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Experimental and numerical study of the natural convection from a heated horizontal cylinder wrapped with a layer of textile material
International Communications in Heat and Mass Transfer 37 (2010) 58–67
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International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t
Experimental and numerical study of the natural convection from a heated horizontal cylinder wrapped with a layer of textile material☆ Ş. Özgür Atayılmaz ⁎, İsmail Teke Department of Mechanical Engineering, Yildiz Technical University, 34349 Istanbul, Turkey
a r t i c l e
i n f o
Available online 20 October 2009 Keywords: Natural convection Heat transfer Horizontal cylinder CFD
a b s t r a c t Natural convection heat transfer enhancement from a horizontal cylinder with a textile coating is studied experimentally and numerically. The coating layer may be used for two purposes. According to the thickness of the coating it may be used as an insulating material or for surface augmentation. In the experimental study, two cylinders having different diameters of 4.8 mm and 9.45 mm are used. The bare cylinders having a radius smaller than a certain critical size were wrapped with a textile material. Wrapped cylinder diameters were increased to 9 and 12.8 mm respectively after coating and constant heat flux was applied to all bare and wrapped cylinders. Experimental study was carried out at different ambient temperatures in a conditioned room which can be maintained at a stable required value and inside a sufficiently designed test cabin. The ambient and cylinder surface temperatures (T∞ and Tw) varied between 10 °C – 40 °C and 20 °C – 60 °C respectively. Heat transfer rates from bare and wrapped horizontal cylinders were compared and heat transfer enhancement was observed. On the basis of the experimental data average Nusselt numbers were calculated and compared with the well known correlations on natural convection heat transfer from a horizontal cylinder in the specified range of Rayleigh number, and it is seen that the results are in good agreement. The problem is also investigated numerically. Experimental and the numerical results fall in ± 30% band. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Energy demand is increasing as a consequence of population growth and economical development. On the other hand, fossil fuels meeting a great portion of the energy demand are very scarce and their availability is decreasing year by year. Today, energy efficiency is a popular topic which covers almost all appliances employed in industry, infrastructure and household appliances, etc. Developing and designing energy efficient systems are two of the main interest areas of engineering. International institutions or comities such as CECED are aiming to decrease energy consumption especially in household appliances because of having an environmental impact. In refrigeration systems, it is possible to reduce energy consumption and increase efficiency by decreasing the condensation temperature so as the compressor power. This study is focused on decreasing the condensation temperature especially in domestic refrigerators. Natural convection heat transfer from horizontal cylinder is found in many technical applications such as boiler design, heat exchangers, and air cooling systems for air conditioning. Wire-and-tube type heat
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. 0735-1933/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2009.09.009
exchangers widely used in small refrigeration appliances are made of cylinders with an outer diameter of 4.8 mm. In the previous study [1], natural convection heat transfer from a horizontal cylinder is studied experimentally and numerically using two different diameters (4.8 mm–9.45 mm) and one of them is preferred especially the one with 4.8 mm outer diameter. The experimental results of bare cylinders are used in this study for comparisons. In literature there is an extensive amount of numerical and experimental studies on natural convection heat transfer from horizontal cylinder and many more correlations were proposed. Morgan [2], after a wide literature research, suggested empirical correlation equations for an average Nusselt number of the type Nu = c.Ran. Fand and Brucker [3] compared the eight empirical and half-empirical correlations obtained from the pre-studies on natural convection around an infinitely long horizontal isothermal cylinder and created a new correlation by using the experimental data in the range between 10− 8 b Ra b 108 and 0.7 b Pr b 104 in the literature. And it was determined that the correlations do not agree closely with each other. They reported that there is an approximately 50% difference between average Nusselt numbers calculated from Churchill and Chu [4] and Raithby and Hollands [5]'s equations for air at Ra = 1. The difference can be calculated as 43% for higher Ra numbers (Ra = 105 and Pr = 0.7). Recently, some other researchers, Misumi et al. [6] and Kitumura et al. [7], who investigated natural convection flows around horizontal cylinders experimentally also discussed the discrepancy on
Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 37 (2010) 58–67
T1:1
Nomenclature
T1:2 T1:3 T1:4 T1:5 T1:6 T1:7 T1:8 T1:9 T1:10 T1:11 T1:12 T1:13 T1:14 T1:15 T1:16 T1:17 T1:18 T1:19 T1:20 T1:21 T1:22 T1:23 T1:24 T1:25 T1:26 T1:27 T1:28
A D Qe Q conv Q rad Q cond V Ge I h L Nu Gr Ra Pr NuD,w k T w 2D XPS CFD LDA DC CECED
T1:29 T1:30 T1:31 T1:32 T1:33 T1:34 T1:35
Subscripts W coating outer surface ∞ ambient c copper cylinder surface exp experimental num numerical
T1:36 T1:37 T1:38 T1:39 T1:40 T1:41 T1:42
Greek letters ε emissivity ν kinematic viscosity, (m2/s) θ angle about cylinder centre from bottom of cylinder σ Stephan–Boltzmann constant = 5.67 × 10− 8 W/m2K4 ρ densities, (kg/m3)
heat transfer area, (m2) cylinder diameter (m) input electrical power, (W) convection heat loss, (W) radiation heat loss, (W) conduction heat loss, (W) heater voltage, (V) Gebhart number heater current, (A) heat transfer coefficient, W/m2K length along cylinder average Nusselt number Grashof number Rayleigh number Prandtl number local Nusselt number thermal conductivity, W/mK temperature, (°C) uncertainty two dimensional extruded polystyrene foam computational fluid dynamics laser doppler anemometer direct current European Committee of Domestic Equipment Manufacturers
the average Nusselt numbers between their results and the previous empirical correlations. Misumi et al. [6] stated that previous empirical equations such as McAdams [8] and Kutateladze [9] may not predict the Nusselt numbers correctly because of poor descriptions on the experimental apparatus and measurement techniques. Churchill and Chu [4] proposed a simple empirical expression for average Nusselt numbers over horizontal cylinder for all Rayleigh and Prandtl numbers by using Churchill and Usagi's [10] model. This expression can be applied for uniform heat flow, uniform wall temperature, mass transfer and simultaneous heat and mass transfer. Also simpler expressions were obtained for the limited conditions. Raithby and Hollands [5] studied heat transfer over elliptic cylinders of arbitrary eccentricity at a constant surface temperature, and proposed correlations for laminar and turbulent natural convection. Thin layer analysis is developed by adding the thick boundary layer found at the lower Rayleigh numbers to the calculation. Fand et al. [11] developed Raithby and Hollands'[5] and evaluated fluid properties at mean film reference temperature tf =t∞ +j(tw −t∞);
59
j = 0.5 in their study. Fujii et al. [12] studied experimentally the free convection from horizontal cylinder in water, spindle oil and mobeltherm oil and defined a reference temperature: tj =t∞ +j(tw −t∞); 0 ≤j ≤ 1. Mean film reference temperature was a special occasion of reference temperature, where tf and tj became equal for j = 0.5. Thermo physical properties were evaluated at the mean film temperature in the present study. The wake formation formed over the heated cylindrical surface at natural convection and the effect of this phenomenon to the heat transfer on the surface are within the context of pre-made researches. Pera and Gebhart [13] aimed to study the characteristic of the flow over the cylinder's surface caused by thermal effects and visualize the wake formation over cylindrical surfaces experimentally. They paid attention to the obscurity about the behavior in a separated region or in the region of wake formation. The flows, along the curved sections, were interacted and joined together to rise in a plume above the curved surface. Kuehn and Goldstein [14] numerically integrated the Navier– Stokes and energy equations by using the finite-difference overrelaxation method for an isothermal horizontal circular cylinder in the range 100 ≤ Ra ≤ 107. Streamlines and isotherms were computed at different values of the Rayleigh numbers. The temperature distribution were calculated at θ = 90° and θ = 180° for Ra = 105, Pr = 0.7 and they have been compared with the experimental results and it is ascertained that the values for θ = 90° are in good agreement. Also they indicated that the boundary layer formulations for θ N 130° were not a sufficient approach for heat transfer. More recently, Reymond et al. [15] studied natural convection heat transfer from a horizontal cylinder bounded with water and indicated that around the circumference of a cylinder, the average Nusselt number distribution show a maximum at the bottom of the cylinder (θ = 0°) and as the boundary layer developing it decreases towards the top (θ = 180°). Merkin [16] described a method of solving the full partial differential equations for the natural convection boundary layer over cylinders of general rounded cross-sectional form which could be used to give reliable results over the whole of the cylinder; the particular example considered there was of a circular cylinder. Muntasser and Mulligan [17] used the local non-similarity method and gave local solutions for different values of the Prandtl number. The change of natural convection along the radius of the horizontal cylinder was studied and the results were given from a lower stagnation point (θ = 0) to 150°. Farouk and Guceri [18] conducted some numerical analysis of the heat transfer around a single cylinder. They demonstrated that heat transfer increases to its maximum at the bottom and decreases towards the top of the cylinder. In this study natural convection heat transfer from a wrapped horizontal cylinder is investigated experimentally and numerically. According to the situation, covering the cylinder may be employed as insulation or surface augmentation. Incropera and DeWitt [19] gave the best answer to the application where the heat transfer rate increases by adding insulation and discussed the answer in detail. For electrical wires, thermal insulation material is needed for electrical insulation and safety. Curved surfaces such as a circular cylinder having a radius smaller than a certain critical size, adding insulation to the surface increase the heat transfer. This phenomenon occurs if the increase in the conduction resistance is less than the decrease in the convection resistance and commonly called the critical radius. The critical radius is represented as a function of thermal conductivity of the object and convective heat transfer coefficient (horcr/kins = 1) in the textbooks on heat transfer [19,20]. This is only valid if both thermal conductivity and convective heat transfer coefficient are constant. In fact, the convective heat transfer coefficient varies with outer diameter of the cylinder while thermal conductivity can be taken as constant [21]. Balmer [22] formulated the critical radius for sphere and cylinder in case of variable convection heat transfer coefficient theoretically.
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They used Churchill and Chu's [4] correlation in order to develop the critical radius equation for horizontal cylinder. Sparrow and Kang [23] investigated natural convection heat transfer from insulated horizontal cylinder numerically in a two dimensional space. Problem consists of conduction in the insulation layer and natural convection in the vicinity of outer surface. They found that the use of Morgan's [2] correlation gave the most accurate set of one dimensional result amongst Mc Adams [8], Morgan [2], Churchill and Chu [4]. Also they reported that the standard critical radius criterion horcr/kins = 1 led to significant errors and should no longer be used. Therefore the critical radius can be calculated from horcr/kins = 3n / (1 + n) where “n” is the exponent of Rayleigh in Nu = c.Ran correlation. Kulkarni [24], defined a new term “cross over point” as a radius greater than the critical radius such that the heat transfer with the corresponding amount of insulating material is equal to that of the bare thermal system. It is pointed out that the cross over insulation radius is applicable when the Biot number (hri/kins) is less than 1 in a cylindrical system. Ait Saada et al. [25] investigated natural convection from a horizontal cylinder with a porous or fibrous coating. It is indicated that porous or fibrous material may also be used as a heat transfer augmentation technique and is achieved by selecting porous media with permeability and/or high effective thermal conductivity. Additionally, natural convection heat transfer inside channels and ducts has been studied by many authors [28–32]. Zeitoun and Ali [31] studied natural convection around isothermal horizontal rectangular ducts numerically. They reported that the far-field boundaries for horizontal cylinder should be located at distances of 5D, 2D and 2D for right, lower and upper boundaries respectively and adopted this for rectangular ducts. They also gave a Nu–Ra correlation for 700 ≤ Ra ≥ 1.3 × 108. Saha [32] investigated unsteady free convection from a heated square cylinder in a vertical channel numerically using MAC method. It is stated that there are many theoretical and experimental studies on natural convection heat transfer from horizontal cylinder. Generally the wide dispersion in the published experimental results was attributed to the distortion of the temperature and velocity fields by bulk fluid movements, the use of under sized test cabin or existence of the temperature measurement system and supports. In the present study, the test cabin was constructed at proper dimensions and all the surfaces except the top were made impermeadable to minimize these factors. Different from the other experimental studies made in the air, all the experiments were performed in the conditioned room to keep the ambient temperature constant during the experiments and to have experimental runs at different ambient temperatures. In addition, sensitive measuring devices were used to minimize the measuring errors. Firstly experimental study is performed with two bare horizontal cylinders (4.8 and 9.45 mm). Afterwards the bare cylinders that have radius smaller than a certain critical size were wrapped with a textile material. Heat transfer rates from bare and wrapped horizontal cylinders were compared and heat transfer enhancement was seen obviously. Despite the contribution of published numerical studies, CFD analysis was not used for natural convection heat transfer from a wrapped horizontal cylinder. In the numerical part of this study, CFD package (FLUENT [26]) was used for the 2D heat transfer analysis. Nusselt and Rayleigh numbers were calculated using the experimental data of wrapped cylinders and compared with the results of numerical simulation. 2. Experimental study 2.1. Experimental apparatus and conditioned room A schematic drawing of the experimental apparatus that consists of twelve parts is shown in Fig. 1. The two test cylinders made from
copper material at 1 m length and with diameters of 4.8 mm and 9.45 mm have been prepared. Silicone covered cylindrical resistant wires, are centered, leaving no air space and close fitted inside the test cylinder, to maintain the required uniform surface temperature. The diameter and the resistance value of the wires used for the first and the second cylinders were 0.35 mm–11.3 Ω and 0.75 mm–3.4 Ω respectively. To provide the uniform surface temperature in the axial direction, test cylinders were made from copper and the wall thickness is made as thick as possible (1 mm). In axial direction 11 notches were formed with a 10 cm space on the surface. Thermocouples can be partly buried in these notches. In order to determine radial temperature distribution three more notches were formed in radial direction with 90°. T type thermocouples with a diameter of 0.3 mm calibrated with sensitive reference thermometer were used. The average surface temperature is determined with the thermocouples brazed to the notches. Also to minimize the end losses, two pieces of insulating material made of XPS are placed on the cylinder's endpoints. These two bare horizontal cylinders which have a radius smaller than a certain critical size were wrapped with a textile material. Wrapped cylinder diameters were increased to 9 mm for 4.8 mm and 12.8 mm for 9.45 mm after coating. 14 new calibrated T type thermocouples with a diameter of 0.3 mm were placed on the textile coating exactly in the same angular direction of the brazed thermocouples on bare cylinders. The average insulation temperature (Tw) is determined with 11 thermocouples and also surface temperature was observed under steady state condition circumferentially with the remaining three thermocouples. Replacement of thermocouples on test cylinder is shown in Fig. 1. Constant heat flux was applied to all bare and wrapped cylinders. The cylinder was connected to a DC power supply with 10 A–60 V value to give the required electrical power. Although the adjustable voltage and current values given by the power supply can be read from the indicators on the device, a power meter with a resolution of ±0.1 W is used to measure the input power accurately. The experiments were performed in the conditioned room in order to provide the desired ambient temperature and the natural convection conditions. In the room with dimensions of 4000 mm× 4900 mm× 2550 mm the environment temperature between 5 °C and 50 °C and the relative humidity between 20% and 95% can be adjusted to the required value. Ambient environment should be quiescent since the experiments will be made under the conditions of natural convection. As the result of the velocity measurements made with the hot wire calibrated with LDA from the different points in the room it is determined that air velocity varies between 0 and 0.25 m/s. A test cabin was constructed from a hard board which has four lateral surfaces and a floor with dimensions of 800 mm × 1250 mm × 1300 mm. A gap on the closed surfaces in the protection cabin with only its top open can cause a stack effect and thus an unwanted bulk fluid movement will affect the temperature and velocity fields. This effect leads to disturbance of the natural convection conditions. Hence, it is checked that there is no gap on the closed surfaces. It is determined that the required quiescent environment was provided as the result of velocity measurements made inside the test cabin. It is stated that the differences between the experimental data obtained from the pre-studies on heat transfer in horizontal cylinder under conditions of natural convection are caused by choosing the insufficient heat measuring system or designed test cabin. To minimize the errors mentioned in the pre-studies highly sensitive measuring tools were used, the test cabin volume was well determined and the experiments were made in the conditioned room to keep the ambient temperature stable at the required values. The work station connected to the data acquisition unit of the room is used for data collection. By means of an HP VEE based software program, all instant experimental data and required average values can be observed graphically. The program was developed
Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 37 (2010) 58–67
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Fig. 1. Schematic diagram of the experimental apparatus: (1) conditioned room; (2) test cabin; (3) test cylinder; (4) silicone covered resistant wire; (5) insulating material made of XPS; (6) thermocouples on cylinder surface(14 pieces); (7) thermocouples in environment(2 pieces); (8) humidity sensor; (9) dataloger; (10) PC; (11) DC power supply; (12) power meter.
on demand and brought into use. The mentioned features help to determine the steady state condition and make an analysis after the experiment. 2.2. Experimental procedure Natural convection heat transfer from bare and wrapped horizontal cylinders with a layer of textile material below critical diameter is studied experimentally by using two cylinders with different diameters, with different uniform wall and ambient temperature. The thermal boundary conditions for bare and wrapped cylinders used in this study are chosen similarly and are given in Table 1. The steps of experimental study are listed in the following order: • The conditioned room temperature was set to provide the required ambient temperature in the test cabin. The ambient temperatures varied between T∞ = 10 °C–40 °C. A quiescent environment was created and this was checked with a hot wire anemometer inside the test cabin. • Input electric power was sensitively regulated by DC power supply for the desired cylinder surface temperature. Eleven pieces of thermocouples on the inner and eleven for the outer surface in the axial direction and two thermocouples in the test cabin are used for measuring the surface and environment temperatures respectively.
It is possible to see the variation of these values graphically with the HP VEE based data collection program. The steady state condition is considered when variation of all temperatures and especially the average temperatures stays in the range of ±0.1–0.2 °C for 20 min. For each experiment steady state condition is realized almost 5 h later. • An approximate uniform wall temperature boundary condition was enabled by using a highly conductive and thick (1 mm) copper cylinder. Maximum variation of the temperatures is 4% between eleven pieces of thermocouples in the axial direction. Besides this the surface temperature has been observed under steady state condition circumferentially. • The experiments were repeated by increasing the outer surface temperature from 10 °C to 60 °C for each experiment. 2.3. Data reduction The dimensional analysis generally shows that natural convection heat transfer from horizontal cylinders depends on Nusselt and Rayleigh numbers. In the experiment facility, sensitively measured input electrical power defined by Eq. (1) gives the total natural convection heat transfer from the surface of horizontal cylinder. Qe = V × I
ð1Þ
Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 37 (2010) 58–67
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Table 1 Thermal boundary conditions for different bare/wrapped test cylinder diameters. Experiment no.
Bare cylinder diameter (mm)
Temperatures (°C) T∞
Tc
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
4.8
11.2 11.2 11.3 11.3 11.3 20.8 20.8 20.8 30.1 30.2 30.3 39.9 40.0 49.5 9.5 9.7 9.5 9.8 20.2 20.2 20.1 20.2 30.5 30.7 30.5 40.2 40.2
20.6 30.6 40.5 50.2 60.5 30.1 40.4 50.0 40.1 50.3 60.1 50.4 60.6 60.7 30.3 40.1 50.3 60.5 30.1 40.3 50.2 60.3 40.2 50.1 60.8 50.0 60.0
9.45
Experiment no. 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
Under steady state conditions the energy equation for the horizontal test cylinder based on the 1st law of thermodynamics is expressed as below:
Wrapped cylinder diameter (mm) 9.0
12.8
Temperatures (°C) T∞
Tc
Tw
11.3 11.3 11.5 11.6 11.6 20.8 21.0 21.0 21.0 30.4 30.4 30.5 40.0 39.9 9.5 9.6 9.6 9.6 20.3 20.3 20.6 20.5 30.2 30.2 30.3 41.5 40.0
25.1 40.9 56.1 71.7 87.5 34.5 49.9 65.8 81.3 44.8 60.8 76.9 71.9 55.5 36.3 50.0 64.1 77.7 33.5 46.3 58.5 71.4 42.4 55.4 69.8 53.5 65.9
20.8 31.0 40.6 50.7 60.1 30.3 40.3 50.1 59.7 40.1 50.4 60.3 60.4 50.1 30.2 40.3 50.6 60.4 30.5 40.1 49.0 58.4 39.4 48.9 59.3 50.5 59.9
The convection heat transfer which is the driving force of the plume can be represented by: Q conv = hAðTc −T∞ Þ for bare cylinder;
Q e = Q conv + Q rad + Q cond
ð2Þ
Since two pieces of insulating material made of XPS are placed on the endpoints of the cylinder the conduction heat loss is neglected. For that reason, heat transfer from the horizontal cylinder surface by convection can be calculated as: Q conv = Q e −Q rad
ð3Þ
Heat transfer from the horizontal cylinder surface by radiation can be represented by:
Q rad =
Ebw −Eb∞ 1−εw Aw εw
+
1 Aw Fw∞
+
1−ε∞ A∞ ε∞
ð4Þ
Ebw = σ:Tw
4
ð5Þ
4
ð6Þ
Eb∞ = σ:T∞
ð7Þ
Q conv = hAðTw −T∞ Þ for wrapped cylinder: Nusselt number is defined as: Nu = hD = k
ð8Þ
The air thermo physical properties (k and ν) in non-dimensional parameters were evaluated at the mean film temperature Tf = ðTc + T∞ Þ = 2 for bare cylinder;
ð9Þ
Tf = ðTw + T∞ Þ = 2 for wrapped cylinder:
gβðTc −T∞ ÞD3 for bare cylinder; ν2 3 gβðTw −T∞ ÞD for wrapped cylinder: Gr = ν2 Gr =
ð10Þ
where
The emissivity of wrapped horizontal cylinder surface εw should be determined accurately to calculate the heat transfer by radiation from Eq. (4). Therefore the outer surface temperature of the wrapped heated horizontal cylinder is measured with T type thermocouple that is calibrated with reference thermometer and thermal camera simultaneously. Thermal camera's emissivity value is adjusted till the measured two temperatures become equal. As a result, emissivity is found as 0.95 in this study. Also the obtained value is in the suggested range of thermal camera's emissivity tables for cloth.
β = 1 = ð273 + Tf Þ
ð11Þ
Ra = Gr × Pr
ð12Þ
2.4. Uncertainty analysis The accuracy of the experimental study can be affected by the errors which may arise during the experiments for different reasons. These errors may appear in two ways. The first one is caused by the researchers and the rest is the measurement error which consists of two
Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 37 (2010) 58–67
components: a random error and a systematic error. A random error reflects the degree of randomness in any real life processes, whereas a systematic error is usually associated with a specific experimental setup and/or procedure. A random error is evaluated using statistical methods, while a systematic error can be reduced or eliminated by means of calibration. Error analysis is the determination of the systematic and random errors and the introduction of the effects on the experimental results. Also, the error analysis must be accomplished before choosing the range of measurement devices in order to minimize the uncertainty of the results. On the other hand, determining the most important parameter will also contribute to minimize the uncertainty of the results by measuring it more accurately. Amongst many error analysis methods, uncertainty analysis method which is firstly proposed by Kline and McClintock [27] is the most widely used one for experimental studies. In this experimental study, the uncertainty analysis method which is more sensitive compared to others is used. The independent variables that may cause error in the experiments are input electrical power, cylinder surface and environment temperatures. So the uncertainty of the Nusselt number can be defined as follows. Uncertainty analysis is not necessary for radiation heat transfer because it is calculated theoretically and the errors on length measurements are neglected; wh =
1 w A:ðTw −T∞ Þ QT
2
+
−Q conv wT A:ðTw −T∞ Þ2 w
2
+
Q conv wT A:ðTw −T∞ Þ2 ∞
2
1
=2
ð13Þ
wNu =
2 1 = 2 D wh k
ð14Þ
As a result of the calculations made the maximum uncertainty is found as 2.87% for heat transfer coefficient (Nusselt number).
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and then generates discretization of the equations which conserves each quantity based on control volume [26]. The GAMBIT mesh generator associated with the solver has been used to plot and mesh the 2D model of the cylinder in the test cabin based on the dimensions in the experimental study. The solution grid created is shown in Fig. 2a. The phenomenon in the boundary layer around the wrapped horizontal cylinder surface is more important and complicated than the rest of the solution domain. Hence, a boundary layer was created in the vicinity of the insulation outer surface with a finer mesh. Detailed view of the solution grid is shown in Fig. 2b. Thermal boundary conditions can be defined in four different types in FLUENT: constant heat flux, constant temperature, convection– radiation and convection. In this study, the constant temperature boundary condition is applied, the lateral and bottom surfaces of the test cabin and the surface of the horizontal test cylinder are defined as wall type boundary condition; the upper surface of the test cabin is defined as pressure-inlet type boundary condition. The temperature of the lateral and bottom surfaces of the test cabin is taken as equal to the ambient temperature and the measured ambient temperature from the experiments is used. The average insulation surface temperature measured in the experimental study is used for the horizontal cylinder surface temperature. The thermal boundary conditions used in the study are given in Table 1. Segregated solution method is used for the solution. The governing equations are solved consecutively in this method. In order to obtain a converged solution, several iterations of the solution loop must be performed because the governing equations are non-linear (and coupled). The standard laminar viscous flow model and surface to surface radiation model were used. For pressure–velocity coupling discretization the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm has been used. For continuity and momentum the residual values were taken 10− 3 and for energy 10− 6. 4. Results and discussion 4.1. Experimental results
3. Numerical analysis and model In the numerical study FLUENT CFD package was used. This package uses a technique based on control volume theory to convert the governing equations to algebraic equations so they can be solved numerically. The control volume technique works by performing the integration of the governing equations about each control volume,
In the experiment facility, sensitively measured input electrical power defined by Eq. (1) gives the total heat transfer rate from the surface of the bare and wrapped horizontal cylinders. Firstly heat transfer rates from bare and wrapped cylinders were measured and then compared with each other. Heat transfer enhancement was observed in Fig. 3. Here, as an example, for T∞ = 20 °C, Tc = 40 °C
Fig. 2. The solution grid of the 2D model of the wrapped cylinder: (a) complete view in the test cabin (b) detailed view of the solution grid.
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boundary conditions heat transfer rate of bare cylinder (4.8 mm) and wrapped cylinder (9 mm) can be read as 4.39 W/m and 5.82 W/m respectively in Fig. 3a. Heat augmentation for other boundary conditions can also be seen in Fig. 3a and for the second cylinder in Fig. 3b. Several researchers have proposed commonly used correlations for the average Nusselt numbers as a function of the Prandtl and Rayleigh numbers. On the basis of the experimental data gathered here for wrapped cylinders, Rayleigh and average Nusselt numbers were calculated. The results of Morgen [2], Churchill and Chu [4], Fand and Brucker [3] are also presented in comparison with the experimental data. The correlations that are used for comparison can be seen as follows: Nu = 0:85 Ra 1=2
Nu
0:188
2 4 10 b Ra b 10 [2]
ð15Þ
1 = 6 h i 9 = 16 16 = 9 12 = 0:6 + 0:387 Ra= 1 + ð0:559= PrÞ Ra≤10 [4] ð16Þ
" Nu = ð0:4Pr −8
10
0:0433
8
Ra
0:25
bRab10 [3]
0:0334
Þ + ð0:503Pr
0:0816
Ra
0:122
Þ+
0:95Ge Pr 0:06 Ra 0:0511
Fig. 4. Comparison of experimental average Nusselt number for the wrapped horizontal cylinder with previous studies [2–4] in ± 30% band.
!#
ð17Þ
Fig. 3. Heat transfer rates from bare/wrapped cylinders (a) for 4.8/9 mm, (b) for 9.45/ 12.8 mm.
Average Nusselt number increases with increasing Rayleigh number as expected. It is shown for validation of experimental data and characteristics of this similar trend can be seen in pre-studies at the same time. The deviation of experimental average Nusselt number
Fig. 5. Experimental and numerical average Nusselt numbers for both two wrapped horizontal cylinders: (a) comparison of data, (b) comparison in ± 30% band.
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and previous studies [2–4] stays in the range of ±30% and is seen in Fig. 4. The max deviation is seen between our experimental result and Churchill and Chu [4]'s empirical correlation and that could be attributed to the wide range (Ra ≤ 1012) of this correlation.
4.2. Numerical results The surface heat transfer coefficient and the related Nusselt number were calculated according to convection from the surface which is the difference between total and radiation heat transfer rates obtained from the results of numerical solution. Nusselt and Rayleigh numbers calculated by using the experimental data and numerical solution results of wrapped cylinders are given in Fig. 5a. The devi-
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ation values between experimental and numerical Nusselt numbers stay in the range of ±30% as seen in Fig. 5b. As a result of numerical solution the temperature distribution inside the model was also drawn. The volume inside the test cabin (800 mm × 1250 mm × 1300 mm) is much bigger than the coated horizontal cylinder and therefore it is seen that the heated wrapped cylinder has no effect on the temperature distribution inside the test cabin. Here, as an example, the results of the 46th experiment (T∞ = 20.3 °C, Tw = 30.5 °C) were given in Fig. 6a. The phenomenon in the boundary layer around the horizontal cylinder surface and in the coated layer is more important and complicated than the rest of the solution domain. Thus the wake formation and the temperature distribution in the main interested area are shown closer in Fig. 6b and c respectively.
Fig. 6. Results and flow view of the numerical solution: (a) the temperature distribution inside the test cabin, (b) wake formation on the heated wrapped horizontal cylinder, (c) temperature distribution and isotherms of heated wrapped horizontal cylinder.
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Experimentally measured outer surface temperatures of the coating (Tw) is also compared with the results of numerical simulation and the deviation between experimental and numerical results stays in the range of ±5% as seen in Fig. 7.
(e) Temperature distribution and isotherms in the textile coating layer and air were obtained from the numerical study. Calculated outer surface temperature from numerical simulation is very close to the experimental measurements.
5. Conclusion
Acknowledgments
Natural convection heat transfer from a heated horizontal cylinder wrapped with a layer of textile material was experimentally and numerically investigated. Accurate and repeatable experiments were carried out using sensitive measuring devices in a conditioned room. CFD analysis were performed as numerical solution in the study and there is no another work using CFD program for the determination of natural convection from a horizontal cylinder with the parameters of study. For that reason, this work is expected to contribute to literature. The following results were obtained:
The authors gratefully acknowledge the financial support for this study received from the Scientific and Technological Research Council of Turkey (TUBITAK) under grant number 107M536. Also they are grateful to Arcelik A.Ş. the leading refrigerator company of Turkey for the usage of measurement devices and conditioned room.
(a) Heat transfer rates for a bare horizontal cylinder which has a radius smaller than a certain critical size and for a wrapped horizontal cylinder were compared and heat transfer enhancement is seen obviously for two different diameters (9.45 and 12.8 mm). (b) Comparison of average Nusselt numbers for wrapped horizontal cylinders was done using the correlations of Morgen [2], Churchill and Chu [4], Fand and Brucker [3] according to the different experimental conditions and test cylinders. The maximum deviation is seen between experimental results and Churchill and Chu [4]'s empirical correlation and that could be attributed to the wide range (Ra ≤ 1012) of this correlation. In addition to this, majority of data belonging to other correlations were seen to fall into the 30% deviation line. (c) Nusselt numbers increase with increasing Rayleigh numbers in this study. Numerical and experimental data points show similar trends (Fig. 5a). Also results of numerical and experimental studies on the average Nusselt numbers are found to be in good agreement and stay in the range of ±30%. (d) Wake formation and temperature distribution over the wrapped horizontal cylinder were obtained by CFD analysis and are shown in figures which have never been seen in the literature before. In addition to this, temperature and velocity fields were checked not to be affected by the heated test cylinder in the test cabin; this result showed that the test cabin's size was designed properly.
Fig. 7. Comparison of experimental and numerical coating outer surface temperatures.
References [1] Ş.Ö. Atayılmaz, İ. Teke, Experimental and numerical study of the natural convection from a heated horizontal cylinder, International Communications in Heat and Mass Transfer 36 (2009) 731–738. [2] V.T. Morgan, The overall convective heat transfer from smooth circular cylinders, Advances in Heat Transfer 11 (1975) 199–211. [3] R.M. Fand, J. Brucker, A correlation for heat transfer by natural convection from horizontal cylinders that accounts for viscous dissipation, International Journal of Heat Mass Transfer 26 (1983) 709–726. [4] S.W. Churchill, H.H.S. Chu, Correlating equations for laminar and turbulent free convection from a horizontal cylinder, International Journal of Heat Mass Transfer 18 (1975) 1049–1053. [5] G.D. Raithby, K.G.T. Hollands, Laminar and turbulent free convection from elliptic cylinders, with a vertical plate and horizontal cylinder as special cases, Transactions of ASME 98 (1976) 72–80. [6] T. Misumi, K. Suzuki, K. Kitamura, Fluid flow and heat transfer of natural convection around large horizontal cylinders: experiments with air, Heat Transfer—Asian Research 32 (2003) 293–305. [7] K. Kitamura, F. Kami-Iwa, T. Misumi, S. Smith, Heat transfer and fluid flow of natural convection around large horizontal, International Journal of Heat Mass Transfer 42 (1999) 4093–4106. [8] W.H. McAdams, Heat transmission, 3rd. ed, McGraw-Hill, 1954, pp. 175–177. [9] S.S. Kutateladze, Fundamentals of Heat Transfer, Academic Pres, 1963, p. 293. [10] S.W. Churchill, R. Usagi, A general expression for the correlation of rates of transfer and other phenomena, AIChE Journal 18 (1972) 1121–1128. [11] R.M. Fand, E.W. Morris, M. Lum, Natural convection heat transfer from horizontal cylinders to air, water and slicone oils for Rayleigh numbers between 3 × 102 and 2 × 107, International Journal of Heat Mass Transfer 20 (1977) 1173–1184. [12] T. Fujii, M. Takeuchi, M. Fujii, K. Suzaki, H. Uehara, Experiments on natural convection heat transfer from the outer surface of a vertical cylinder to liquids, International Journal of Heat Mass Transfer 13 (1970) 753–787. [13] L. Pera, B. Gebhart, Experimental observations of wake formation over cylindrical surfaces in natural convection flows, International Journal of Heat Mass Transfer 15 (1972) 175–177. [14] T.H. Kuehn, R.J. Goldstein, Numerical solution to the Navier–Stokes equations for laminar natural convection about a horizontal isothermal circular cylinder, International Journal of Heat Mass Transfer 23 (1980) 971–979. [15] O. Reymond, D.B. Murray, T.S. O'Donovan, Natural convection heat transfer from two horizontal cylinders, Experimental Thermal and Fluid Science 32 (2008) 1702–1709. [16] J.H. Merkin, Free convection boundary layers on cylinders of elliptic cross section, Transactions of the ASME 99 (1977) 453–457. [17] M.A. Muntasser, J.C. Mulligan, A local nonsimilarity analysis of free convection from a horizontal cylindrical surface, Journal of Heat Transfer 100 (1978) 165–167. [18] B. Farouk, S.İ. Güçeri, Natural convection from a horizontal cylinder–laminar regime, Transactions of ASME 103 (1981) 522–527. [19] F.P. Incropera, D.P. DeWitt, Introduction to Heat Transfer, John Wiley Publisher, New York, 1996. [20] Yunus A. Çengel, Heat Transfer: A Practical Approach, McGraw-Hill Book Company, New York, 2003. [21] Ş. Özgür Atayılmaz, Demir Hakan, Ağra Özden, Numerical study of the natural convection around an isolated horizontal cylinder and determination of critical radius effect with a variable heat transfer coefficient, ASME Summer Heat Transfer Conference, San Francisco, 2009. [22] R.T. Balmer, The critical radius affect with a variable heat transfer coefficient, AIChE Journal 24 (1978) 547–548. [23] E.M. Sparrow, S.S. Kang, Two dimensional heat transfer and critical radius results for natural convection about an insulated horizontal cylinder, International Journal of Heat Mass Transfer 28 (1985) 2049–2060. [24] M.R. Kulkarni, Critical radius for radial heat conduction: a necessary criterion but not always sufficient, Applied Thermal Engineering 24 (2004) 967–979. [25] M. Ait Saada, S. Chikh, A. Campo, Natural convection around a horizontal solid cylinder wrapped with a layer of fibrous or porous material, International Journal of Heat and Fluid Flow 28 (2007) 483–495. [26] Fluent User's Guide, release 6.2.16, Fluent Incorporated.
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[30] A. Andreozzi, Y. Jaluria, O. Manca, Numerical investigation of transient natural convection in a horizontal channel heated from upper wall, Numerical Heat Transfer Part A, Applications 51 (2007) 815–842. [31] O. Zeitoun, M. Ali, Numerical investigation of natural convection around isothermal horizontal rectangular ducts, Numerical Heat Transfer Part A, Applications 50 (2006) 189–204. [32] A.K. Saha, Unsteady free convection in a vertical channel with a built in heated square cylinder, Numerical Heat Transfer Part A, Applications 38 (2000) 795–818.
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t
Experimental and numerical study of the natural convection from a heated horizontal cylinder wrapped with a layer of textile material☆ Ş. Özgür Atayılmaz ⁎, İsmail Teke Department of Mechanical Engineering, Yildiz Technical University, 34349 Istanbul, Turkey
a r t i c l e
i n f o
Available online 20 October 2009 Keywords: Natural convection Heat transfer Horizontal cylinder CFD
a b s t r a c t Natural convection heat transfer enhancement from a horizontal cylinder with a textile coating is studied experimentally and numerically. The coating layer may be used for two purposes. According to the thickness of the coating it may be used as an insulating material or for surface augmentation. In the experimental study, two cylinders having different diameters of 4.8 mm and 9.45 mm are used. The bare cylinders having a radius smaller than a certain critical size were wrapped with a textile material. Wrapped cylinder diameters were increased to 9 and 12.8 mm respectively after coating and constant heat flux was applied to all bare and wrapped cylinders. Experimental study was carried out at different ambient temperatures in a conditioned room which can be maintained at a stable required value and inside a sufficiently designed test cabin. The ambient and cylinder surface temperatures (T∞ and Tw) varied between 10 °C – 40 °C and 20 °C – 60 °C respectively. Heat transfer rates from bare and wrapped horizontal cylinders were compared and heat transfer enhancement was observed. On the basis of the experimental data average Nusselt numbers were calculated and compared with the well known correlations on natural convection heat transfer from a horizontal cylinder in the specified range of Rayleigh number, and it is seen that the results are in good agreement. The problem is also investigated numerically. Experimental and the numerical results fall in ± 30% band. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Energy demand is increasing as a consequence of population growth and economical development. On the other hand, fossil fuels meeting a great portion of the energy demand are very scarce and their availability is decreasing year by year. Today, energy efficiency is a popular topic which covers almost all appliances employed in industry, infrastructure and household appliances, etc. Developing and designing energy efficient systems are two of the main interest areas of engineering. International institutions or comities such as CECED are aiming to decrease energy consumption especially in household appliances because of having an environmental impact. In refrigeration systems, it is possible to reduce energy consumption and increase efficiency by decreasing the condensation temperature so as the compressor power. This study is focused on decreasing the condensation temperature especially in domestic refrigerators. Natural convection heat transfer from horizontal cylinder is found in many technical applications such as boiler design, heat exchangers, and air cooling systems for air conditioning. Wire-and-tube type heat
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. 0735-1933/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2009.09.009
exchangers widely used in small refrigeration appliances are made of cylinders with an outer diameter of 4.8 mm. In the previous study [1], natural convection heat transfer from a horizontal cylinder is studied experimentally and numerically using two different diameters (4.8 mm–9.45 mm) and one of them is preferred especially the one with 4.8 mm outer diameter. The experimental results of bare cylinders are used in this study for comparisons. In literature there is an extensive amount of numerical and experimental studies on natural convection heat transfer from horizontal cylinder and many more correlations were proposed. Morgan [2], after a wide literature research, suggested empirical correlation equations for an average Nusselt number of the type Nu = c.Ran. Fand and Brucker [3] compared the eight empirical and half-empirical correlations obtained from the pre-studies on natural convection around an infinitely long horizontal isothermal cylinder and created a new correlation by using the experimental data in the range between 10− 8 b Ra b 108 and 0.7 b Pr b 104 in the literature. And it was determined that the correlations do not agree closely with each other. They reported that there is an approximately 50% difference between average Nusselt numbers calculated from Churchill and Chu [4] and Raithby and Hollands [5]'s equations for air at Ra = 1. The difference can be calculated as 43% for higher Ra numbers (Ra = 105 and Pr = 0.7). Recently, some other researchers, Misumi et al. [6] and Kitumura et al. [7], who investigated natural convection flows around horizontal cylinders experimentally also discussed the discrepancy on
Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 37 (2010) 58–67
T1:1
Nomenclature
T1:2 T1:3 T1:4 T1:5 T1:6 T1:7 T1:8 T1:9 T1:10 T1:11 T1:12 T1:13 T1:14 T1:15 T1:16 T1:17 T1:18 T1:19 T1:20 T1:21 T1:22 T1:23 T1:24 T1:25 T1:26 T1:27 T1:28
A D Qe Q conv Q rad Q cond V Ge I h L Nu Gr Ra Pr NuD,w k T w 2D XPS CFD LDA DC CECED
T1:29 T1:30 T1:31 T1:32 T1:33 T1:34 T1:35
Subscripts W coating outer surface ∞ ambient c copper cylinder surface exp experimental num numerical
T1:36 T1:37 T1:38 T1:39 T1:40 T1:41 T1:42
Greek letters ε emissivity ν kinematic viscosity, (m2/s) θ angle about cylinder centre from bottom of cylinder σ Stephan–Boltzmann constant = 5.67 × 10− 8 W/m2K4 ρ densities, (kg/m3)
heat transfer area, (m2) cylinder diameter (m) input electrical power, (W) convection heat loss, (W) radiation heat loss, (W) conduction heat loss, (W) heater voltage, (V) Gebhart number heater current, (A) heat transfer coefficient, W/m2K length along cylinder average Nusselt number Grashof number Rayleigh number Prandtl number local Nusselt number thermal conductivity, W/mK temperature, (°C) uncertainty two dimensional extruded polystyrene foam computational fluid dynamics laser doppler anemometer direct current European Committee of Domestic Equipment Manufacturers
the average Nusselt numbers between their results and the previous empirical correlations. Misumi et al. [6] stated that previous empirical equations such as McAdams [8] and Kutateladze [9] may not predict the Nusselt numbers correctly because of poor descriptions on the experimental apparatus and measurement techniques. Churchill and Chu [4] proposed a simple empirical expression for average Nusselt numbers over horizontal cylinder for all Rayleigh and Prandtl numbers by using Churchill and Usagi's [10] model. This expression can be applied for uniform heat flow, uniform wall temperature, mass transfer and simultaneous heat and mass transfer. Also simpler expressions were obtained for the limited conditions. Raithby and Hollands [5] studied heat transfer over elliptic cylinders of arbitrary eccentricity at a constant surface temperature, and proposed correlations for laminar and turbulent natural convection. Thin layer analysis is developed by adding the thick boundary layer found at the lower Rayleigh numbers to the calculation. Fand et al. [11] developed Raithby and Hollands'[5] and evaluated fluid properties at mean film reference temperature tf =t∞ +j(tw −t∞);
59
j = 0.5 in their study. Fujii et al. [12] studied experimentally the free convection from horizontal cylinder in water, spindle oil and mobeltherm oil and defined a reference temperature: tj =t∞ +j(tw −t∞); 0 ≤j ≤ 1. Mean film reference temperature was a special occasion of reference temperature, where tf and tj became equal for j = 0.5. Thermo physical properties were evaluated at the mean film temperature in the present study. The wake formation formed over the heated cylindrical surface at natural convection and the effect of this phenomenon to the heat transfer on the surface are within the context of pre-made researches. Pera and Gebhart [13] aimed to study the characteristic of the flow over the cylinder's surface caused by thermal effects and visualize the wake formation over cylindrical surfaces experimentally. They paid attention to the obscurity about the behavior in a separated region or in the region of wake formation. The flows, along the curved sections, were interacted and joined together to rise in a plume above the curved surface. Kuehn and Goldstein [14] numerically integrated the Navier– Stokes and energy equations by using the finite-difference overrelaxation method for an isothermal horizontal circular cylinder in the range 100 ≤ Ra ≤ 107. Streamlines and isotherms were computed at different values of the Rayleigh numbers. The temperature distribution were calculated at θ = 90° and θ = 180° for Ra = 105, Pr = 0.7 and they have been compared with the experimental results and it is ascertained that the values for θ = 90° are in good agreement. Also they indicated that the boundary layer formulations for θ N 130° were not a sufficient approach for heat transfer. More recently, Reymond et al. [15] studied natural convection heat transfer from a horizontal cylinder bounded with water and indicated that around the circumference of a cylinder, the average Nusselt number distribution show a maximum at the bottom of the cylinder (θ = 0°) and as the boundary layer developing it decreases towards the top (θ = 180°). Merkin [16] described a method of solving the full partial differential equations for the natural convection boundary layer over cylinders of general rounded cross-sectional form which could be used to give reliable results over the whole of the cylinder; the particular example considered there was of a circular cylinder. Muntasser and Mulligan [17] used the local non-similarity method and gave local solutions for different values of the Prandtl number. The change of natural convection along the radius of the horizontal cylinder was studied and the results were given from a lower stagnation point (θ = 0) to 150°. Farouk and Guceri [18] conducted some numerical analysis of the heat transfer around a single cylinder. They demonstrated that heat transfer increases to its maximum at the bottom and decreases towards the top of the cylinder. In this study natural convection heat transfer from a wrapped horizontal cylinder is investigated experimentally and numerically. According to the situation, covering the cylinder may be employed as insulation or surface augmentation. Incropera and DeWitt [19] gave the best answer to the application where the heat transfer rate increases by adding insulation and discussed the answer in detail. For electrical wires, thermal insulation material is needed for electrical insulation and safety. Curved surfaces such as a circular cylinder having a radius smaller than a certain critical size, adding insulation to the surface increase the heat transfer. This phenomenon occurs if the increase in the conduction resistance is less than the decrease in the convection resistance and commonly called the critical radius. The critical radius is represented as a function of thermal conductivity of the object and convective heat transfer coefficient (horcr/kins = 1) in the textbooks on heat transfer [19,20]. This is only valid if both thermal conductivity and convective heat transfer coefficient are constant. In fact, the convective heat transfer coefficient varies with outer diameter of the cylinder while thermal conductivity can be taken as constant [21]. Balmer [22] formulated the critical radius for sphere and cylinder in case of variable convection heat transfer coefficient theoretically.
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They used Churchill and Chu's [4] correlation in order to develop the critical radius equation for horizontal cylinder. Sparrow and Kang [23] investigated natural convection heat transfer from insulated horizontal cylinder numerically in a two dimensional space. Problem consists of conduction in the insulation layer and natural convection in the vicinity of outer surface. They found that the use of Morgan's [2] correlation gave the most accurate set of one dimensional result amongst Mc Adams [8], Morgan [2], Churchill and Chu [4]. Also they reported that the standard critical radius criterion horcr/kins = 1 led to significant errors and should no longer be used. Therefore the critical radius can be calculated from horcr/kins = 3n / (1 + n) where “n” is the exponent of Rayleigh in Nu = c.Ran correlation. Kulkarni [24], defined a new term “cross over point” as a radius greater than the critical radius such that the heat transfer with the corresponding amount of insulating material is equal to that of the bare thermal system. It is pointed out that the cross over insulation radius is applicable when the Biot number (hri/kins) is less than 1 in a cylindrical system. Ait Saada et al. [25] investigated natural convection from a horizontal cylinder with a porous or fibrous coating. It is indicated that porous or fibrous material may also be used as a heat transfer augmentation technique and is achieved by selecting porous media with permeability and/or high effective thermal conductivity. Additionally, natural convection heat transfer inside channels and ducts has been studied by many authors [28–32]. Zeitoun and Ali [31] studied natural convection around isothermal horizontal rectangular ducts numerically. They reported that the far-field boundaries for horizontal cylinder should be located at distances of 5D, 2D and 2D for right, lower and upper boundaries respectively and adopted this for rectangular ducts. They also gave a Nu–Ra correlation for 700 ≤ Ra ≥ 1.3 × 108. Saha [32] investigated unsteady free convection from a heated square cylinder in a vertical channel numerically using MAC method. It is stated that there are many theoretical and experimental studies on natural convection heat transfer from horizontal cylinder. Generally the wide dispersion in the published experimental results was attributed to the distortion of the temperature and velocity fields by bulk fluid movements, the use of under sized test cabin or existence of the temperature measurement system and supports. In the present study, the test cabin was constructed at proper dimensions and all the surfaces except the top were made impermeadable to minimize these factors. Different from the other experimental studies made in the air, all the experiments were performed in the conditioned room to keep the ambient temperature constant during the experiments and to have experimental runs at different ambient temperatures. In addition, sensitive measuring devices were used to minimize the measuring errors. Firstly experimental study is performed with two bare horizontal cylinders (4.8 and 9.45 mm). Afterwards the bare cylinders that have radius smaller than a certain critical size were wrapped with a textile material. Heat transfer rates from bare and wrapped horizontal cylinders were compared and heat transfer enhancement was seen obviously. Despite the contribution of published numerical studies, CFD analysis was not used for natural convection heat transfer from a wrapped horizontal cylinder. In the numerical part of this study, CFD package (FLUENT [26]) was used for the 2D heat transfer analysis. Nusselt and Rayleigh numbers were calculated using the experimental data of wrapped cylinders and compared with the results of numerical simulation. 2. Experimental study 2.1. Experimental apparatus and conditioned room A schematic drawing of the experimental apparatus that consists of twelve parts is shown in Fig. 1. The two test cylinders made from
copper material at 1 m length and with diameters of 4.8 mm and 9.45 mm have been prepared. Silicone covered cylindrical resistant wires, are centered, leaving no air space and close fitted inside the test cylinder, to maintain the required uniform surface temperature. The diameter and the resistance value of the wires used for the first and the second cylinders were 0.35 mm–11.3 Ω and 0.75 mm–3.4 Ω respectively. To provide the uniform surface temperature in the axial direction, test cylinders were made from copper and the wall thickness is made as thick as possible (1 mm). In axial direction 11 notches were formed with a 10 cm space on the surface. Thermocouples can be partly buried in these notches. In order to determine radial temperature distribution three more notches were formed in radial direction with 90°. T type thermocouples with a diameter of 0.3 mm calibrated with sensitive reference thermometer were used. The average surface temperature is determined with the thermocouples brazed to the notches. Also to minimize the end losses, two pieces of insulating material made of XPS are placed on the cylinder's endpoints. These two bare horizontal cylinders which have a radius smaller than a certain critical size were wrapped with a textile material. Wrapped cylinder diameters were increased to 9 mm for 4.8 mm and 12.8 mm for 9.45 mm after coating. 14 new calibrated T type thermocouples with a diameter of 0.3 mm were placed on the textile coating exactly in the same angular direction of the brazed thermocouples on bare cylinders. The average insulation temperature (Tw) is determined with 11 thermocouples and also surface temperature was observed under steady state condition circumferentially with the remaining three thermocouples. Replacement of thermocouples on test cylinder is shown in Fig. 1. Constant heat flux was applied to all bare and wrapped cylinders. The cylinder was connected to a DC power supply with 10 A–60 V value to give the required electrical power. Although the adjustable voltage and current values given by the power supply can be read from the indicators on the device, a power meter with a resolution of ±0.1 W is used to measure the input power accurately. The experiments were performed in the conditioned room in order to provide the desired ambient temperature and the natural convection conditions. In the room with dimensions of 4000 mm× 4900 mm× 2550 mm the environment temperature between 5 °C and 50 °C and the relative humidity between 20% and 95% can be adjusted to the required value. Ambient environment should be quiescent since the experiments will be made under the conditions of natural convection. As the result of the velocity measurements made with the hot wire calibrated with LDA from the different points in the room it is determined that air velocity varies between 0 and 0.25 m/s. A test cabin was constructed from a hard board which has four lateral surfaces and a floor with dimensions of 800 mm × 1250 mm × 1300 mm. A gap on the closed surfaces in the protection cabin with only its top open can cause a stack effect and thus an unwanted bulk fluid movement will affect the temperature and velocity fields. This effect leads to disturbance of the natural convection conditions. Hence, it is checked that there is no gap on the closed surfaces. It is determined that the required quiescent environment was provided as the result of velocity measurements made inside the test cabin. It is stated that the differences between the experimental data obtained from the pre-studies on heat transfer in horizontal cylinder under conditions of natural convection are caused by choosing the insufficient heat measuring system or designed test cabin. To minimize the errors mentioned in the pre-studies highly sensitive measuring tools were used, the test cabin volume was well determined and the experiments were made in the conditioned room to keep the ambient temperature stable at the required values. The work station connected to the data acquisition unit of the room is used for data collection. By means of an HP VEE based software program, all instant experimental data and required average values can be observed graphically. The program was developed
Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 37 (2010) 58–67
61
Fig. 1. Schematic diagram of the experimental apparatus: (1) conditioned room; (2) test cabin; (3) test cylinder; (4) silicone covered resistant wire; (5) insulating material made of XPS; (6) thermocouples on cylinder surface(14 pieces); (7) thermocouples in environment(2 pieces); (8) humidity sensor; (9) dataloger; (10) PC; (11) DC power supply; (12) power meter.
on demand and brought into use. The mentioned features help to determine the steady state condition and make an analysis after the experiment. 2.2. Experimental procedure Natural convection heat transfer from bare and wrapped horizontal cylinders with a layer of textile material below critical diameter is studied experimentally by using two cylinders with different diameters, with different uniform wall and ambient temperature. The thermal boundary conditions for bare and wrapped cylinders used in this study are chosen similarly and are given in Table 1. The steps of experimental study are listed in the following order: • The conditioned room temperature was set to provide the required ambient temperature in the test cabin. The ambient temperatures varied between T∞ = 10 °C–40 °C. A quiescent environment was created and this was checked with a hot wire anemometer inside the test cabin. • Input electric power was sensitively regulated by DC power supply for the desired cylinder surface temperature. Eleven pieces of thermocouples on the inner and eleven for the outer surface in the axial direction and two thermocouples in the test cabin are used for measuring the surface and environment temperatures respectively.
It is possible to see the variation of these values graphically with the HP VEE based data collection program. The steady state condition is considered when variation of all temperatures and especially the average temperatures stays in the range of ±0.1–0.2 °C for 20 min. For each experiment steady state condition is realized almost 5 h later. • An approximate uniform wall temperature boundary condition was enabled by using a highly conductive and thick (1 mm) copper cylinder. Maximum variation of the temperatures is 4% between eleven pieces of thermocouples in the axial direction. Besides this the surface temperature has been observed under steady state condition circumferentially. • The experiments were repeated by increasing the outer surface temperature from 10 °C to 60 °C for each experiment. 2.3. Data reduction The dimensional analysis generally shows that natural convection heat transfer from horizontal cylinders depends on Nusselt and Rayleigh numbers. In the experiment facility, sensitively measured input electrical power defined by Eq. (1) gives the total natural convection heat transfer from the surface of horizontal cylinder. Qe = V × I
ð1Þ
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Table 1 Thermal boundary conditions for different bare/wrapped test cylinder diameters. Experiment no.
Bare cylinder diameter (mm)
Temperatures (°C) T∞
Tc
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
4.8
11.2 11.2 11.3 11.3 11.3 20.8 20.8 20.8 30.1 30.2 30.3 39.9 40.0 49.5 9.5 9.7 9.5 9.8 20.2 20.2 20.1 20.2 30.5 30.7 30.5 40.2 40.2
20.6 30.6 40.5 50.2 60.5 30.1 40.4 50.0 40.1 50.3 60.1 50.4 60.6 60.7 30.3 40.1 50.3 60.5 30.1 40.3 50.2 60.3 40.2 50.1 60.8 50.0 60.0
9.45
Experiment no. 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
Under steady state conditions the energy equation for the horizontal test cylinder based on the 1st law of thermodynamics is expressed as below:
Wrapped cylinder diameter (mm) 9.0
12.8
Temperatures (°C) T∞
Tc
Tw
11.3 11.3 11.5 11.6 11.6 20.8 21.0 21.0 21.0 30.4 30.4 30.5 40.0 39.9 9.5 9.6 9.6 9.6 20.3 20.3 20.6 20.5 30.2 30.2 30.3 41.5 40.0
25.1 40.9 56.1 71.7 87.5 34.5 49.9 65.8 81.3 44.8 60.8 76.9 71.9 55.5 36.3 50.0 64.1 77.7 33.5 46.3 58.5 71.4 42.4 55.4 69.8 53.5 65.9
20.8 31.0 40.6 50.7 60.1 30.3 40.3 50.1 59.7 40.1 50.4 60.3 60.4 50.1 30.2 40.3 50.6 60.4 30.5 40.1 49.0 58.4 39.4 48.9 59.3 50.5 59.9
The convection heat transfer which is the driving force of the plume can be represented by: Q conv = hAðTc −T∞ Þ for bare cylinder;
Q e = Q conv + Q rad + Q cond
ð2Þ
Since two pieces of insulating material made of XPS are placed on the endpoints of the cylinder the conduction heat loss is neglected. For that reason, heat transfer from the horizontal cylinder surface by convection can be calculated as: Q conv = Q e −Q rad
ð3Þ
Heat transfer from the horizontal cylinder surface by radiation can be represented by:
Q rad =
Ebw −Eb∞ 1−εw Aw εw
+
1 Aw Fw∞
+
1−ε∞ A∞ ε∞
ð4Þ
Ebw = σ:Tw
4
ð5Þ
4
ð6Þ
Eb∞ = σ:T∞
ð7Þ
Q conv = hAðTw −T∞ Þ for wrapped cylinder: Nusselt number is defined as: Nu = hD = k
ð8Þ
The air thermo physical properties (k and ν) in non-dimensional parameters were evaluated at the mean film temperature Tf = ðTc + T∞ Þ = 2 for bare cylinder;
ð9Þ
Tf = ðTw + T∞ Þ = 2 for wrapped cylinder:
gβðTc −T∞ ÞD3 for bare cylinder; ν2 3 gβðTw −T∞ ÞD for wrapped cylinder: Gr = ν2 Gr =
ð10Þ
where
The emissivity of wrapped horizontal cylinder surface εw should be determined accurately to calculate the heat transfer by radiation from Eq. (4). Therefore the outer surface temperature of the wrapped heated horizontal cylinder is measured with T type thermocouple that is calibrated with reference thermometer and thermal camera simultaneously. Thermal camera's emissivity value is adjusted till the measured two temperatures become equal. As a result, emissivity is found as 0.95 in this study. Also the obtained value is in the suggested range of thermal camera's emissivity tables for cloth.
β = 1 = ð273 + Tf Þ
ð11Þ
Ra = Gr × Pr
ð12Þ
2.4. Uncertainty analysis The accuracy of the experimental study can be affected by the errors which may arise during the experiments for different reasons. These errors may appear in two ways. The first one is caused by the researchers and the rest is the measurement error which consists of two
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components: a random error and a systematic error. A random error reflects the degree of randomness in any real life processes, whereas a systematic error is usually associated with a specific experimental setup and/or procedure. A random error is evaluated using statistical methods, while a systematic error can be reduced or eliminated by means of calibration. Error analysis is the determination of the systematic and random errors and the introduction of the effects on the experimental results. Also, the error analysis must be accomplished before choosing the range of measurement devices in order to minimize the uncertainty of the results. On the other hand, determining the most important parameter will also contribute to minimize the uncertainty of the results by measuring it more accurately. Amongst many error analysis methods, uncertainty analysis method which is firstly proposed by Kline and McClintock [27] is the most widely used one for experimental studies. In this experimental study, the uncertainty analysis method which is more sensitive compared to others is used. The independent variables that may cause error in the experiments are input electrical power, cylinder surface and environment temperatures. So the uncertainty of the Nusselt number can be defined as follows. Uncertainty analysis is not necessary for radiation heat transfer because it is calculated theoretically and the errors on length measurements are neglected; wh =
1 w A:ðTw −T∞ Þ QT
2
+
−Q conv wT A:ðTw −T∞ Þ2 w
2
+
Q conv wT A:ðTw −T∞ Þ2 ∞
2
1
=2
ð13Þ
wNu =
2 1 = 2 D wh k
ð14Þ
As a result of the calculations made the maximum uncertainty is found as 2.87% for heat transfer coefficient (Nusselt number).
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and then generates discretization of the equations which conserves each quantity based on control volume [26]. The GAMBIT mesh generator associated with the solver has been used to plot and mesh the 2D model of the cylinder in the test cabin based on the dimensions in the experimental study. The solution grid created is shown in Fig. 2a. The phenomenon in the boundary layer around the wrapped horizontal cylinder surface is more important and complicated than the rest of the solution domain. Hence, a boundary layer was created in the vicinity of the insulation outer surface with a finer mesh. Detailed view of the solution grid is shown in Fig. 2b. Thermal boundary conditions can be defined in four different types in FLUENT: constant heat flux, constant temperature, convection– radiation and convection. In this study, the constant temperature boundary condition is applied, the lateral and bottom surfaces of the test cabin and the surface of the horizontal test cylinder are defined as wall type boundary condition; the upper surface of the test cabin is defined as pressure-inlet type boundary condition. The temperature of the lateral and bottom surfaces of the test cabin is taken as equal to the ambient temperature and the measured ambient temperature from the experiments is used. The average insulation surface temperature measured in the experimental study is used for the horizontal cylinder surface temperature. The thermal boundary conditions used in the study are given in Table 1. Segregated solution method is used for the solution. The governing equations are solved consecutively in this method. In order to obtain a converged solution, several iterations of the solution loop must be performed because the governing equations are non-linear (and coupled). The standard laminar viscous flow model and surface to surface radiation model were used. For pressure–velocity coupling discretization the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm has been used. For continuity and momentum the residual values were taken 10− 3 and for energy 10− 6. 4. Results and discussion 4.1. Experimental results
3. Numerical analysis and model In the numerical study FLUENT CFD package was used. This package uses a technique based on control volume theory to convert the governing equations to algebraic equations so they can be solved numerically. The control volume technique works by performing the integration of the governing equations about each control volume,
In the experiment facility, sensitively measured input electrical power defined by Eq. (1) gives the total heat transfer rate from the surface of the bare and wrapped horizontal cylinders. Firstly heat transfer rates from bare and wrapped cylinders were measured and then compared with each other. Heat transfer enhancement was observed in Fig. 3. Here, as an example, for T∞ = 20 °C, Tc = 40 °C
Fig. 2. The solution grid of the 2D model of the wrapped cylinder: (a) complete view in the test cabin (b) detailed view of the solution grid.
Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 37 (2010) 58–67
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boundary conditions heat transfer rate of bare cylinder (4.8 mm) and wrapped cylinder (9 mm) can be read as 4.39 W/m and 5.82 W/m respectively in Fig. 3a. Heat augmentation for other boundary conditions can also be seen in Fig. 3a and for the second cylinder in Fig. 3b. Several researchers have proposed commonly used correlations for the average Nusselt numbers as a function of the Prandtl and Rayleigh numbers. On the basis of the experimental data gathered here for wrapped cylinders, Rayleigh and average Nusselt numbers were calculated. The results of Morgen [2], Churchill and Chu [4], Fand and Brucker [3] are also presented in comparison with the experimental data. The correlations that are used for comparison can be seen as follows: Nu = 0:85 Ra 1=2
Nu
0:188
2 4 10 b Ra b 10 [2]
ð15Þ
1 = 6 h i 9 = 16 16 = 9 12 = 0:6 + 0:387 Ra= 1 + ð0:559= PrÞ Ra≤10 [4] ð16Þ
" Nu = ð0:4Pr −8
10
0:0433
8
Ra
0:25
bRab10 [3]
0:0334
Þ + ð0:503Pr
0:0816
Ra
0:122
Þ+
0:95Ge Pr 0:06 Ra 0:0511
Fig. 4. Comparison of experimental average Nusselt number for the wrapped horizontal cylinder with previous studies [2–4] in ± 30% band.
!#
ð17Þ
Fig. 3. Heat transfer rates from bare/wrapped cylinders (a) for 4.8/9 mm, (b) for 9.45/ 12.8 mm.
Average Nusselt number increases with increasing Rayleigh number as expected. It is shown for validation of experimental data and characteristics of this similar trend can be seen in pre-studies at the same time. The deviation of experimental average Nusselt number
Fig. 5. Experimental and numerical average Nusselt numbers for both two wrapped horizontal cylinders: (a) comparison of data, (b) comparison in ± 30% band.
Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 37 (2010) 58–67
and previous studies [2–4] stays in the range of ±30% and is seen in Fig. 4. The max deviation is seen between our experimental result and Churchill and Chu [4]'s empirical correlation and that could be attributed to the wide range (Ra ≤ 1012) of this correlation.
4.2. Numerical results The surface heat transfer coefficient and the related Nusselt number were calculated according to convection from the surface which is the difference between total and radiation heat transfer rates obtained from the results of numerical solution. Nusselt and Rayleigh numbers calculated by using the experimental data and numerical solution results of wrapped cylinders are given in Fig. 5a. The devi-
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ation values between experimental and numerical Nusselt numbers stay in the range of ±30% as seen in Fig. 5b. As a result of numerical solution the temperature distribution inside the model was also drawn. The volume inside the test cabin (800 mm × 1250 mm × 1300 mm) is much bigger than the coated horizontal cylinder and therefore it is seen that the heated wrapped cylinder has no effect on the temperature distribution inside the test cabin. Here, as an example, the results of the 46th experiment (T∞ = 20.3 °C, Tw = 30.5 °C) were given in Fig. 6a. The phenomenon in the boundary layer around the horizontal cylinder surface and in the coated layer is more important and complicated than the rest of the solution domain. Thus the wake formation and the temperature distribution in the main interested area are shown closer in Fig. 6b and c respectively.
Fig. 6. Results and flow view of the numerical solution: (a) the temperature distribution inside the test cabin, (b) wake formation on the heated wrapped horizontal cylinder, (c) temperature distribution and isotherms of heated wrapped horizontal cylinder.
Ş.Ö. Atayılmaz, İ. Teke / International Communications in Heat and Mass Transfer 37 (2010) 58–67
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Experimentally measured outer surface temperatures of the coating (Tw) is also compared with the results of numerical simulation and the deviation between experimental and numerical results stays in the range of ±5% as seen in Fig. 7.
(e) Temperature distribution and isotherms in the textile coating layer and air were obtained from the numerical study. Calculated outer surface temperature from numerical simulation is very close to the experimental measurements.
5. Conclusion
Acknowledgments
Natural convection heat transfer from a heated horizontal cylinder wrapped with a layer of textile material was experimentally and numerically investigated. Accurate and repeatable experiments were carried out using sensitive measuring devices in a conditioned room. CFD analysis were performed as numerical solution in the study and there is no another work using CFD program for the determination of natural convection from a horizontal cylinder with the parameters of study. For that reason, this work is expected to contribute to literature. The following results were obtained:
The authors gratefully acknowledge the financial support for this study received from the Scientific and Technological Research Council of Turkey (TUBITAK) under grant number 107M536. Also they are grateful to Arcelik A.Ş. the leading refrigerator company of Turkey for the usage of measurement devices and conditioned room.
(a) Heat transfer rates for a bare horizontal cylinder which has a radius smaller than a certain critical size and for a wrapped horizontal cylinder were compared and heat transfer enhancement is seen obviously for two different diameters (9.45 and 12.8 mm). (b) Comparison of average Nusselt numbers for wrapped horizontal cylinders was done using the correlations of Morgen [2], Churchill and Chu [4], Fand and Brucker [3] according to the different experimental conditions and test cylinders. The maximum deviation is seen between experimental results and Churchill and Chu [4]'s empirical correlation and that could be attributed to the wide range (Ra ≤ 1012) of this correlation. In addition to this, majority of data belonging to other correlations were seen to fall into the 30% deviation line. (c) Nusselt numbers increase with increasing Rayleigh numbers in this study. Numerical and experimental data points show similar trends (Fig. 5a). Also results of numerical and experimental studies on the average Nusselt numbers are found to be in good agreement and stay in the range of ±30%. (d) Wake formation and temperature distribution over the wrapped horizontal cylinder were obtained by CFD analysis and are shown in figures which have never been seen in the literature before. In addition to this, temperature and velocity fields were checked not to be affected by the heated test cylinder in the test cabin; this result showed that the test cabin's size was designed properly.
Fig. 7. Comparison of experimental and numerical coating outer surface temperatures.
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