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Experiments on mist flow and heat transfer in a tube fitted with porous media
International Journal of Thermal Sciences 137 (2019) 388–398
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Experiments on mist flow and heat transfer in a tube fitted with porous media
T
Shahram Baragha, Hossein Shokouhmandb,∗, Seyed Soheil Mousavi Ajarostaghic a
Faculty of Mechanical Engineering, Islamic Azad University, Takestan Branch, Takestan, Iran School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran c Faculty of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran b
A R T I C LE I N FO
A B S T R A C T
Keywords: Porous media Mist flow Heat transfer enhancement Force convection
The issues related to porous media are more important in the design and analysis of heat exchangers. Reducing size of heat transfer devices for using of this media was led to be feasible of creating flow with smaller Reynolds numbers. In present study, an experimental investigation of air mist flow is carried out in tube which fitted with porous media. The studied porous region has different geometry. Also the effect of operating parameter like Reynolds number is analyzed. Results indicate that presence of porous media leads that the thermal flux applied to walls of channel be transferred into fluid due to creating a uniform space and high conductivity of porous media. Also, the results depicted that in comparison with the single-phase, mist cooling in porous media can increase the heat transfer rate. Results show that combine these two method (porous medium and mist flow) has significant effect on heat transfer enhancement. According to obtained results, at low Reynolds number with mist flow, the case that porous zone inserted adjacent to wall with 4 cm height has best thermal performance and at high Reynolds number with mist flow, highest thermal performance is belonging to the case that porous zone inserted at the center of the channel with 6 cm diameter. As a final result, between the all investigated models, the case that porous zone inserted at the center of the channel with 6 cm diameter with mist flow has the best heat transfer performance ratio with 24% improvement in comparison with clear channel.
1. Introduction In order to improve the heat transfer rate in the industrial processes, utilizing porous medium is a promising tool. The porous media is a material consists of solid matrix with an interconnected [1]. Beside the using porous medium, mist flow is the other way to enhance the heat transfer rate. Using the advantages of these two method with together can enhance the heat transfer rate significantly in comparison with the single phase in a clear tube. The application of using these both methods in engineering processes consists of hydrocarbon recovery [2], CO2 storage in underground reservoirs [3,4], and proton exchange membrane fuel cells [5–8]. Actually, heat exchanger is a major application of these practical method. Most works on flow in porous media have used, and to a large extent still use. Kuznetsov [9] represented an analytical method to investigate the force convection in a parallel plate channel with porous media. To model the porous media, the Brinkman-Forchheimer-extended Darcy equation was utilised. Results illustrated that porous media increase the heat transfer rate. Alkam and Al-Nimr [10] numerically evaluated the
∗
heat transfer rate in a cylindrical channel partially filled with a porous media. The Brinkman-Forchheimer-extended Darcy model was used to model the flow within the porous domain. Results indicated that the existence of the porous media raise the Nusselt number at the fully developed region. Also, it was shown that steady state time increases by reduction in Darcy number. Shokouhmand et al. [11] investigated the convective heat transfer between two parallel plates of a conduit numerically. The lattice Boltzmann method is used to perform the numerical simulation. The both condition of fully and partially filled porous medium were considered. Teamah et al. [12] perform the numerical simulation to study the laminar forced convection flow in a pipe partially and completely filled with a porous medium. It was observed that pumping power and thermal performance of the investigated domain decreases by increasing the radius of porous material. Also, Yang et al. [13] studied the forced convection in a heated tube with a porous medium core and a tube with a wall covered with a porous medium layer. Tube with a porous medium core showed better thermal performance in comparison with the tube with a wall covered with a porous medium.
Corresponding author. E-mail addresses: [email protected] (S. Baragh), [email protected] (H. Shokouhmand), [email protected] (S.S.M. Ajarostaghi).
https://doi.org/10.1016/j.ijthermalsci.2018.11.030 Received 24 April 2018; Received in revised form 2 November 2018; Accepted 25 November 2018 1290-0729/ © 2018 Elsevier Masson SAS. All rights reserved.
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Nomenclature A D d q'' Q L ˙ m V.I T X hi hi U k Nui f Re NuER NuPR Pr P
Greek symbol ε ρ μ υ
Area, (m2) Outer diameter of porous zone, (m) Inner diameter of porous zone, (m) Heat flux, (W/m2) Heat, (W) Distance between porous zones Mass flowrate, (kg/s) Thermal power of heater, (W) Temperature, (K) Distance between sensor and entrance of test section Local heat transfer coefficient, W/(m2.K) Mean heat transfer coefficient, W/(m2.K) Velocity, (m/s) Thermal conductivity, (W/(m.K)) Local Nusselt number friction coefficient Reynolds number Heat transfer enhancement ratio, (PR) Heat transfer performance ratio, (ER) Prandtl number Pressure, (Pa)
Porosity in porous media Density, (kg/m3) Dynamic viscosity, (kg/(m. s)) Kinematic viscosity, (m2/s)
Subscript and superscript tot w rad cond conv am loss L in s f h c eff b
Nikian et al. [14] investigate the effect of mist flow through the channel fitted with the porous medium experimentally. In this study, the effects of porous medium porosity and permeability on the thermal performance were studied. Shokouhmand and Nikian [15] carried out an experimental test to study the force convection of mist flow in a channel equipped with porous medium. The effects of porous medium characteristics including porosity, permeability and thickness were investigated experimentally. Kumari et al. [16] studied the forced convective heat transfer by the mist flow analytically and numerically. The results indicated that the heat transfer rate with the mist flow is better in comparison with the single phase flow. Huang et al. [17] experimentally and numerically investigated the effect of inserting porous media with a slightly smaller diameter in the core of the tube under the constant and uniform heat flux condition. Three different porosity of porous zone were considered including 0.951, 0.966 and 0.975. Also, the effect of porous radius ratio on the heat transfer performance was analyzed numerically. Results show that the convective heat transfer is significantly enhanced by inserting porous zone in the tube. Baragh et al. [18] studied a single-phase flow of air in channel having circle cross-section with different arrangements of porous media is experimentally. The effect of different arrangement of inserting porous zone in the tube was investigated. The analyze was done in three different air flow regimes including laminar, transient and turbulence. The results show that in both laminar and turbulent flows, fully filled channel of porous media has the best heat transfer and the channel with annulus shape porous zones (the porous zone inserted adjacent to wall) has the best thermal performance in turbulent flow. Bhargavi and SharathKumar Reddy [19] numerically investigated the Laminar forced convection in the parallel plate channels partially filled with a porous material. Constant wall heat flux was considered as boundary condition. Porous insert is attached to both the walls of the channel with equal thickness. Results show that the non-dimensional temperature at the wall attains maximum values at a certain porous fraction. Siavashi et al. [20] simulated nanofluid flow inside the porous media using a two-phase model. Some multi-layered porous foams gave the same performance as the gradient ones. Particle swarm optimization (PSO) algorithm is used to find the optimal arrangements of porous layers. The addition of mist to a flow of steam or gas offers enhanced
Total Wall Radiation Conduction Convection Ambient Lost Local Inlet Surface Fluid Hydraulic Cross-section Effective Bulk
cooling in many applications, including cooling of gas turbine blades [21–23]. Cold droplets impinging on hot surfaces can provide a significant cooling effect, mainly due to the evaporative latent heat effect. This physical mechanism, thus, has been used widely in industry to improve heat transfer rates [24], to designmist-cooled heat exchangers [25], and for different kinds of spray cooling of hot surfaces [26]. Mistcooled heat exchangers can be used for large power or chemical plants, or small refrigerator radiators. The hot fluid flows inside a tube bundle and is cooled by an air stream in across flow with water droplets injected in the air stream at upstream of the bank of tubes. In this study, the effects of different porous media and mist flow on the heat transfer rate are experimentally investigated. Six different porous media where emplaced at the center of the channel. A constant uniform heat flux boundary condition is used. The dry air and mist air flow are flowing inside the channel. An experiment is carried out here to study the effects of mist flow on the heat transfer in a channel which equipped with porous medium. The influence of some operational and geometrical parameters are investigated which the considered geometrical parameters are the inner and outer diameters of porous zone. Also the effect of Reynolds number is analyzed experimentally. The water mass fraction is kept constant at 10% and is injected to the air flow at the entrance of the test section to provide the mist flow. 2. Experimental investigation For the current study, the test section of experimental apparatus is shown in Fig. 1a and schematic diagram of TFHE experimental set up is shown in Fig. 2a and test rig is shown in Fig. 2b. In this section, the detailed information about the present laboratory equipment and apparatus are explained. Diagram, schematic and photographs of the experimental setup are shown in Fig. 1a and (1b) and (1c) respectively. In this device, a suction fan was used in order to pull air into the channel. The fan is located at the end of this device. Also, a motor attached to fan drives it. Alternating voltage that is required for fan different speeds is provided by an inverter. At the front of channel, a perforated chamber is used for converging air. After part of air nozzle, the rectangular channel is used in order to development flow. After part of channel, we have a circularshape part in order to conduct test. At the end of part of test section, 389
International Journal of Thermal Sciences 137 (2019) 388–398
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Fig. 1. (a). Diagram of the experimental test section (b) Schematic of the experimental setup (c) Photograph of the experimental apparatus (d) Photograph of the porous media used in the test.
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Fig. 2. Schematic of porous media models used in the test.
measurements helps to consider the uncertainty in the experimental results. The wall temperature, velocity and pressure drop and their corresponding uncertainty are calculated from manufacturer-supplied calibrations, mist flow rate through the heated test section, the inlet air and mist temperature and their corresponding uncertainty are obtained by calibration. Engineering Equation Solver (EES) code by the built-in error propagation analysis is utilised to calculate the uncertainty for bulk temperature and uniform wall heat flux. Experimental uncertainty in measurement categories is given in Table (2).
there is a part that is isolated by using foam. Foam is fastened to two sides of channel under study by means of several bolts. Test section is heated by electrical current by a constant flux. In fact, test section is heated under a process of constant heat flux. Electric flux is changeable for heating section test by a transformer. In the upper part of the circular channel, 24 thermal sensors are connected to the body of channel in order to show the channel temperature. These sensors are connected to computer by means of a series of wires in order to display the temperature. In order to insulate the body of channel, a layer of rock wool and a layer of foam were used. Within the channels consisted of net-shape porous media in various sizes, in order to evaluate our test. After test section, a rectangular channel was used in order to exit current. A temperature sensor was used for measuring the output temperature. In input rectangular channel, a hole was created for measuring air velocity. Measuring speed is done by a tachometer. At the end of the outlet channel, a blower fan is used with a drive motor. Angular velocity of fan can be changed by an inverter. Device is fastened by foundations and supports. In the following discussion, we will further explore the components of this device. A schematic diagram and a photograph of the experimental apparatus are shown in Fig. 1 in the modified manuscript. It is consisted of four major components: (a) the flow system, (b) test section, (c) heating unit, and (d) measurement system. The flow system was operated in a suction mode and oriented horizontally. Air as a working fluid passes through the test section, and then is exhausted by 1.1 kW blowers. The open test loop has an entrance length of 1.5 m. Long entry region was provided so that flow would be fully developed as it enters the test section. The system is designed to operate in a once-through mode with either air as the carrier gas and water as the atomizing liquid. All signals from temperature and humidity sensors were conveyed to a data acquisition system. Experiments aimed at quantifying the effect of porous medium geometry while maintaining the same water injection rate. The water mass fraction is kept constant at 10%. In this study, test section is a circular channel. Thickness of sheet of channel is 7 mm. Steel channel is made of a silicic aluminum alloy sheet. Aluminum wire meshes are embedded in the channel as porous media which are made f AISI 1010 Steel with meshing 17 wires per inch (Fig. 1). In order to being partially-filled of porous media, different sizes of wire mesh were used. Photographs of the porous media used in the test are shown in Fig. 1D. Size and shape of the used porous media and investigated models are given in Table (1). These meshes were embedded by a series of rigid rods, with a certain distance from each other within the channel. Porosity and permeability of used porous media is approximately 0.9 and 6.99 × 10−6 m2 respectively. The cross section of the channel has a diameter of 10 cm and a length of 70 cm that is shown in Fig. 2. The method which defined by Holman [27] is used for the uncertainty analysis. Finding the main sources of errors in the
3. Data reduction In this section, according to the existing and proposed relationships in the heat transfer, we determine coefficient of forced convective heat transfer and Nusselt number, then the results are shown in the form of diagrams. In each experiment, the heat transfer coefficients are achieved in terms of the heat transferred through the channel walls to passing flow and the temperature difference between them is described as following. The amount of the forced convective heat transfer fluid is the result of bulk movement. The fluid motion can be caused to an external force; such force transferred to the fluid by the pump. Heat transfer takes place by forced displacement of a fluid on a surface with different temperature to fluid temperature. In order to prevent heat loss from the experiment, through natural convection with the surrounding environment, all external surfaces of heater are insulated as well as in order to avoid thermal conductivity of the connection, one or two layers of insulation were used, however, very little heat penetrates to the environment by heat transfer. Total dissipated power is expressed by the heater using heat flux q''tot and area of heated surface Qtot = q''tot ⋅AS . This heat flux can be divided into 3 parts: 1. Heat flux heat q''tot from the walls to the air passing through channel 2. Heat flux of radiation q''rad in the outer surface of the insulator 3. The free movement and conduction q ''conv.cond in the outer surface of the insulation. Above energy equilibrium is presented as equation (1).
Table 1 Dimensions of the porous media. Model Model Model Model Model Model Model
391
1 2 3 4 5 6
d (cm)
D (cm)
0 0 0 0 2 4
4 6 8 10 10 10
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q"w = q"tot − q"rad − q "conv.cond
Table 2 Experimental uncertainties. Parameters
Values
Source
Velocity Pressure drop Inlet temperature Wall temperature Bulk temperature Mist flow rate Heat flux Reynolds number Heat transfer coefficient
0.5% 1.6% 0.3 °C 0.9 °C 0.6 °C 1.1% 1.8% 1.7% 5.9%
Calibration Calibration Calibration Calibration Calculated Calibration Calculated Calculated Calculated
(1)
In this experiment, sum of two last words is insignificant to the total heat flux, but for more precise calculations, heat loss through the natural convection and its temperature difference to the surrounding environment have been obtained by measuring the temperature on the surface of the insulation of the study area and then were subtracted from amount of the total heat flux. By defining the coefficient of thermal performance q, convective heat flux and transmitted through wall to air passing through channel can be obtained by using equation (2).
q"w = q"tot − q "conv
(2)
where q "conv is also calculated from equation (3).
q "conv = q"loss = hf (Tam − Tloss)
(3)
In the above relation, hf , Tam , and Tloss are heat transfer coefficient of air at ambient temperature, ambient temperature around the laboratory, and lost temperature through the natural convection of insulation, respectively. All properties of air are replaced in temperature Tf .
Tf =
Ts + T∞ 2
(4)
where Ts and T∞ are outer/external surface temperature of insulation and the ambient temperature, respectively.
NuL =
h¯.D kf
(5)
Q i is input heat for each sensor throughout the annular channel.
Q i = V. I×
Fig. 3. Validation of the present experimental results of single phase flow in a clear channel with the correlation of Dittus–Boelter [28].
X L°
(6)
Q i is heat input for sensor i, i is indicating the number of sensor, thermal
Fig. 4. Convective heat transfer coefficient through the channel for different models and different Reynolds numbers and fixed heat flux (Q = 595 W). 392
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Fig. 5. Effect of porous media in mist flow on heat transfer enhancement for all models at laminar fluid flow (Q = 275 W and Re = 1125).
power of heater in each experiment is the product of V ∙ I, x is distance between sensor and entrance of test section (cylinder), L° is entire ˙ is given by length of test (cylinder). Mass rate of flow passing through m equation (7).
˙ = ρf UA c m
(12).
n
h¯ =
Qi ˙ cp m
V⋅I As
h¯Dh k eff
(14)
In Eq (14), k eff is thermal conductivity of the fluid and hydraulic diameter of the study area is defined as Eq. (15).
(9)
Dh =
4A c =D p
(15)
Ac is cross-section on the channel under test. It should be stated that the definition of Nusselt number in this study is based on the thermal conductivity (k eff ) . Local Nusselt number based on channel hydraulic diameter is defined as Eq. (16).
(10)
where V ∙ I is thermal power of heater. According to the environment of channel P and L° is heated length of channel, lateral area A s of channel under testing is calculate by equation (11).
A s = p ⋅L °
(13)
n
NuDh =
˙ , c p are where Tin is input/inlet temperature for each sensor. The Qi, m respectively input/inlet heat, mass rate of the passing flow, and specific heat of fluid when pressure is the constant. Convective heat flux q'' = q"tot is calculated as equation (10). q'' =
∑1 hi
where n is the number of calculated local h. The mean Nusselt number is defined in terms of the channel hydraulic diameter.
(8)
where, D is the diameter of the cylinder. Bulk temperature (Tb) of the fluid flow is calculated as equation (9):
Tb = Tin +
(12)
where Twi is temperature of cylinder outer/external wall in sensor ith. Mean convective heat transfer coefficient is average of local heat transfer coefficient that is obtained as equation (13).
(7)
ρf is fluid density, U and A c are respectively fluid velocity and crosssection passing through test section in each test that is calculated as equation (8). D2 Ac = π 4
q'' w Twi − Tb
hi =
NuDh =
hi Dh k eff
(16)
According to [8]:
(11)
K eff = (1− ε)K s + εKf
Local convective heat transfer coefficient is calculating by equation 393
(17)
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Fig. 6. Effect of porous media in mist flow on heat transfer enhancement for all models at transient fluid flow (Q = 275 W and Re = 3500).
good agreement with the results obtained from the Dittus–Boelter correlation witch the maximum error is 4.9%.
equation (17) can be rewritten as following:
K eff =
K s(1 − ε)
K εf
(18)
4.2. Local heat transfer coefficient
Reynolds number based on hydraulic diameter:
ReDh =
ρf UDh UDh = μf νf
Fig. 4 shows changes in local convective heat transfer coefficient hi in terms of distance and position of the sensors from the first channel (X/L) in different Reynolds numbers but at the fixed channel wall heat fluxes. The diameters of the porous material used in the experiment, are respectively 10, 8, 6, 4 cm and a porous media with an outer diameter 10 cm and internal and external diameters 2 and 4 cm. With constant heat flux and Reynolds number, procedure of the heat transfer factors mentioned are observed. In Fig. 4, changes of convective heat transfer coefficient according to different Reynolds numbers in a constant heat flux for different models are shown respectively. Three different Reynolds number with different fluid flow regime laminar, transient and turbulence are investigated. In the experimental tests, fixed heat flux (595 W) is incorporated. As illustrated in Fig. 4, in the presence of porous media in fixed heat flux for models (1, 2 and 5), as Reynolds numbers increases, convective heat transfer coefficient increases. When the porous medium inserted at the center of the channel (Models 1–4), until the radius of the porous medium is low (model 1 and 2), the flow passes the porous medium by changing the direction to the region near the channel's wall (clear region) so the effect of porous region on the heat transfer is low. Accordingly, at low Re number, the flow changes the direction to the clear region near the channel's wall with heat flux and the heat transfers to the fluid but by increasing the velocity at this situation, the time for exchanging the heat becomes low and heat transfer decreases. By increasing the radius of the porous medium inserted at the center of the channel (models 3 and 4), the effect of porous medium appears,
(19)
That νf is kinematic viscosity of the fluid and μ f is the dynamic viscosity of the fluid:
νf =
μf ρf
dimensionless length =
(20)
x L
(21)
where x is variable distance from beginning of test section and L is length of test section. 4. Results and discussions 4.1. Validation of the experimental results The experimental results were validated with the results obtained by the correlation of Dittus–Boelter [22] which calculate the Nusselt number for different Reynolds number. This correlation is used for the clear channel and single phase flow. The average Nusselt number for different Reynolds number or fully developed flow in straight clear channels (without porous zone) is depicted in Fig. 3. According to Fig. 3, the experimental results of the present setup for single phase flow in a clear channel are compared with the Dittus–Boelter correlation. As it can be seen, the experimental results have 394
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Fig. 7. Effect of porous media in mist flow on heat transfer enhancement for all models at turbulant fluid flow (Q = 275 W and Re = 6437). Table 3 Average Nusselt number for different models and Reynolds number. Models
Re = 1125
Clear Channel Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Re = 3500
Re = 6437
No Mist
Mist Flow
No Mist
Mist Flow
No Mist
Mist Flow
21 14.7 20.4 17.9 28.2 26.6 16
64.5 54.5 186.5 76.1 54.6 190.1 91
21.1 16.3 21 19.2 28.3 26.3 20.2
32.1 31 60.1 57.1 30.9 96 62.2
18.5 17.8 25.3 21.2 30.6 28.2 23
49.7 48.2 95.8 112.64 48.2 160.1 74
flux wall is low which make the heat transfer to increase. As it is shown in Fig. 4, the maximum convective heat transfer coefficient is belonging to the model 5 even more than model 4 (fully filled porous medium channel). According to the results of Mahdavi et al. [29], in some cases with specific porous medium radius and thermal conductivity ratio (Rk = keff/kf), provide better thermal performance when porous medium is adhered to inner wall (model 5) in comparison with the fully filled porous medium channel (model 4). The local heat transfer coefficient for different models and axial position in a channel with and without porous media and mist flow are shown in Figs. 5-7. The local heat transfer coefficient is illustrated for three fluid flow regimes including laminar, transient and turbulence in Figs. 5–7, respectively. The effect of porous media, mist flow and flow regime are shown obviously. As it can be seen in Fig. 5, at low Re number (Re = 1125), using mist flow and porous medium have significant effect in increasing the heat transfer coefficient. In some cases, the effect of using mist flow is
Fig. 8. Average Nusselt number for different models.
so porous medium causes pressure drop and by increasing the velocity, pressure drop increases which increases the heat transfer (and it should be noted that in these models, the gap of the clear channel near the heat 395
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Fig. 9. (a) Pressure drop in channel for different inlet velocities (b) The friction coefficient (f) in channel for different models (mist flow) and Reynolds numbers at Q = 275 W.
Fig. 10. Heat transfer enhancement ratio for different models (mist flow and no mist flow) and different Reynolds numbers (Re = 1125, 3500 and 6437). Fig. 11. Heat transfer performance ratio (NuPR) for different models and different Reynolds numbers.
Table 4 Heat transfer enhancement ratio (NuER) for different models at three different flow regimes (Re = 1125, 3500 and 6437). Models
Clear Channel Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Re = 1125
Re = 3500
coefficient than the others. In model 1, the radius of the porous medium is the lowest one and flow passes the channel by changing the direction and the effect of the porous zone is low. In model 4, the channel is fully filled porous medium and mist flow has higher thermal conductivity ratio in comparison with the single phase so the heat transfer is higher than the single phase flow but the pressure drop of mist flow in this model is more than the other models (even more than single flow in the same model) so it affects the heat transfer process. The maximum heat transfer coefficient is belonging to the model 5 with mist flow which show the effect of using mist flow and the results are the same with the results of the Mahdavi et al. [29]. The heat transfer coefficient for different models at transient regime (Re = 3500) are illustrated in Fig. 6. As the same with Fig. 5, the maximum heat transfer coefficient is belonging to the model 5. The heat transfer coefficient for different models at turbulent regime (Re = 6437) are illustrated in Fig. 7. The trend of the local heat transfer coefficient profiles for all models are the same approximately with the other flow regimes (laminar and transient). According to Fig. 7, the maximum heat transfer coefficient is belonging to the model 5 (same with Figs. 5 and 6).
Re = 6437
Mist Flow
No Mist
Mist Flow
No Mist
Mist Flow
No Mist
1 0.97 1.93 2.26 0.97 3.22 1.49
1 0.96 1.37 1.14 1.65 1.52 1.24
1 0.96 1.87 1.78 0.96 2.99 1.94
1 0.77 0.99 0.91 1.34 1.25 0.96
1 0.84 2.89 1.17 0.84 2.94 1.41
1 0.7 0.97 0.85 1.34 1.26 0.76
more than porous medium. For instance, in models 1 and 4, the clear channel with mist flow has higher heat transfer coefficient in comparison with the channel with porous medium and without mist flow but there is not significant difference between the results of the clear channel with mist flow and channel with porous medium and mist flow. This case shows that in some cases the effect of mist flow is more than using porous zone (without mist flow). For different models, the channel with porous medium and mist flow has higher heat transfer 396
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It can be find that higher heat transfer rate can be achieved by increasing the porous thickness. Because increasing the porous medium thickness caused that fluid flows in space between the porous material and channel wall with high velocity so convective heat transfer increases. Also, because of high conduction rate in the porous medium, the model with fully filled porous material has the highest improvement in heat transfer with mist flow in comparison with the clear channel. Average Nusselt numbers for different models and Reynolds number are listed in Table (3). The effect of mist flow in porous media on heat transfer enhancement is shown completely. Also, the average Nusselt number for different models are illustrated in Fig. 8. Table (3) and Fig. 8 show variations of the average Nusselt number for mist flow in circular channels with different porous media. In the presence of porous media, using mist flow causes more average Nusselt number for all flow regimes. At low Reynolds number, the average Nusselt number enhancement is more than 200%. Also, model 5 with has the best thermal performance with average Nusselt number enhancement more than 600%. At transient flow regime, for all models heat transfer enhancement is between 100 and 265%. Model 5 with 265% average Nusselt number enhancement has the best heat transfer rate. At high Reynolds number model 5 with 467.7% heat transfer enhancement has the best thermal performance.
4.4. Heat transfer enhancement ratio (NuER) and heat transfer performance ratio (NuPR) The effectiveness of using the porous zone evaluated by studying ratio of mean Nusselt number (Nu) and the mean Nusselt number (Nu0) for fully developed flow in a clear channel (without porous medium):
NuER = Nu/Nu 0
Nu 0 is referred to a clear channel without any porous region. This ratio will be referred to as the heat transfer enhancement ratio (NuER). The variation of this heat transfer enhancement ratio (NuER) with Reynolds number for different models is shown in Fig. 10 and the results are listed in Table (4) for a fixed value of heat flux (Q = 275 W). In Fig. 10, data labels of the all models (mist flow with porous medium) are shown. Accordingly, at low Re number (Re = 1125), in all models except model 4, using mist flow increases the heat transfer enhancement ratio (NuER) in comparison with the no mist flow and generally, by mist flow, all models except models 1 and 4 (−3% for both of them), have better NuER in comparison with the clear channel. Without mist flow, all models except model 1 have better NuER in comparison with the clear channel. In mist flow and no mist flow situation (with porous medium in both), the highest NuER are belonging to model 5 and model 4, respectively at low Re number (Re = 1125) and the average Nusselt number of models 5 and 4 for mist flow and no mist flow are 222% and 65% more than the clear channel at Re = 1125. As shown in Fig. 10, at transient flow regime (Re = 3500), all models have better NuER except model 1 and model 4 (−4% for both of them) by using mist flow with porous medium in comparison with the clear channel and at single phase flow with porous medium, models 4 and 5 have the better NuER in comparison with the clear channel. Generally, using mist flow with porous medium increases thermal performance in NuER for all models except models 2 and 4 in comparison with the single phase flow (air) with porous medium. The average Nusselt number of models 5 and 4 (as the best models) for mist flow and no mist flow (with porous medium in both of them) are 199% and 34% more than the clear channel at Re = 3500 (transient flow). At high Re number, turbulent flow (Re = 6437), using mist flow increases the NuER for all models except models 1 and 4 (−16% for both of them) in comparison with the clear channel. Also, in single phase flow with porous medium, models 4 and 5 with 34% and 26% increasing have the better NuER in comparison with the clear channel. The average Nusselt number of models 5 and 4 (as the best models) for mist flow and no mist flow (with porous medium in both of them) are 194% and 34% more than the clear channel at Re = 6437 (turbulant flow). The effectiveness of using the porous region also be studied evaluating the heat transfer performance ratio. The heat transfer performance ratio (PR) is defined as the ratio of heat transfer enhancement to unit increase in pumping power:
4.3. Pressure drop and friction coefficient of channel Although using porous material in heat exchanger enhances heat transfer rate, it causes pressure loss increase. Figs. 9a and 9b show the pressure drop and friction coefficient in channel for all models and fixed heat flux. The friction coefficient (f) in a channel flow can be determined by measuring the pressure drop across the flow channel and average velocity of the air. Average friction coefficient can, therefore, be calculated from equation (22).
f= (2ρΔPDh)/(V 2LP)
(23)
(22)
Results are investigated for different inlet velocity ranges from 0.18 to 2.13 m/s. It should be noted that at Vinlet = 0.357 m/sec, the fluid flow is laminar (Re < 2100) and for 0.357 m/sec < Vinlet < 0.68 m/ sec, the fluid flow regime is transient. For the inlet velocity more than 0.68 m/sec, the flow regime is turbulent (Re > 4000). It can be observed that the f increases with decreases of the Re number. These are the expected results. As it is illustrated in Fig. 9a, it can be seen that at the low Reynolds number, the differences of pressure drop between the models are very low and by increasing the inlet velocity (consequently Reynolds number), the differences of pressure drop between the models become greater. Between the models 1–4 where the porous zone inserted at the tube core, by increasing the diameters of the porous zones (from model 1 to 4), pressure drop increases. The pressure drop results have the same trend with the Mahdavi et al. [29] works. Also, based on Fig. 9a, the pressure loss (consequently, the required pumping power) for the models which porous zone is inserted at the tube core is lower than the models it is located adjacent to the wall at the same Darcy number. In comparison between the models, at the turbulent regime, model 4 has the greatest pressure drop. On the other hand, at the low Reynolds number (laminar to transient fluid flow regime), the trend of the pressure drop with Reynolds number rise for all models is the same except models 5 and 6. But at the high Reynolds number (turbulent fluid flow regime), the trend is the same for all models and for model 4, the pressure drop increases significantly. In Model 4, the channel is full of porous zone. In the other models, the channel is partially filled by porous zone so by increasing the velocity, the fluid changes the direction to the clear part of the channel but at model 4, the channel is full of porous zone and cannot change its direction so the pressure drop increases.
NuPR = NuER /(f/f 0)1/3
(24)
f 0 is referred to a tube without any porous region. In this ratio, the friction factors are raised to the one-third power as the pumping power is proportional to the one-third power of the friction factor [10,11]. The variation of this heat transfer performance ratio (NuPR) with Reynolds number for all models is shown in Fig. 11 at a fixed value of heat flux (Q = 275 W). NuPR factor including the effects of pressure drop and the heat transfer coefficient. On the other side, according to equation (24), increasing the value of NuPR means the better heat transfer with low pressure drop. It should be noted that using mist flow increases the pressure drop in comparison with the single phase flow significantly which affects the heat transfer performance ratio (NuPR) according to equation (24). According to Fig. 11, it can be seen that at low Re number (Re = 1125), model 5 has the highest NuPR and model 2 is the second 397
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one in using mist flow. At transient flow regime, the highest NuPR is belonging to the model 5 and model 2 is the second one. For the high Re number (Re = 6437-turbulant flow) the maximum NuPR is belonging to the model 2 and model 5 is the second one. Generally, between the all models, models 2 and 5 have the best performance based on the NuPR. At low and high Re number, models 5 and 2 have the best thermal performance, respectively. As a final result, between the all investigated models, model 2 with mist flow has the best NuPR with 24% improvement.
number, models 5 and 2 have the best thermal performance, respectively. References [1] Donald A. Nield, Adrian Bejan, Nield-Bejan, Convection in Porous Media vol. 3, springer, New York, 2006. [2] J. Bear, Dynamics of Fluids in Porous Media–American Elsevier Pub, Comp., inc., New York, 1972 764pp.. [3] Ruben Juanes, et al., Impact of relative permeability hysteresis on geological CO2 storage, Water Resour. Res. 42 (12) (2006). [4] Karsten Pruess, Julio Garcia, Multiphase flow dynamics during CO 2 disposal into saline aquifers, Environ. Geol. 42 (2) (2002) 282–295. [5] Delavar, Mojtaba Aghajani, Ebrahim Alizadeh, and Seyed Soheil Mousavi Ajarostaghi. "Experimental and Lattice Boltzmann Method Investigation of Direct Methanol Fuel Cell Performance.". [6] Mohamed El Amine Ben Amara, Sassi Ben Nasrallah, Numerical simulation of droplet dynamics in a proton exchange membrane (PEMFC) fuel cell micro-channel, Int. J. Hydrogen Energy 40 (2) (2015) 1333–1342. [7] Yuan Gao, et al., Lattice Boltzmann simulation of water and gas flow in porous gas diffusion layers in fuel cells reconstructed from micro-tomography, Comput. Math. Appl. 65 (6) (2013) 891–900. [8] Bo Han, Hua Meng, Numerical studies of interfacial phenomena in liquid water transport in polymer electrolyte membrane fuel cells using the lattice Boltzmann method, Int. J. Hydrogen Energy 38 (12) (2013) 5053–5059. [9] A.V. Kuznetsov, Influence of thermal dispersion on forced convection in a composite parallel-plate channel, Z. Angew. Math. Phys. 52 (1) (2001) 135–150. [10] M.K. Alkam, M.A. Al-Nimr, Transient non-Darcian forced convection flow in a pipe partially filled with a porous material, Int. J. Heat Mass Tran. 41 (2) (1998) 347–356. [11] H. Shokouhmand, F. Jam, M.R. Salimpour, Simulation of laminar flow and convective heat transfer in conduits filled with porous media using Lattice Boltzmann Method, Int. Commun. Heat Mass Tran. 36 (4) (2009) 378–384. [12] Mohamed A. Teamah, Wael M. El-Maghlany, Mohamed M. Khairat Dawood, Numerical simulation of laminar forced convection in horizontal pipe partially or completely filled with porous material, Int. J. Therm. Sci. 50 (8) (2011) 1512–1522. [13] Chen Yang, Akira Nakayama, Wei Liu, Heat transfer performance assessment for forced convection in a tube partially filled with a porous medium, Int. J. Therm. Sci. 54 (2012) 98–108. [14] Mohammad Nikian, et al., Experimental investigation of two-phase mist flow and heat transfer in porous media, J. Porous Media 16 (8) (2013). [15] H. Shokouhmand, M. Nikian, Effect of mist flow on heat transfer enhancement in porous media, Arabian J. Sci. Eng. 39 (6) (2014) 5063–5072. [16] Niru Kumari, et al., Analysis of evaporating mist flow for enhanced convective heat transfer, Int. J. Heat Mass Tran. 53 (15) (2010) 3346–3356. [17] Z. Huang, A. Nakayama, et al., Enhancing heat transfer in the core flow by using porous medium insert in a tube, Int. J. Heat Mass Tran. 53 (5) (2010) 1164–1174. [18] S. Baragh, H. Shokouhmand, S.S. Ajarostaghi, M. Nikian, An experimental investigation on forced convection heat transfer of single-phase flow in a channel with different arrangements of porous media, Int. J. Therm. Sci. 134 (2018 Dec 1) 370–379. [19] D. Bhargavi, J.S. Reddy, Effect of heat transfer in the thermally developing region of the channel partially filled with a porous medium: constant wall heat flux, Int. J. Therm. Sci. 130 (2018 Aug 31) 484–495. [20] M. Siavashi, H.R. Bahrami, E. Aminian, Optimization of heat transfer enhancement and pumping power of a heat exchanger tube using nanofluid with gradient and multi-layered porous foams, Appl. Therm. Eng. 138 (2018 Jun 25) 465–474. [21] T. Guo, T. Wang, J.L. Gaddis, Mist/steam cooling in a heated horizontal tube part I: experimental system and part II: results and modeling, ASME J. Turbomach. 122 (2000) 360–374. [22] T. Guo, T. Wang, J.L. Gaddis, Mist/steam cooling in a 180-degree tube, ASME J. Heat Transf. 122 (2000) 749–756. [23] M.J. Goodyer, R.M. Waterston, Mist-cooled turbines, Conference of Heat and Fluid Flow in Steam and Gas Turbine Plant, Proceedings of Institution of Mechanical Engineers, 1973, pp. 166–174. [24] A. Ozsunar, G. Peker, A numerical investigation into the cooling curves of stainless steel porous materials for the quenching process, Arabian J. Sci. Eng. 36 (2011) 339–356. [25] Y. Hayashi, A. Takimoto, O. Matsuda, Heat transfer from tubes in mist flows, J. Exp. Heat Transf. 4 (1999) 291–308. [26] B.W. Webb, M. Queiroz, K.N. Oliphant, M.P. Bonin, Onset of dry-wall heat transfer in low-mass-flux spray cooling, Exp. Heat Tran. 5 (1992) 33–50. [27] Jack Philip Holman, Walter J. Gajda, Experimental Methods for Engineers vol. 7, McGraw-Hill, New York, 2001. [28] F.W. Dittus, L.M.K. Boelter, University of California Publications on Engineering vol. 2, University of California publications in Engineering, 1930, p. 371. [29] M. Mahdavi, M. Saffar-Avval, S. Tiari, Z. Mansoori, Entropy generation and heat transfer numerical analysis in pipes partially filled with porous medium, Int. J. Heat Mass Tran. 79 (2014) 496–506.
5. Conclusion An experimental study on forced convection heat transfer of twophase flow (mist flow) in a channel with different arrangements of porous media is investigated. This investigation experimentally studies the convective heat transfer in uniform heat flux pipe with porous zone. Also the present experimental article presents the potential of twophase flow and a porous inserted to increase the heat transfer rate occurring between the surfaces of a channel and the mist air flowing inside it. Different models of porous media inside the channel are used. It was observed that a larger value of heat transfer rates can be achieved by increasing the diameter of a porous media and increasing the flow rate of mist air. Porous media apply the heat flux to the inside of the channel and transfer it to the fluid then the average temperature of the fluid increases. This increase in temperature leads to reduce the temperature difference between the channel wall and the average temperature of the fluid. Also by increasing the Reynolds number in all positions of the porous media, heat transfer coefficient increases. From the obtained results, it can be said that improve heat transfer by using porous media is carried out when the diameter of porous media be closed to the diameter of the channel. As porous medium thickness and mass flowrate of gas increase, the heat transfer rate and consequently Nusselt number increase. The results show that mist cooling coupled with the porous zone can increase the heat transfer rate significantly in comparison with the single phase cooling without porous zone. The obtained results are following:
• The results show that at low Reynolds number, the average Nusselt
• •
•
number enhancement is more than 200%. At transient flow regime, for all models heat transfer enhancement is between 100 and 265%. At high Reynolds number, 467.7% heat transfer enhancement is the best thermal performance improvement based on using porous zone and mist flow. From the obtained results, it can be realized that improve heat transfer by using porous media is carried out when the diameter of porous media be closed to the diameter of the channel. The heat transfer enhancement ratio (NuER) increases with increase in Re (transition to turbulent). In models which the porous zone inserted at the tube core, by increasing the diameter of porous media, the heat transfer enhancement ratio (NuER) increases (in both laminar and turbulent flows). But in models with the porous zone inserted adjacent to the wall (annulus shape of porous zone), increase the inner diameter of the porous zone decreases the heat transfer enhancement ratio (NuER) in all flow regimes. At low Re number (Re = 1125), model 5 has the highest NuPR and model 2 is the second one in using mist flow. At transient flow regime, the highest NuPR is belonging to the model 5 and model 2 is the second one. For the high Re number (Re = 6437-turbulant flow) the maximum NuPR is belonging to the model 2 and model 5 is the second one. Generally, between the all models, models 2 and 5 have the best performance based on the NuPR. At low and high Re
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Experiments on mist flow and heat transfer in a tube fitted with porous media
T
Shahram Baragha, Hossein Shokouhmandb,∗, Seyed Soheil Mousavi Ajarostaghic a
Faculty of Mechanical Engineering, Islamic Azad University, Takestan Branch, Takestan, Iran School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran c Faculty of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran b
A R T I C LE I N FO
A B S T R A C T
Keywords: Porous media Mist flow Heat transfer enhancement Force convection
The issues related to porous media are more important in the design and analysis of heat exchangers. Reducing size of heat transfer devices for using of this media was led to be feasible of creating flow with smaller Reynolds numbers. In present study, an experimental investigation of air mist flow is carried out in tube which fitted with porous media. The studied porous region has different geometry. Also the effect of operating parameter like Reynolds number is analyzed. Results indicate that presence of porous media leads that the thermal flux applied to walls of channel be transferred into fluid due to creating a uniform space and high conductivity of porous media. Also, the results depicted that in comparison with the single-phase, mist cooling in porous media can increase the heat transfer rate. Results show that combine these two method (porous medium and mist flow) has significant effect on heat transfer enhancement. According to obtained results, at low Reynolds number with mist flow, the case that porous zone inserted adjacent to wall with 4 cm height has best thermal performance and at high Reynolds number with mist flow, highest thermal performance is belonging to the case that porous zone inserted at the center of the channel with 6 cm diameter. As a final result, between the all investigated models, the case that porous zone inserted at the center of the channel with 6 cm diameter with mist flow has the best heat transfer performance ratio with 24% improvement in comparison with clear channel.
1. Introduction In order to improve the heat transfer rate in the industrial processes, utilizing porous medium is a promising tool. The porous media is a material consists of solid matrix with an interconnected [1]. Beside the using porous medium, mist flow is the other way to enhance the heat transfer rate. Using the advantages of these two method with together can enhance the heat transfer rate significantly in comparison with the single phase in a clear tube. The application of using these both methods in engineering processes consists of hydrocarbon recovery [2], CO2 storage in underground reservoirs [3,4], and proton exchange membrane fuel cells [5–8]. Actually, heat exchanger is a major application of these practical method. Most works on flow in porous media have used, and to a large extent still use. Kuznetsov [9] represented an analytical method to investigate the force convection in a parallel plate channel with porous media. To model the porous media, the Brinkman-Forchheimer-extended Darcy equation was utilised. Results illustrated that porous media increase the heat transfer rate. Alkam and Al-Nimr [10] numerically evaluated the
∗
heat transfer rate in a cylindrical channel partially filled with a porous media. The Brinkman-Forchheimer-extended Darcy model was used to model the flow within the porous domain. Results indicated that the existence of the porous media raise the Nusselt number at the fully developed region. Also, it was shown that steady state time increases by reduction in Darcy number. Shokouhmand et al. [11] investigated the convective heat transfer between two parallel plates of a conduit numerically. The lattice Boltzmann method is used to perform the numerical simulation. The both condition of fully and partially filled porous medium were considered. Teamah et al. [12] perform the numerical simulation to study the laminar forced convection flow in a pipe partially and completely filled with a porous medium. It was observed that pumping power and thermal performance of the investigated domain decreases by increasing the radius of porous material. Also, Yang et al. [13] studied the forced convection in a heated tube with a porous medium core and a tube with a wall covered with a porous medium layer. Tube with a porous medium core showed better thermal performance in comparison with the tube with a wall covered with a porous medium.
Corresponding author. E-mail addresses: [email protected] (S. Baragh), [email protected] (H. Shokouhmand), [email protected] (S.S.M. Ajarostaghi).
https://doi.org/10.1016/j.ijthermalsci.2018.11.030 Received 24 April 2018; Received in revised form 2 November 2018; Accepted 25 November 2018 1290-0729/ © 2018 Elsevier Masson SAS. All rights reserved.
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Nomenclature A D d q'' Q L ˙ m V.I T X hi hi U k Nui f Re NuER NuPR Pr P
Greek symbol ε ρ μ υ
Area, (m2) Outer diameter of porous zone, (m) Inner diameter of porous zone, (m) Heat flux, (W/m2) Heat, (W) Distance between porous zones Mass flowrate, (kg/s) Thermal power of heater, (W) Temperature, (K) Distance between sensor and entrance of test section Local heat transfer coefficient, W/(m2.K) Mean heat transfer coefficient, W/(m2.K) Velocity, (m/s) Thermal conductivity, (W/(m.K)) Local Nusselt number friction coefficient Reynolds number Heat transfer enhancement ratio, (PR) Heat transfer performance ratio, (ER) Prandtl number Pressure, (Pa)
Porosity in porous media Density, (kg/m3) Dynamic viscosity, (kg/(m. s)) Kinematic viscosity, (m2/s)
Subscript and superscript tot w rad cond conv am loss L in s f h c eff b
Nikian et al. [14] investigate the effect of mist flow through the channel fitted with the porous medium experimentally. In this study, the effects of porous medium porosity and permeability on the thermal performance were studied. Shokouhmand and Nikian [15] carried out an experimental test to study the force convection of mist flow in a channel equipped with porous medium. The effects of porous medium characteristics including porosity, permeability and thickness were investigated experimentally. Kumari et al. [16] studied the forced convective heat transfer by the mist flow analytically and numerically. The results indicated that the heat transfer rate with the mist flow is better in comparison with the single phase flow. Huang et al. [17] experimentally and numerically investigated the effect of inserting porous media with a slightly smaller diameter in the core of the tube under the constant and uniform heat flux condition. Three different porosity of porous zone were considered including 0.951, 0.966 and 0.975. Also, the effect of porous radius ratio on the heat transfer performance was analyzed numerically. Results show that the convective heat transfer is significantly enhanced by inserting porous zone in the tube. Baragh et al. [18] studied a single-phase flow of air in channel having circle cross-section with different arrangements of porous media is experimentally. The effect of different arrangement of inserting porous zone in the tube was investigated. The analyze was done in three different air flow regimes including laminar, transient and turbulence. The results show that in both laminar and turbulent flows, fully filled channel of porous media has the best heat transfer and the channel with annulus shape porous zones (the porous zone inserted adjacent to wall) has the best thermal performance in turbulent flow. Bhargavi and SharathKumar Reddy [19] numerically investigated the Laminar forced convection in the parallel plate channels partially filled with a porous material. Constant wall heat flux was considered as boundary condition. Porous insert is attached to both the walls of the channel with equal thickness. Results show that the non-dimensional temperature at the wall attains maximum values at a certain porous fraction. Siavashi et al. [20] simulated nanofluid flow inside the porous media using a two-phase model. Some multi-layered porous foams gave the same performance as the gradient ones. Particle swarm optimization (PSO) algorithm is used to find the optimal arrangements of porous layers. The addition of mist to a flow of steam or gas offers enhanced
Total Wall Radiation Conduction Convection Ambient Lost Local Inlet Surface Fluid Hydraulic Cross-section Effective Bulk
cooling in many applications, including cooling of gas turbine blades [21–23]. Cold droplets impinging on hot surfaces can provide a significant cooling effect, mainly due to the evaporative latent heat effect. This physical mechanism, thus, has been used widely in industry to improve heat transfer rates [24], to designmist-cooled heat exchangers [25], and for different kinds of spray cooling of hot surfaces [26]. Mistcooled heat exchangers can be used for large power or chemical plants, or small refrigerator radiators. The hot fluid flows inside a tube bundle and is cooled by an air stream in across flow with water droplets injected in the air stream at upstream of the bank of tubes. In this study, the effects of different porous media and mist flow on the heat transfer rate are experimentally investigated. Six different porous media where emplaced at the center of the channel. A constant uniform heat flux boundary condition is used. The dry air and mist air flow are flowing inside the channel. An experiment is carried out here to study the effects of mist flow on the heat transfer in a channel which equipped with porous medium. The influence of some operational and geometrical parameters are investigated which the considered geometrical parameters are the inner and outer diameters of porous zone. Also the effect of Reynolds number is analyzed experimentally. The water mass fraction is kept constant at 10% and is injected to the air flow at the entrance of the test section to provide the mist flow. 2. Experimental investigation For the current study, the test section of experimental apparatus is shown in Fig. 1a and schematic diagram of TFHE experimental set up is shown in Fig. 2a and test rig is shown in Fig. 2b. In this section, the detailed information about the present laboratory equipment and apparatus are explained. Diagram, schematic and photographs of the experimental setup are shown in Fig. 1a and (1b) and (1c) respectively. In this device, a suction fan was used in order to pull air into the channel. The fan is located at the end of this device. Also, a motor attached to fan drives it. Alternating voltage that is required for fan different speeds is provided by an inverter. At the front of channel, a perforated chamber is used for converging air. After part of air nozzle, the rectangular channel is used in order to development flow. After part of channel, we have a circularshape part in order to conduct test. At the end of part of test section, 389
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Fig. 1. (a). Diagram of the experimental test section (b) Schematic of the experimental setup (c) Photograph of the experimental apparatus (d) Photograph of the porous media used in the test.
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Fig. 2. Schematic of porous media models used in the test.
measurements helps to consider the uncertainty in the experimental results. The wall temperature, velocity and pressure drop and their corresponding uncertainty are calculated from manufacturer-supplied calibrations, mist flow rate through the heated test section, the inlet air and mist temperature and their corresponding uncertainty are obtained by calibration. Engineering Equation Solver (EES) code by the built-in error propagation analysis is utilised to calculate the uncertainty for bulk temperature and uniform wall heat flux. Experimental uncertainty in measurement categories is given in Table (2).
there is a part that is isolated by using foam. Foam is fastened to two sides of channel under study by means of several bolts. Test section is heated by electrical current by a constant flux. In fact, test section is heated under a process of constant heat flux. Electric flux is changeable for heating section test by a transformer. In the upper part of the circular channel, 24 thermal sensors are connected to the body of channel in order to show the channel temperature. These sensors are connected to computer by means of a series of wires in order to display the temperature. In order to insulate the body of channel, a layer of rock wool and a layer of foam were used. Within the channels consisted of net-shape porous media in various sizes, in order to evaluate our test. After test section, a rectangular channel was used in order to exit current. A temperature sensor was used for measuring the output temperature. In input rectangular channel, a hole was created for measuring air velocity. Measuring speed is done by a tachometer. At the end of the outlet channel, a blower fan is used with a drive motor. Angular velocity of fan can be changed by an inverter. Device is fastened by foundations and supports. In the following discussion, we will further explore the components of this device. A schematic diagram and a photograph of the experimental apparatus are shown in Fig. 1 in the modified manuscript. It is consisted of four major components: (a) the flow system, (b) test section, (c) heating unit, and (d) measurement system. The flow system was operated in a suction mode and oriented horizontally. Air as a working fluid passes through the test section, and then is exhausted by 1.1 kW blowers. The open test loop has an entrance length of 1.5 m. Long entry region was provided so that flow would be fully developed as it enters the test section. The system is designed to operate in a once-through mode with either air as the carrier gas and water as the atomizing liquid. All signals from temperature and humidity sensors were conveyed to a data acquisition system. Experiments aimed at quantifying the effect of porous medium geometry while maintaining the same water injection rate. The water mass fraction is kept constant at 10%. In this study, test section is a circular channel. Thickness of sheet of channel is 7 mm. Steel channel is made of a silicic aluminum alloy sheet. Aluminum wire meshes are embedded in the channel as porous media which are made f AISI 1010 Steel with meshing 17 wires per inch (Fig. 1). In order to being partially-filled of porous media, different sizes of wire mesh were used. Photographs of the porous media used in the test are shown in Fig. 1D. Size and shape of the used porous media and investigated models are given in Table (1). These meshes were embedded by a series of rigid rods, with a certain distance from each other within the channel. Porosity and permeability of used porous media is approximately 0.9 and 6.99 × 10−6 m2 respectively. The cross section of the channel has a diameter of 10 cm and a length of 70 cm that is shown in Fig. 2. The method which defined by Holman [27] is used for the uncertainty analysis. Finding the main sources of errors in the
3. Data reduction In this section, according to the existing and proposed relationships in the heat transfer, we determine coefficient of forced convective heat transfer and Nusselt number, then the results are shown in the form of diagrams. In each experiment, the heat transfer coefficients are achieved in terms of the heat transferred through the channel walls to passing flow and the temperature difference between them is described as following. The amount of the forced convective heat transfer fluid is the result of bulk movement. The fluid motion can be caused to an external force; such force transferred to the fluid by the pump. Heat transfer takes place by forced displacement of a fluid on a surface with different temperature to fluid temperature. In order to prevent heat loss from the experiment, through natural convection with the surrounding environment, all external surfaces of heater are insulated as well as in order to avoid thermal conductivity of the connection, one or two layers of insulation were used, however, very little heat penetrates to the environment by heat transfer. Total dissipated power is expressed by the heater using heat flux q''tot and area of heated surface Qtot = q''tot ⋅AS . This heat flux can be divided into 3 parts: 1. Heat flux heat q''tot from the walls to the air passing through channel 2. Heat flux of radiation q''rad in the outer surface of the insulator 3. The free movement and conduction q ''conv.cond in the outer surface of the insulation. Above energy equilibrium is presented as equation (1).
Table 1 Dimensions of the porous media. Model Model Model Model Model Model Model
391
1 2 3 4 5 6
d (cm)
D (cm)
0 0 0 0 2 4
4 6 8 10 10 10
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q"w = q"tot − q"rad − q "conv.cond
Table 2 Experimental uncertainties. Parameters
Values
Source
Velocity Pressure drop Inlet temperature Wall temperature Bulk temperature Mist flow rate Heat flux Reynolds number Heat transfer coefficient
0.5% 1.6% 0.3 °C 0.9 °C 0.6 °C 1.1% 1.8% 1.7% 5.9%
Calibration Calibration Calibration Calibration Calculated Calibration Calculated Calculated Calculated
(1)
In this experiment, sum of two last words is insignificant to the total heat flux, but for more precise calculations, heat loss through the natural convection and its temperature difference to the surrounding environment have been obtained by measuring the temperature on the surface of the insulation of the study area and then were subtracted from amount of the total heat flux. By defining the coefficient of thermal performance q, convective heat flux and transmitted through wall to air passing through channel can be obtained by using equation (2).
q"w = q"tot − q "conv
(2)
where q "conv is also calculated from equation (3).
q "conv = q"loss = hf (Tam − Tloss)
(3)
In the above relation, hf , Tam , and Tloss are heat transfer coefficient of air at ambient temperature, ambient temperature around the laboratory, and lost temperature through the natural convection of insulation, respectively. All properties of air are replaced in temperature Tf .
Tf =
Ts + T∞ 2
(4)
where Ts and T∞ are outer/external surface temperature of insulation and the ambient temperature, respectively.
NuL =
h¯.D kf
(5)
Q i is input heat for each sensor throughout the annular channel.
Q i = V. I×
Fig. 3. Validation of the present experimental results of single phase flow in a clear channel with the correlation of Dittus–Boelter [28].
X L°
(6)
Q i is heat input for sensor i, i is indicating the number of sensor, thermal
Fig. 4. Convective heat transfer coefficient through the channel for different models and different Reynolds numbers and fixed heat flux (Q = 595 W). 392
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Fig. 5. Effect of porous media in mist flow on heat transfer enhancement for all models at laminar fluid flow (Q = 275 W and Re = 1125).
power of heater in each experiment is the product of V ∙ I, x is distance between sensor and entrance of test section (cylinder), L° is entire ˙ is given by length of test (cylinder). Mass rate of flow passing through m equation (7).
˙ = ρf UA c m
(12).
n
h¯ =
Qi ˙ cp m
V⋅I As
h¯Dh k eff
(14)
In Eq (14), k eff is thermal conductivity of the fluid and hydraulic diameter of the study area is defined as Eq. (15).
(9)
Dh =
4A c =D p
(15)
Ac is cross-section on the channel under test. It should be stated that the definition of Nusselt number in this study is based on the thermal conductivity (k eff ) . Local Nusselt number based on channel hydraulic diameter is defined as Eq. (16).
(10)
where V ∙ I is thermal power of heater. According to the environment of channel P and L° is heated length of channel, lateral area A s of channel under testing is calculate by equation (11).
A s = p ⋅L °
(13)
n
NuDh =
˙ , c p are where Tin is input/inlet temperature for each sensor. The Qi, m respectively input/inlet heat, mass rate of the passing flow, and specific heat of fluid when pressure is the constant. Convective heat flux q'' = q"tot is calculated as equation (10). q'' =
∑1 hi
where n is the number of calculated local h. The mean Nusselt number is defined in terms of the channel hydraulic diameter.
(8)
where, D is the diameter of the cylinder. Bulk temperature (Tb) of the fluid flow is calculated as equation (9):
Tb = Tin +
(12)
where Twi is temperature of cylinder outer/external wall in sensor ith. Mean convective heat transfer coefficient is average of local heat transfer coefficient that is obtained as equation (13).
(7)
ρf is fluid density, U and A c are respectively fluid velocity and crosssection passing through test section in each test that is calculated as equation (8). D2 Ac = π 4
q'' w Twi − Tb
hi =
NuDh =
hi Dh k eff
(16)
According to [8]:
(11)
K eff = (1− ε)K s + εKf
Local convective heat transfer coefficient is calculating by equation 393
(17)
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Fig. 6. Effect of porous media in mist flow on heat transfer enhancement for all models at transient fluid flow (Q = 275 W and Re = 3500).
good agreement with the results obtained from the Dittus–Boelter correlation witch the maximum error is 4.9%.
equation (17) can be rewritten as following:
K eff =
K s(1 − ε)
K εf
(18)
4.2. Local heat transfer coefficient
Reynolds number based on hydraulic diameter:
ReDh =
ρf UDh UDh = μf νf
Fig. 4 shows changes in local convective heat transfer coefficient hi in terms of distance and position of the sensors from the first channel (X/L) in different Reynolds numbers but at the fixed channel wall heat fluxes. The diameters of the porous material used in the experiment, are respectively 10, 8, 6, 4 cm and a porous media with an outer diameter 10 cm and internal and external diameters 2 and 4 cm. With constant heat flux and Reynolds number, procedure of the heat transfer factors mentioned are observed. In Fig. 4, changes of convective heat transfer coefficient according to different Reynolds numbers in a constant heat flux for different models are shown respectively. Three different Reynolds number with different fluid flow regime laminar, transient and turbulence are investigated. In the experimental tests, fixed heat flux (595 W) is incorporated. As illustrated in Fig. 4, in the presence of porous media in fixed heat flux for models (1, 2 and 5), as Reynolds numbers increases, convective heat transfer coefficient increases. When the porous medium inserted at the center of the channel (Models 1–4), until the radius of the porous medium is low (model 1 and 2), the flow passes the porous medium by changing the direction to the region near the channel's wall (clear region) so the effect of porous region on the heat transfer is low. Accordingly, at low Re number, the flow changes the direction to the clear region near the channel's wall with heat flux and the heat transfers to the fluid but by increasing the velocity at this situation, the time for exchanging the heat becomes low and heat transfer decreases. By increasing the radius of the porous medium inserted at the center of the channel (models 3 and 4), the effect of porous medium appears,
(19)
That νf is kinematic viscosity of the fluid and μ f is the dynamic viscosity of the fluid:
νf =
μf ρf
dimensionless length =
(20)
x L
(21)
where x is variable distance from beginning of test section and L is length of test section. 4. Results and discussions 4.1. Validation of the experimental results The experimental results were validated with the results obtained by the correlation of Dittus–Boelter [22] which calculate the Nusselt number for different Reynolds number. This correlation is used for the clear channel and single phase flow. The average Nusselt number for different Reynolds number or fully developed flow in straight clear channels (without porous zone) is depicted in Fig. 3. According to Fig. 3, the experimental results of the present setup for single phase flow in a clear channel are compared with the Dittus–Boelter correlation. As it can be seen, the experimental results have 394
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Fig. 7. Effect of porous media in mist flow on heat transfer enhancement for all models at turbulant fluid flow (Q = 275 W and Re = 6437). Table 3 Average Nusselt number for different models and Reynolds number. Models
Re = 1125
Clear Channel Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Re = 3500
Re = 6437
No Mist
Mist Flow
No Mist
Mist Flow
No Mist
Mist Flow
21 14.7 20.4 17.9 28.2 26.6 16
64.5 54.5 186.5 76.1 54.6 190.1 91
21.1 16.3 21 19.2 28.3 26.3 20.2
32.1 31 60.1 57.1 30.9 96 62.2
18.5 17.8 25.3 21.2 30.6 28.2 23
49.7 48.2 95.8 112.64 48.2 160.1 74
flux wall is low which make the heat transfer to increase. As it is shown in Fig. 4, the maximum convective heat transfer coefficient is belonging to the model 5 even more than model 4 (fully filled porous medium channel). According to the results of Mahdavi et al. [29], in some cases with specific porous medium radius and thermal conductivity ratio (Rk = keff/kf), provide better thermal performance when porous medium is adhered to inner wall (model 5) in comparison with the fully filled porous medium channel (model 4). The local heat transfer coefficient for different models and axial position in a channel with and without porous media and mist flow are shown in Figs. 5-7. The local heat transfer coefficient is illustrated for three fluid flow regimes including laminar, transient and turbulence in Figs. 5–7, respectively. The effect of porous media, mist flow and flow regime are shown obviously. As it can be seen in Fig. 5, at low Re number (Re = 1125), using mist flow and porous medium have significant effect in increasing the heat transfer coefficient. In some cases, the effect of using mist flow is
Fig. 8. Average Nusselt number for different models.
so porous medium causes pressure drop and by increasing the velocity, pressure drop increases which increases the heat transfer (and it should be noted that in these models, the gap of the clear channel near the heat 395
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Fig. 9. (a) Pressure drop in channel for different inlet velocities (b) The friction coefficient (f) in channel for different models (mist flow) and Reynolds numbers at Q = 275 W.
Fig. 10. Heat transfer enhancement ratio for different models (mist flow and no mist flow) and different Reynolds numbers (Re = 1125, 3500 and 6437). Fig. 11. Heat transfer performance ratio (NuPR) for different models and different Reynolds numbers.
Table 4 Heat transfer enhancement ratio (NuER) for different models at three different flow regimes (Re = 1125, 3500 and 6437). Models
Clear Channel Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Re = 1125
Re = 3500
coefficient than the others. In model 1, the radius of the porous medium is the lowest one and flow passes the channel by changing the direction and the effect of the porous zone is low. In model 4, the channel is fully filled porous medium and mist flow has higher thermal conductivity ratio in comparison with the single phase so the heat transfer is higher than the single phase flow but the pressure drop of mist flow in this model is more than the other models (even more than single flow in the same model) so it affects the heat transfer process. The maximum heat transfer coefficient is belonging to the model 5 with mist flow which show the effect of using mist flow and the results are the same with the results of the Mahdavi et al. [29]. The heat transfer coefficient for different models at transient regime (Re = 3500) are illustrated in Fig. 6. As the same with Fig. 5, the maximum heat transfer coefficient is belonging to the model 5. The heat transfer coefficient for different models at turbulent regime (Re = 6437) are illustrated in Fig. 7. The trend of the local heat transfer coefficient profiles for all models are the same approximately with the other flow regimes (laminar and transient). According to Fig. 7, the maximum heat transfer coefficient is belonging to the model 5 (same with Figs. 5 and 6).
Re = 6437
Mist Flow
No Mist
Mist Flow
No Mist
Mist Flow
No Mist
1 0.97 1.93 2.26 0.97 3.22 1.49
1 0.96 1.37 1.14 1.65 1.52 1.24
1 0.96 1.87 1.78 0.96 2.99 1.94
1 0.77 0.99 0.91 1.34 1.25 0.96
1 0.84 2.89 1.17 0.84 2.94 1.41
1 0.7 0.97 0.85 1.34 1.26 0.76
more than porous medium. For instance, in models 1 and 4, the clear channel with mist flow has higher heat transfer coefficient in comparison with the channel with porous medium and without mist flow but there is not significant difference between the results of the clear channel with mist flow and channel with porous medium and mist flow. This case shows that in some cases the effect of mist flow is more than using porous zone (without mist flow). For different models, the channel with porous medium and mist flow has higher heat transfer 396
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It can be find that higher heat transfer rate can be achieved by increasing the porous thickness. Because increasing the porous medium thickness caused that fluid flows in space between the porous material and channel wall with high velocity so convective heat transfer increases. Also, because of high conduction rate in the porous medium, the model with fully filled porous material has the highest improvement in heat transfer with mist flow in comparison with the clear channel. Average Nusselt numbers for different models and Reynolds number are listed in Table (3). The effect of mist flow in porous media on heat transfer enhancement is shown completely. Also, the average Nusselt number for different models are illustrated in Fig. 8. Table (3) and Fig. 8 show variations of the average Nusselt number for mist flow in circular channels with different porous media. In the presence of porous media, using mist flow causes more average Nusselt number for all flow regimes. At low Reynolds number, the average Nusselt number enhancement is more than 200%. Also, model 5 with has the best thermal performance with average Nusselt number enhancement more than 600%. At transient flow regime, for all models heat transfer enhancement is between 100 and 265%. Model 5 with 265% average Nusselt number enhancement has the best heat transfer rate. At high Reynolds number model 5 with 467.7% heat transfer enhancement has the best thermal performance.
4.4. Heat transfer enhancement ratio (NuER) and heat transfer performance ratio (NuPR) The effectiveness of using the porous zone evaluated by studying ratio of mean Nusselt number (Nu) and the mean Nusselt number (Nu0) for fully developed flow in a clear channel (without porous medium):
NuER = Nu/Nu 0
Nu 0 is referred to a clear channel without any porous region. This ratio will be referred to as the heat transfer enhancement ratio (NuER). The variation of this heat transfer enhancement ratio (NuER) with Reynolds number for different models is shown in Fig. 10 and the results are listed in Table (4) for a fixed value of heat flux (Q = 275 W). In Fig. 10, data labels of the all models (mist flow with porous medium) are shown. Accordingly, at low Re number (Re = 1125), in all models except model 4, using mist flow increases the heat transfer enhancement ratio (NuER) in comparison with the no mist flow and generally, by mist flow, all models except models 1 and 4 (−3% for both of them), have better NuER in comparison with the clear channel. Without mist flow, all models except model 1 have better NuER in comparison with the clear channel. In mist flow and no mist flow situation (with porous medium in both), the highest NuER are belonging to model 5 and model 4, respectively at low Re number (Re = 1125) and the average Nusselt number of models 5 and 4 for mist flow and no mist flow are 222% and 65% more than the clear channel at Re = 1125. As shown in Fig. 10, at transient flow regime (Re = 3500), all models have better NuER except model 1 and model 4 (−4% for both of them) by using mist flow with porous medium in comparison with the clear channel and at single phase flow with porous medium, models 4 and 5 have the better NuER in comparison with the clear channel. Generally, using mist flow with porous medium increases thermal performance in NuER for all models except models 2 and 4 in comparison with the single phase flow (air) with porous medium. The average Nusselt number of models 5 and 4 (as the best models) for mist flow and no mist flow (with porous medium in both of them) are 199% and 34% more than the clear channel at Re = 3500 (transient flow). At high Re number, turbulent flow (Re = 6437), using mist flow increases the NuER for all models except models 1 and 4 (−16% for both of them) in comparison with the clear channel. Also, in single phase flow with porous medium, models 4 and 5 with 34% and 26% increasing have the better NuER in comparison with the clear channel. The average Nusselt number of models 5 and 4 (as the best models) for mist flow and no mist flow (with porous medium in both of them) are 194% and 34% more than the clear channel at Re = 6437 (turbulant flow). The effectiveness of using the porous region also be studied evaluating the heat transfer performance ratio. The heat transfer performance ratio (PR) is defined as the ratio of heat transfer enhancement to unit increase in pumping power:
4.3. Pressure drop and friction coefficient of channel Although using porous material in heat exchanger enhances heat transfer rate, it causes pressure loss increase. Figs. 9a and 9b show the pressure drop and friction coefficient in channel for all models and fixed heat flux. The friction coefficient (f) in a channel flow can be determined by measuring the pressure drop across the flow channel and average velocity of the air. Average friction coefficient can, therefore, be calculated from equation (22).
f= (2ρΔPDh)/(V 2LP)
(23)
(22)
Results are investigated for different inlet velocity ranges from 0.18 to 2.13 m/s. It should be noted that at Vinlet = 0.357 m/sec, the fluid flow is laminar (Re < 2100) and for 0.357 m/sec < Vinlet < 0.68 m/ sec, the fluid flow regime is transient. For the inlet velocity more than 0.68 m/sec, the flow regime is turbulent (Re > 4000). It can be observed that the f increases with decreases of the Re number. These are the expected results. As it is illustrated in Fig. 9a, it can be seen that at the low Reynolds number, the differences of pressure drop between the models are very low and by increasing the inlet velocity (consequently Reynolds number), the differences of pressure drop between the models become greater. Between the models 1–4 where the porous zone inserted at the tube core, by increasing the diameters of the porous zones (from model 1 to 4), pressure drop increases. The pressure drop results have the same trend with the Mahdavi et al. [29] works. Also, based on Fig. 9a, the pressure loss (consequently, the required pumping power) for the models which porous zone is inserted at the tube core is lower than the models it is located adjacent to the wall at the same Darcy number. In comparison between the models, at the turbulent regime, model 4 has the greatest pressure drop. On the other hand, at the low Reynolds number (laminar to transient fluid flow regime), the trend of the pressure drop with Reynolds number rise for all models is the same except models 5 and 6. But at the high Reynolds number (turbulent fluid flow regime), the trend is the same for all models and for model 4, the pressure drop increases significantly. In Model 4, the channel is full of porous zone. In the other models, the channel is partially filled by porous zone so by increasing the velocity, the fluid changes the direction to the clear part of the channel but at model 4, the channel is full of porous zone and cannot change its direction so the pressure drop increases.
NuPR = NuER /(f/f 0)1/3
(24)
f 0 is referred to a tube without any porous region. In this ratio, the friction factors are raised to the one-third power as the pumping power is proportional to the one-third power of the friction factor [10,11]. The variation of this heat transfer performance ratio (NuPR) with Reynolds number for all models is shown in Fig. 11 at a fixed value of heat flux (Q = 275 W). NuPR factor including the effects of pressure drop and the heat transfer coefficient. On the other side, according to equation (24), increasing the value of NuPR means the better heat transfer with low pressure drop. It should be noted that using mist flow increases the pressure drop in comparison with the single phase flow significantly which affects the heat transfer performance ratio (NuPR) according to equation (24). According to Fig. 11, it can be seen that at low Re number (Re = 1125), model 5 has the highest NuPR and model 2 is the second 397
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one in using mist flow. At transient flow regime, the highest NuPR is belonging to the model 5 and model 2 is the second one. For the high Re number (Re = 6437-turbulant flow) the maximum NuPR is belonging to the model 2 and model 5 is the second one. Generally, between the all models, models 2 and 5 have the best performance based on the NuPR. At low and high Re number, models 5 and 2 have the best thermal performance, respectively. As a final result, between the all investigated models, model 2 with mist flow has the best NuPR with 24% improvement.
number, models 5 and 2 have the best thermal performance, respectively. References [1] Donald A. Nield, Adrian Bejan, Nield-Bejan, Convection in Porous Media vol. 3, springer, New York, 2006. [2] J. Bear, Dynamics of Fluids in Porous Media–American Elsevier Pub, Comp., inc., New York, 1972 764pp.. [3] Ruben Juanes, et al., Impact of relative permeability hysteresis on geological CO2 storage, Water Resour. Res. 42 (12) (2006). [4] Karsten Pruess, Julio Garcia, Multiphase flow dynamics during CO 2 disposal into saline aquifers, Environ. Geol. 42 (2) (2002) 282–295. [5] Delavar, Mojtaba Aghajani, Ebrahim Alizadeh, and Seyed Soheil Mousavi Ajarostaghi. "Experimental and Lattice Boltzmann Method Investigation of Direct Methanol Fuel Cell Performance.". [6] Mohamed El Amine Ben Amara, Sassi Ben Nasrallah, Numerical simulation of droplet dynamics in a proton exchange membrane (PEMFC) fuel cell micro-channel, Int. J. Hydrogen Energy 40 (2) (2015) 1333–1342. [7] Yuan Gao, et al., Lattice Boltzmann simulation of water and gas flow in porous gas diffusion layers in fuel cells reconstructed from micro-tomography, Comput. Math. Appl. 65 (6) (2013) 891–900. [8] Bo Han, Hua Meng, Numerical studies of interfacial phenomena in liquid water transport in polymer electrolyte membrane fuel cells using the lattice Boltzmann method, Int. J. Hydrogen Energy 38 (12) (2013) 5053–5059. [9] A.V. Kuznetsov, Influence of thermal dispersion on forced convection in a composite parallel-plate channel, Z. Angew. Math. Phys. 52 (1) (2001) 135–150. [10] M.K. Alkam, M.A. Al-Nimr, Transient non-Darcian forced convection flow in a pipe partially filled with a porous material, Int. J. Heat Mass Tran. 41 (2) (1998) 347–356. [11] H. Shokouhmand, F. Jam, M.R. Salimpour, Simulation of laminar flow and convective heat transfer in conduits filled with porous media using Lattice Boltzmann Method, Int. Commun. Heat Mass Tran. 36 (4) (2009) 378–384. [12] Mohamed A. Teamah, Wael M. El-Maghlany, Mohamed M. Khairat Dawood, Numerical simulation of laminar forced convection in horizontal pipe partially or completely filled with porous material, Int. J. Therm. Sci. 50 (8) (2011) 1512–1522. [13] Chen Yang, Akira Nakayama, Wei Liu, Heat transfer performance assessment for forced convection in a tube partially filled with a porous medium, Int. J. Therm. Sci. 54 (2012) 98–108. [14] Mohammad Nikian, et al., Experimental investigation of two-phase mist flow and heat transfer in porous media, J. Porous Media 16 (8) (2013). [15] H. Shokouhmand, M. Nikian, Effect of mist flow on heat transfer enhancement in porous media, Arabian J. Sci. Eng. 39 (6) (2014) 5063–5072. [16] Niru Kumari, et al., Analysis of evaporating mist flow for enhanced convective heat transfer, Int. J. Heat Mass Tran. 53 (15) (2010) 3346–3356. [17] Z. Huang, A. Nakayama, et al., Enhancing heat transfer in the core flow by using porous medium insert in a tube, Int. J. Heat Mass Tran. 53 (5) (2010) 1164–1174. [18] S. Baragh, H. Shokouhmand, S.S. Ajarostaghi, M. Nikian, An experimental investigation on forced convection heat transfer of single-phase flow in a channel with different arrangements of porous media, Int. J. Therm. Sci. 134 (2018 Dec 1) 370–379. [19] D. Bhargavi, J.S. Reddy, Effect of heat transfer in the thermally developing region of the channel partially filled with a porous medium: constant wall heat flux, Int. J. Therm. Sci. 130 (2018 Aug 31) 484–495. [20] M. Siavashi, H.R. Bahrami, E. Aminian, Optimization of heat transfer enhancement and pumping power of a heat exchanger tube using nanofluid with gradient and multi-layered porous foams, Appl. Therm. Eng. 138 (2018 Jun 25) 465–474. [21] T. Guo, T. Wang, J.L. Gaddis, Mist/steam cooling in a heated horizontal tube part I: experimental system and part II: results and modeling, ASME J. Turbomach. 122 (2000) 360–374. [22] T. Guo, T. Wang, J.L. 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5. Conclusion An experimental study on forced convection heat transfer of twophase flow (mist flow) in a channel with different arrangements of porous media is investigated. This investigation experimentally studies the convective heat transfer in uniform heat flux pipe with porous zone. Also the present experimental article presents the potential of twophase flow and a porous inserted to increase the heat transfer rate occurring between the surfaces of a channel and the mist air flowing inside it. Different models of porous media inside the channel are used. It was observed that a larger value of heat transfer rates can be achieved by increasing the diameter of a porous media and increasing the flow rate of mist air. Porous media apply the heat flux to the inside of the channel and transfer it to the fluid then the average temperature of the fluid increases. This increase in temperature leads to reduce the temperature difference between the channel wall and the average temperature of the fluid. Also by increasing the Reynolds number in all positions of the porous media, heat transfer coefficient increases. From the obtained results, it can be said that improve heat transfer by using porous media is carried out when the diameter of porous media be closed to the diameter of the channel. As porous medium thickness and mass flowrate of gas increase, the heat transfer rate and consequently Nusselt number increase. The results show that mist cooling coupled with the porous zone can increase the heat transfer rate significantly in comparison with the single phase cooling without porous zone. The obtained results are following:
• The results show that at low Reynolds number, the average Nusselt
• •
•
number enhancement is more than 200%. At transient flow regime, for all models heat transfer enhancement is between 100 and 265%. At high Reynolds number, 467.7% heat transfer enhancement is the best thermal performance improvement based on using porous zone and mist flow. From the obtained results, it can be realized that improve heat transfer by using porous media is carried out when the diameter of porous media be closed to the diameter of the channel. The heat transfer enhancement ratio (NuER) increases with increase in Re (transition to turbulent). In models which the porous zone inserted at the tube core, by increasing the diameter of porous media, the heat transfer enhancement ratio (NuER) increases (in both laminar and turbulent flows). But in models with the porous zone inserted adjacent to the wall (annulus shape of porous zone), increase the inner diameter of the porous zone decreases the heat transfer enhancement ratio (NuER) in all flow regimes. At low Re number (Re = 1125), model 5 has the highest NuPR and model 2 is the second one in using mist flow. At transient flow regime, the highest NuPR is belonging to the model 5 and model 2 is the second one. For the high Re number (Re = 6437-turbulant flow) the maximum NuPR is belonging to the model 2 and model 5 is the second one. Generally, between the all models, models 2 and 5 have the best performance based on the NuPR. At low and high Re
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