45]. They also modeled temperature filed within different layers of the developed blanket. A good agreement between the measured temperature and the numerical results for the outermost layer was seen. If number of radiation shield exceeds a certain amount, it is possible to increase the heat transfer between the two main surfaces. This point has been mentioned in an article by Augusto [46]. Therefore, for multiple radiation shields an optimization procedure could be useful to find an optimum number of radiation shields and consequently the minimum heat transfer between the two surfaces. The main aim of this work is devoted to present experimental and numerical studies, to reduce conjugate radiation and natural convection heat transfer loss by inserting two radiation shields between two finite concentric cylinders at different enclosure pressures. For this purpose two radial radiation shields are inserted between two cylindrical surfaces. Three different radial positions between two cylinders have been considered. Three different materials, namely aluminum, copper, and steel, for radiation shields are used. Due to the direct effect of emissivity on the radiation, temperature dependent emissivity was considered for all materials. In the numerical modeling, a conjugate analysis is carried out in which the mass, momentum and energy balance equations in the enclosure are solved together. Furthermore, it was assumed that the density of the air is a function of temperature, and pressure follows the ideal gas law. The rest of this study has been divided into four sections. Section 2 illustrates the experimental procedure. Section 3 gives information regarding the numerical modeling and solution of involved equations. Section 4 provides graphs and tables about temperature and heat flux within studied structures. This section discusses the heat transfer reduction with application of radiation shields from both experimental and numerical points of view. Finally, Section 5 gives conclusion. It should be noted here that by considering previous studies about radiation heat loss reduction by radiation shields such as Ref. [46], it is seen that in most cases multiple shields have been used to maximize the heat reduction between main surfaces. Furthermore, in our recently published work [47], we have investigated the heat loss reduction between two concentric cylinders using one radiation shield. To extend our previous work [47] and at the same time make use of multiple radiation shields to minimize heat loss from two finite concentric cylinders, two radiation shields have been applied in this work. Further analyses to characterize the effect of radiation shield number on the heat loss reduction and the financial aspects of this research are under investigation.
3
2. Experimental setup Fig. 1 shows the schematic of the experimental setup. The main parts of the system are a cylindrical enclosure, temperature sensors, resistance heating wire, vacuum pump, vacuum gage, and DAS (data acquisition system). The enclosure has two concentric cylinders which the inner one is heated with electrical heaters. It is filled with air during the experiments using two different pressures, i.e., 1 and 0.2 atm. Two cylindrical shields are inserted between the two main cylinders of the enclosure during experiments. Each cylindrical shield which is used as radiation shield has 2 mm thickness. Inner and outer cylinders' material together with the upper and lower bases of the cylindrical enclosure is steel. Three different materials, namely aluminum, copper and steel are used for radiation shields. Fig. 2 shows the main cylindrical enclosure and the used radiation shields. Experiments are carried out by changing the inner cylinder temperature, radiation shield materials and/or diameters, and enclosure air pressure. Using different inputs for power sources and fixing the temperature of the inner cylinder, the temperature of the radiation shields and the outer cylinder can be measured with K-type thermocouples. At different experiments the inner cylinder temperatures were measured in the range of 473e673 K and the thermocouple signals were sent to a data acquisition system. The heating was supplied by a resistance heating wire controlled by changing the electrical current of resistance wire to maintain a constant temperature. This electrical heating system that is used extensively in industrial applications is capable of withstanding severe temperatures which are applied in our experiments. Thermocouples are mounted at the central location of each cylinder. The upper and lower base sides of the structure were insulated, although in high temperatures it was not totally effective. A ceramic fiber material which has a recommended operating temperature more than 1000 K is suggested as the insulator. This material has high stability at elevated temperatures and low thermal shrinkage to less than 1% after more than 100 h. The low thermal conductivity of this material which is about 1 W/m.K offers an acceptable insulation of the base sides. The insulation of the base sides and the high aspect ratio of height to radius of the cylindrical system would allow us to assume negligible heat transfer from the bottom and top surfaces of the structure. The system operates in a room with ambient temperature of 303 K. By changing different parameters and specifications of the system, it has been tried to obtain an optimum condition. The optimum condition is considered as the situation which less heat is transferred through the inner cylinder to the outer one, using specific radiation shields in specific radius. The amount of heat loss was measured by multiplying the electrical current of resistance wire by its voltage. 3. Numerical modeling To construct the numerical analysis a three-dimensional model of two finite concentric cylinders with two different positions for radiation shields are prepared. For solving the continuity, momentum and energy equations, FLUENT 6.3.26 unsteady solver has been used and SIMPLE algorithm imposed for decoupling pressure and velocity fields. A time step of 0.5 s has been used. The simulation is continued to reach a steady value for the temperature of the radiation shield and its neighbor fluid flow. Obtaining this condition shows that the steady state is achieved. It is curios to note that using steady solver directly, the convergence of the velocity field cannot be ensured, and therefore we are urged to employ the unsteady solver. In another word, in natural convection problems in the enclosures, the solution will depend on the mass inside the domain. To obtain the enclosed mass the density of fluid should be
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Fig. 1. Schematic of the experimental setup (left), and cylindrical enclosure cross section with radiation shields (right).
Fig. 2. Experimental facilities, (a) cylindrical enclosure, (b) radiation shields.
known. When the temperature gradients in the domain are small, the Boussinesq model is suitable and steady state solver can be used. However, for large temperature differences the ideal gas model is employed. In this approach, the initial density will be computed from the initial pressure and temperature. Therefore, the initial mass is known and by solving the governing equations over time, the mass will be properly conserved [48]. Since the latter approach has been used in this work, the transient solution is adopted. As mentioned in Section 2, the upper and lower surfaces are assumed isolated. The differential equation of the continuity for a compressible fluid can be written as follows:
! vr þ V: r V ¼ 0 vt
(1)
Also momentum equation is presented in its deferential form as [49]:
! ! v rV ! ! ! ! þ V :V r V ¼ r g Vp þ mV2 V þ lV V: V vt
(2)
! where V is the velocity vector in (r,q,z) directions, p indicates the pressure, r refers to the density, m is the dynamic viscosity, and l stands for the second coefficient of viscosity. It was assumed that the enclosed air is isotropic and treated as an ideal gas, hence, the equation of state is valid for correlating the pressure, temperature and density to each other. According to the Stokes assumption the second coefficient of viscosity for the compressible enclosed air assumed as l ¼ 2=3m. DO (discrete ordinate) model is selected for radiation modeling, which solves the RTE (radiation transfer equation) for a finite number of discrete solid angles, each associated with a ! vector direction s fixed in the global system. The DO model ! ! which considers RTE at position r in the direction s as follows [48]:
4
sT ! !! ! ! V:ðIð r ; s Þ s Þ ¼ ða þ ss ÞIð r ; s Þ þ an2 p Z4p ! !0 ! !0 ss þ I r ; s F s ; s dU0 4p
(3)
0
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!0
! where, I is the radiation intensity, s is the direction vector, s indicates the scattering direction vector, a is the absorption coefficient, ss refers to the scattering coefficient, F is the scattering phase function which indicates the angular distribution of radiation 0 intensity scattered by a particle, U is the solid angle and n expresses the refractive index. In the present work, it was assumed that there are no aerosols, moisture and carbon dioxide molecules or other particles in the air. Hence, the scattering was neglected. The time step for RTE equation is set 5 times of flow time step (i.e. 2.5 s). Each octant of the angular space 4p at any spatial location is discretized into 2 2 solid angles in polar and azimuthal directions (q,f). The flow regime in natural convection is governed by the Grashof number in an enclosure, which represents the ratio of the buoyancy force to the viscous force acting on the fluid [50].
Gr ¼
gbðTh Tc ÞL3c n2
(4)
where, g is the gravitational acceleration, b indicates the coefficient of volume expansion, Th and Tc are the temperature of hot and cold surfaces, Lc is the characteristic length of the geometry (the distance between the hot and cold surfaces), and n is the kinematic viscosity of the fluid. In the current work, it is assumed that the emissivity of the walls material is a function of temperature and other thermo-physical properties are independent of temperature. The fluid is viscous, heat-conducting, Newtonian, and the ideal gas low is valid for correlating the pressure, temperature and density to each other. Also, it is assumed that the flow is laminar, which is conducted from comparing the Grashof number to its critical value (about 109) [50,51]. The temperature-dependent emissivity of wall's material extracted from trustworthy reference (Fig. 3) [51]. From this plot the best curve has been fitted and following relationships are achieved. The best formulas regarding emissivity versus temperature for aluminum, copper and steel are:
εðTÞal ¼ 4 1011 T 3 2 108 T 2 0:0004T þ 0:943
(5)
εðTÞcu ¼ 0:0002T 0:0035
(6)
εðTÞs ¼ 3 1011 T 3 þ 2 107 T 2 þ 8 105 T þ 0:0794 (7) Fig. 4 shows thermal boundary conditions for this problem. As it
Fig. 3. Temperature-dependent emissivity of aluminum, steel and copper [51].
5
was seen from this figure, in defining the boundary conditions for the above described governing equations, it is assumed that the inner cylinder has a constant temperature, while outer one has free convection with the ambient air. In addition, the top and bottom walls are both assumed to be perfectly insulated. In addition, the no-slip boundary condition imposes on all solid walls. The ambient temperature was assumed as initial temperature of the enclosure and the initial pressure was set equal to 0.2 atm and 1.0 atm, according to different experiments. To have less time consuming computations, only inside of enclosure was modeled, and available correlation was used to estimate the convective heat coefficient on the external side of the enclosure. In the laminar free convection problems around a vertical cylinder, Sparrow and Gregg [52] concluded that the vertical flat plate solution is acceptable for air when
D ðGrD PrÞ1=4 > 38 L
(8)
This means that the diameter of the cylinder is sufficiently large so that the curvature effects are negligible. The dimensions and operating conditions of this work satisfy the above inequality. Hence, for calculating the convection coefficient of the outer cylinder with the periphery air, Churchill and Chu [53] correlation for vertical plate was used:
0:670Ra1=4 Nu ¼ 0:68 þ h i4=9 1 þ ð0:492=PrÞ9=16
for RaL < 109
(9)
4. Results and discussions Both numerical and experimental analyses with two radiation shields between two main cylinders with three different positions along with previously mentioned different materials are examined. The geometrical characteristics of main cylinders by referring to Fig. 5 are reported in Table 1. The numerical analyses have been extended to mesh-independency calculations. The analyses were performed with different mesh numbers and finally a structured mesh of 228,000, 204,000, and 204,000 cells were chosen for Cases 1 to 3, respectively. These numbers of meshes are the least ones which the numerical simulations can be done with negligible inaccuracy. Validation of the numerical model is made by a comparison to the experimental data. Fig. 6 shows both numerical and experimental data for the temperature of the first radiation shield, i.e., aluminum, and the second radiation shield, i.e., copper, for all three cases. The symbol of AleCu in this figure means that the first shield which is near to the hotter inner cylinder is aluminum and the next one which is near to the outer cylinder is copper. The comparison shows a good agreement with experimental data. Nevertheless, a slight deviation is shown in Fig. 6. This small difference may arise from the adiabatic walls assumption for the top and down annular plates in the numerical procedure, which is not compatible very well with the experiments. For the other combinations of radiation shields similar agreements between simulations and experimental data have been seen, which are not repeated here. Temperature distributions along with isothermal surfaces at different pressures for case 1 to 3 with aluminum shield as the first and copper shield as the second layer are depicted in Fig. 7. As it can be seen from this figure, at low pressures the air temperature is relatively high, which arises from the low heat capacity (mcp) of enclosed air. The hotter air moves towards the top of the enclosure, because of its lower density, and yields to non-uniform temperature distribution at the radiation shields walls.
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
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Fig. 4. Boundary conditions of the problem.
2 np2 np1 !2 !2 !2 2 mp2 rp1 ideal gas mp2 P1 2 Grp1 P ¼ ¼ 0 f 1 mp1 rp2 mp1 P2 Grp2 P2
Grp1 ¼ Grp2
(11)
Fig. 5. Top view configurations of main cylinders and radiation shields.
Considering the ideal gas conditions (P ¼ rRT) the air volume expansion coefficient b, is equivalent to inverse of temperature:
b¼
1 T
(10)
Hence, for ideal gases with specific temperatures, reducing the enclosure pressure has no effect on the volume expansion coefficient. Therefore, the Gr number ratio for different pressures is evaluated as follows:
Hence, Gr number ratio is proportional to the square of pressure ratios. When the pressure descends from 1.0 atm to 0.2 atm, Gr number reduces by the ratio of 25, indicating the lower buoyancy force with respect to the viscous force at lower pressures and yields to low fluctuation for the flow field. Fig. 7 clearly illustrates this fact by comparing the isothermal surfaces of two enclosure pressures. The total heat loss from inner cylinder to the fluid is computed as [48]:
00 00 qtot ¼ hf Tw Tf þ qrad
(12)
where, Tw is the inner cylinder wall temperature, Tf is the local fluid 00 temperature, qrad is the radiation heat loss, and hf is the local heat transfer coefficient. The first term in the Eq. (12) is the convection heat loss and in the laminar flows it is computed using Fourier's law as follows:
Table 1 Main geometrical characteristics of concentric finite cylinders and radiation shields.
Case 1 Case 2 Case 3
Inner cylinder diameter (D1)
Outer cylinder diameter (D5)
Cylinders length (L)
First radiation shield diameter
Second radiation shield diameter
16 cm 16 cm 16 cm
50 cm 50 cm 50 cm
60 cm 60 cm 60 cm
26 cm 26 cm 34 cm
34 cm 42 cm 42 cm
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7
Fig. 6. The comparison between numerical and experimental results for AleCu radiation shields for Case 1 to 3.
hf Tw Tf
vT ¼ kf vr wall
(13)
where, kf is the fluid thermal conductivity and r is the radial coordinate normal to the cylinder wall. The second term in the Eq. (12) is radiation heat loss, and it is calculated using the following equation:
00
Z
qrad ¼ ð1 εw Þ$
!! 4 Iinc s : n dU þ n2 εw sTw
(14)
!! s : n >0 ! where, Iinc is the incident radiation intensity, s is the direction vector, n expresses the refractive index of medium next to the wall, εw is the wall emissivity, and s is the StefaneBoltzmann's constant.
The amount of total heat losses without radiation shields has been tabulated within Table 2. A comparison between the reported values by this table and the amount of total heat losses using radiation shields, i.e., Tables 3e5, confirms that radiation shields greatly contribute to lessen the heat loss within the cylindrical enclosure. Effects of locating the radiation shields with different conditions are detailed in Tables 3e5. Table 3 reports the effect of aluminum, copper and steel shields on the heat loss reduction from inner cylinder at two different temperatures for Case 1. Radiation shields' temperatures, radiation and convection heat losses from the inner cylinder are presented in this table. As can be seen, the temperature of the first shield increases when the pressure decreases. Therefore, the enclosure pressure modifies the flow fields, and reduces the first shield temperature by increasing the convection heat losses. On the other hand, with increasing the first shield temperature along with pressure reduction, the radiation heat losses are slightly
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
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Fig. 7. Temperature distribution and iso-surfaces for Case 1 to 3 at different pressures.
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
S. Saedodin, M.S. Motaghedi Barforoush / Energy xxx (2015) 1e11 Table 2 Total heat transfer loss through the cylinder enclosure without radiation shield. 00
Original case
Tin [K]
Penc [atm]
qtot [w/m2]
Without shield
473.15
1.0 0.2 1.0 0.2
993.5735 578.9321 3021.835 2174.176
673.15
9
significant. Comparing the results of this table indicates that using the copper as the first shield with lower emissivity comparing to steel and aluminum better decreases the total heat transfer loss by alleviating the amount of radiation loss. Hence, when the copper shield is used in the first layer and the steel shield is located at the second layer the minimum heat transfer loss is achieved. The same behavior of reduction in the heat losses at various
Table 3 Heat loss reduction at different enclosure pressures and inner cylinder temperatures in Case 1. 00
00
00
Case 1
Tin [K]
Penc [atm]
qtot [w/m2]
qrad [w/m2]
qcon [w/m2]
Tsh1 [K]
Tsh2 [K]
AleCu
473.15
1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2
396.5734 229.9469 1307.107 937.3605 422.5654 261.6159 1452.711 1107.082 362.3963 201.674 1102.047 786.2101 349.1902 185.5182 1032.969 696.4203 394.9779 237.0998 1287.275 981.7267 361.3965 194.6464 1100.284 745.0569
198.8161 170.4714 1078.092 875.3813 209.4459 190.9324 1187.114 1027.877 110.2451 107.9862 713.5259 668.0712 107.3371 101.6668 680.3275 601.8067 147.2163 144.6958 919.7992 864.5757 137.5726 123.7006 809.6854 672.0205
197.7573 59.4755 229.015 61.9792 213.1195 70.6835 265.597 79.205 252.1512 93.6878 388.5211 118.1389 241.8531 83.8514 352.6415 94.6136 247.7616 92.404 367.4758 117.151 223.8239 70.9458 290.5986 73.0364
412.3034 419.3417 583.3635 599.8065 408.2677 411.437 571.7998 584.0599 400.8778 397.7585 542.2319 549.9031 403.7475 404.2562 552.5386 568.8359 401.1309 397.8523 545.4039 550.9116 407.5154 412.2043 567.9555 587.9086
358.7117 360.5854 469.9551 491.2754 358.5709 361.506 472.4442 495.2074 347.0186 338.9377 427.657 426.0544 350.2428 345.272 435.884 441.6292 349.8253 344.7159 440.412 446.6236 353.6019 351.9884 449.4905 462.52
673.15 AleSt
473.15 673.15
CueAl
473.15 673.15
CueSt
473.15 673.15
SteAl
473.15 673.15
SteCu
473.15 673.15
Table 4 Heat loss reduction at different enclosure pressures and inner cylinder temperatures for Case 2. 00
00
00
Case 2
Tin [K]
Penc [atm]
qtot [w/m2]
qrad [w/m2]
qcon [w/m2]
Tsh1 [K]
Tsh2 [K]
AleCu
473.15
1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2
417.8251 251.9402 1373.349 1042.663 444.2729 282.6831 1519.305 1205.347 377.8359 208.9802 1122.551 809.8032 364.867 195.0259 1056.824 735.1973 409.949 244.9875 1307.837 1010.148 376.3656 201.3687 1134.054 807.2021
209.8266 185.8119 1136.237 971.1304 220.099 204.8305 1243.796 1115.661 113.3113 110.9212 726.8194 685.2079 110.8545 105.9412 698.1395 631.9539 151.3809 148.5261 936.3123 886.9631 142.7667 134.6752 838.5148 725.0999
207.9985 66.1283 237.112 71.5326 224.1739 77.8526 275.509 89.686 264.5246 98.059 395.7316 124.5953 254.0125 89.0847 358.6845 103.2434 258.5681 96.4614 371.5247 123.1849 233.5989 66.6935 295.5392 82.1022
385.08 405.211 540.0067 578.8179 382.2583 398.2309 532.2805 564.7611 371.3587 383.6279 487.953 525.1131 374.187 389.3623 498.1909 542.2836 373.4127 385.2159 498.1085 530.2628 379.0213 392.0936 517.0708 562.9022
325.6722 342.4008 388.009 440.5428 326.6785 344.1147 392.894 446.437 319.6078 326.9337 362.3113 391.1952 320.5641 330.1716 364.4581 398.441 321.8845 331.9597 372.6505 409.3558 322.5032 330.6328 372.448 414.2155
673.15 AleSt
473.15 673.15
CueAl
473.15 673.15
CueSt
473.15 673.15
SteAl
473.15 673.15
SteCu
473.15 673.15
reduced because of decreasing the temperature difference between the inner cylinder and the first shield. In lower pressures, the power of electromagnetic radiation waves to travel through the vacuum medium makes thermal radiation the main mode of heat transfer and its contribution to the total heat transfer rate becomes
temperatures and pressures have been achieved for Cases 2 and 3 and results are reported in Tables 4 and 5, respectively. Comparing the results of these tables to Table 3 indicates that the heat transfer losses in Case 1 are much less than Cases 2 and 3. Hence, locating the radiation shield closer to the hotter surface has the maximum
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Table 5 Heat loss reduction at different enclosure pressures and inner cylinder temperatures for Case 3. 00
00
00
Case 3
Tin [K]
Penc [atm]
qtot [w/m2]
qrad [w/m2]
qcon [w/m2]
Tsh1 [K]
Tsh2 [K]
AleCu
473.15
1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2 1.0 0.2
444.0579 262.8758 1425.074 1066.651 471.4276 294.62 1574.529 1236.465 421.6281 236.4019 1258.222 921.5991 404.4398 219.3997 1174.172 826.0812 453.8656 272.5266 1443.526 1120.452 419.8839 228.6463 1230.227 874.3762
209.1243 185.5805 1154.508 980.4564 218.9335 204.5564 1259.356 1127.829 130.8206 128.1522 831.8172 780.1287 127.4313 121.4852 792.2551 709.9549 165.372 163.3278 1029.087 975.1588 152.3533 142.3886 909.7609 779.5037
234.9336 77.2953 270.566 86.1946 252.4941 90.0636 315.173 108.636 290.8075 108.2497 426.4048 141.4704 277.0085 97.9145 381.9169 116.1263 288.4936 109.1988 414.439 145.2932 267.5306 86.2577 320.4661 94.8725
384.0189 404.4431 533.6197 576.21 381.4832 397.7226 526.7566 562.2176 371.4208 383.4179 486.9471 524.5009 374.6093 389.6682 497.8376 542.8329 373.0345 384.3096 495.4409 528.1301 386.2597 397.3663 514.6194 562.4971
362.3618 360.6566 480.6047 489.1952 361.7086 361.1475 480.6359 492.5062 351.745 342.1176 440.9426 433.7897 354.8558 347.2532 449.4638 445.9893 354.1431 347.3705 452.0475 452.3701 351.1204 353.2953 462.867 464.4673
673.15 AleSt
473.15 673.15
CueAl
473.15 673.15
CueSt
473.15 673.15
SteAl
473.15 673.15
SteCu
473.15 673.15
heat loss reduction. This fact has been pointed out in previous theoretical studies by Saedodin et al. [42] and Torabi et al. [43] for the application of radiation shields between two surfaces, when completely vacuum condition is considered. With the increasing of the distance between cylinders Gr number (Eq. (4)) will increase and thus will magnify the heat transfer. This phenomenon is clearly visible by comparing the results of Tables 3e5. As in the first Case, the distance between the first shield and the inner cylinder is equal to 8 cm and second shield is located 8 cm far from the first shield, the convective losses reach their minimum value. Therefore, it is inferred that the enclosure pressure affects the convection heat losses, and the shield emissivity impacts on the radiation heat losses. Therefore, the both heat loss mechanisms will be responsible for reducing the total heat loss from the inner cylinder. Another point is that, Tables 3 and 5 express the heat loss increment with increasing the distance between the inner cylinder and radiation shields. It was found that for Cu-St radiation shields by setting the inner cylinder wall's temperature at 673.15 K and fixing enclosure pressure at 1.0 atm, heat losses ascend from 1032.969 to 1174.172 (W/m2) from Case 1 to Case 3, addressing 13.67% of growth. 5. Conclusions This work presents a numerical and experimental study about the cylindrical radiation shields with temperature-dependent emissivity between two finite concentric cylinders, and discusses effects of various parameters on the heat transfer and flow field. Two different pressures have been assumed for the enclosure and three different materials, namely aluminum, copper and steel, have been used as radiation shields. Results showed that radiation shields vastly decrease the total amount of heat transfer through the cylindrical enclosure. According to the results, radiation heat losses ascend with emissivity of radiation shields. Also, the convection contribution decreases the temperatures of the radiation shields, addressing the increase of the radiation loss from inner cylinder. The total heat losses for each case decreases by reducing the enclosure pressure, because of weakening both convection and radiation effects. Obtained results for copper deduce that the copper is more appropriate to be used as a radiation shield compared
with aluminum and steel because of its lower emissivity. It was found that using radiation shields between the two main surfaces vastly reduces the heat transfer between them. Also, it was indicated that the total heat losses is more reduced when the radiation shields are positioned near the hotter inner cylinder. As an example, for Cu-St radiation shields and inner cylinder temperature of 673.15 K and the enclosure pressure of 1 atm, the total heat losses for Cases 1 to 3 are found to be 1032.969, 1056.824, 1174.172 [w/m2] which is 40.63%, 43.73% and 34.1% lower than Al-St shields, respectively. References [1] Bouchair A. Steady state theoretical model of fired clay hollow bricks for enhanced external wall thermal insulation. Build Environ 2008;43:1603e18. Martin K, Urresti A, García-Romero A, Sala JM. [2] Diarce G, Campos-Celador A, A comparative study of the CFD modeling of a ventilated active façade including phase change materials. Appl Energy 2014;126:307e17. rez Sierra JL, Pen ~ uelas Sa nchez I. Non-linear [3] Del Coz Díaz JJ, García Nieto PJ, Sua thermal optimization and design improvement of a new internal light concrete multi-holed brick walls by FEM. Appl Therm Eng 2008;28:1090e100. [4] Hemmer C, Polidori G, Popa C. Case studies in thermal engineering temperature optimization of an electric heater by emissivity variation of heating elements. Case Stud Therm Eng 2014;4:187e92. [5] Senve V, Narasimham GSVL. Effective thermal conductivity of a heat generating rod bundle dissipating heat by natural convection and radiation. Nucl Eng Des 2011;241:4331e40. [6] Tsuji N, Nakano M, Takada E, Tokuhara K, Ohashi K, Okamoto F, et al. Study of the applicability of CFD calculation for HTTR reactor. Nucl Eng Des 2014;271: 564e8. [7] Malik AH, Alvi MS, Khushnood S, Mahfouz FM, Ghauri MKK, Shah A. Experimental study of conjugate heat transfer within a bottom heated vertical concentric cylindrical enclosure. Int J Heat Mass Transf 2012;55:1154e63. [8] Malik AH, Shah A, Khushnood S. CFD analysis of heat transfer within a bottom heated vertical concentric cylindrical enclosure. J Phys Conf Ser 2013;439: 012004. [9] Al-Nimr MA, Kodah Z, Nassar B. A theoretical and experimental investigation of a radiative cooling system. Sol Energy 1998;63:367e73. [10] Torabi M, Aziz A, Zhang K. A comparative study of longitudinal fins of rectangular, trapezoidal and concave parabolic profiles with multiple nonlinearities. Energy 2013;51:243e56. [11] Torabi M, Zhang QB. Analytical solution for evaluating the thermal performance and efficiency of convectiveeradiative straight fins with various profiles and considering all non-linearities. Energy Convers Manage 2013;66: 199e210. [12] Hatami M, Ganji DD. Thermal performance of circular convectiveeradiative porous fins with different section shapes and materials. Energy Convers Manage 2013;76:185e93.
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091
S. Saedodin, M.S. Motaghedi Barforoush / Energy xxx (2015) 1e11 [13] Abdesslem J, Khalifa S, Abdelaziz N, Abdallah M. Radiative properties effects on unsteady natural convection inside a saturated porous medium. Application for porous heat exchangers. Energy 2013;61:224e33. F, Zhao CY, Baeyens J, Degre ve J, Zhang HL. Circulating fluidized bed heat [14] Pitie recovery/storage and its potential to use coated phase-change-material (PCM) particles. Appl Energy 2013;109:505e13. [15] Sawant SM, Gururaja Rao C. Conjugate mixed convection with surface radiation from a vertical electronic board with multiple discrete heat sources. Heat Mass Transf 2008;44:1485e95. [16] Baïri A. Transient thermal characteristics of airborne electronic equipment with discrete hot bands in square cavities. Appl Energy 2008;85:951e67. [17] Saedodin S, Barforoush MSM. Comprehensive analytical study for convectiveeradiative continuously moving plates with multiple non-linearities. Energy Convers Manage 2014;81:160e8. [18] Wang Y, Meng X, Yang X, Liu J. Influence of convection and radiation on the thermal environment in an industrial building with buoyancy-driven natural ventilation. Energy Build 2014;75:394e401. [19] Rahimi M, Sabernaeemi A. Experimental study of radiation and free convection in an enclosure with under-floor heating system. Energy Convers Manage 2011;52:2752e7. [20] Rahimi M, Sabernaeemi A. Experimental study of radiation and free convection in an enclosure with a radiant ceiling heating system. Energy Build 2010;42:2077e82. [21] Slimi K, Mhimid A, Ben Salah M, Ben Nasrallah S, Mohamad AA, Storesletten L. Anisotropy effects on heat and fluid flow by unsteady natural convection and radiation in saturated porous media. Numer Heat Transf Part A Appl 2005;48: 763e90. [22] Slimi K. A two-temperature model for predicting heat and fluid flow by natural convection and radiation within a saturated porous vertical channel. J Porous Media 2009;12:43e63. [23] Kuznetsov GV, Sheremet MA. Numerical simulation of turbulent natural convection in a rectangular enclosure having finite thickness walls. Int J Heat Mass Transf 2010;53:163e77. [24] Rashidi I, Mahian O, Lorenzini G, Biserni C, Wongwises S. Natural convection of Al2O3/water nanofluid in a square cavity: effects of heterogeneous heating. Int J Heat Mass Transf 2014;74:391e402. [25] Saha SC, Gu YT. Natural convection in a triangular enclosure heated from below and non-uniformly cooled from top. Int J Heat Mass Transf 2015;80: 529e38. [26] Ahmed M, Eslamian M. Natural convection in a differentially-heated square enclosure filled with a nanofluid: significance of the thermophoresis force and slip/drift velocity. Int Commun Heat Mass Transf 2014;58:1e11. € [27] Rahman MM, Oztop HF, Mekhilef S, Saidur R, Al-Salem K. Unsteady natural convection in Al2O3-water nanoliquid filled in isosceles triangular enclosure with sinusoidal thermal boundary condition on bottom wall. Superlattices Microstruct 2014;67:181e96. [28] Kuznetsov GV, Sheremet MA. Conjugate natural convection with radiation in an enclosure. Int J Heat Mass Transf 2009;52:2215e23. [29] Martyushev SG, Sheremet MA. Conjugate natural convection combined with surface thermal radiation in a three-dimensional enclosure with a heat source. Int J Heat Mass Transf 2014;73:340e53. [30] Sharma AK, Velusamy K, Balaji C, Venkateshan SP. Conjugate turbulent natural convection with surface radiation in air filled rectangular enclosures. Int J Heat Mass Transf 2007;50:625e39. [31] Rao VD, Naidu SV, Rao BG, Sharma KV. Heat transfer from a horizontal fin array by natural convection and radiationda conjugate analysis. Int J Heat Mass Transf 2006;49:3379e91.
11
[32] Rabhi M, Bouali H, Mezrhab A. Radiationenatural convection heat transfer in inclined rectangular enclosures with multiple partitions. Energy Convers Manage 2008;49:1228e36. gue HF, Bilgen E. Heat transfer by convection, conduction and radia[33] Nouane tion in solar chimney systems for ventilation of dwellings. Int J Heat Fluid Flow 2009;30:150e7. nier E, Lauriat G. Effect of surface radiation on the breakdown of [34] Sun H, Che steady natural convection flows in a square, air-filled cavity containing a centered inner body. Appl Therm Eng 2011;31:1252e62. [35] Premachandran B, Balaji C. Conjugate mixed convection with surface radiation from a vertical channel with protruding heat sources. Numer Heat Transf Part A Appl 2011;60:171e96. [36] Saravanan S, Sivaraj C. Coupled thermal radiation and natural convection heat transfer in a cavity with a heated plate inside. Int J Heat Fluid Flow 2013;40:54e64. n-Vidales HI, Bautista-Orozco A, [37] Montiel-Gonz alez M, Hinojosa JF, Villafa Estrada CA. Theoretical and experimental study of natural convection with surface thermal radiation in a side open cavity. Appl Therm Eng 2014:1e11. [38] De Faoite D, Browne DJ, Del Valle Gamboa JI, Stanton KT. Inverse estimate of heat flux on a plasma discharge tube to steady-state conditions using thermocouple data and a radiation boundary condition. Int J Heat Mass Transf 2014;77:564e76. [39] Moghadassian B, Kowsary F. Inverse boundary design problem of natural convectioneradiation in a square enclosure. Int J Therm Sci 2014;75:116e26. [40] Thevenet J, Siroux M, Desmet B. Measurements of brake disc surface temperature and emissivity by two-color pyrometry. Appl Therm Eng 2010;30: 753e9. [41] Akamine S, Fujita M. Controlling heat radiation for development of hightemperature insulating materials. J Eur Ceram Soc 2014:3e8. [42] Saedodin S, Motaghedi Barforoush MS, Torabi M. Reducing heat transfer between two concentric semi-cylinders using radiation shields with temperature-dependent emissivity. Front Heat Mass Transf 2012;2:2e5. [43] Torabi M, Aziz A, Saedodin S. Application of hemisphere radiation shields with temperature-dependent emissivity for reducing heat transfer between two concentric hemispheres. Thermophys Aeromech 2013;19:481e8. [44] Bowers JA, Hyde RA, Ishikawa MY, Jung EKY, Kare JT, Leuthardt EC, et al. Multilayer insulation composite material including bandgap material, storage container using same, and related methods. U.S. Patent US 8,703,259 B2. 2014. [45] Miyakita T, Hatakenaka R, Sugita H, Saitoh M, Hirai T. Development of a new multi-layer insulation blanket with non-interlayer-contact spacer for space cryogenic mission. Cryogenics (Guildf) NovembereDecember 2014;64:112e20. [46] Augusto PA, Castelo-Grande T, Augusto P, Barbosa D. Optimization of refrigerated shields using multilayer thermal insulation: cryostats design e analytical solution. Cryogenics (Guildf) 2006;46:449e57. [47] Barforoush MSM, Saedodin S. Heat transfer reduction between two finite concentric cylinders using radiation shields; experimental and numerical studies. Int Commun Heat Mass Transf 2015;65:94e102. [48] FLUENT. User's guide 6.3. USA: Fluent Inc; 2005. [49] Lai M, Krempl E, Ruben D. Introduction to continuum mechanics. 4th ed. ButterwortheHeinemann; 2010. [50] Bejan A. Convection heat transfer. 4th ed. John Wiley & Sons, Inc; 2013. [51] Bergman TL, Lavine AS, Incropera FP, DeWitt DP. Introduction to heat transfer. 6th ed. John Wiley and Sons, Inc; 2011. [52] Sparrow EM, Gregg JL. Laminar free convection heat transfer from the outer surface of a vertical circular cylinder. Trans ASME 1956;78:183e9. [53] Churchill SW, Chu HHS. Correlating equations for laminar and turbulent free convection from a horizontal cylinder. Int J Heat Mass Transf 1975;18: 1049e53.
Please cite this article in press as: Saedodin S, Motaghedi Barforoush MS, Experimental and numerical investigations on enclosure pressure effects on radiation and convection heat losses from two finite concentric cylinders using two radiation shields, Energy (2015), http:// dx.doi.org/10.1016/j.energy.2015.07.091