NUMERICAL ANALYSIS OF FORCED CONVECTION HEAT TRANSFER FROM TWO TANDEM CIRCULAR CYLINDERS EMBEDDED IN A POROUS MEDIUM

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1 THERMAL SCIENCE, Year 2017, Vol. 21, No. 5, pp Introduction NUMERICAL ANALYSIS OF FORCED CONVECTION HEAT TRANSFER FROM TWO TANDEM CIRCULAR CYLINDERS EMBEDDED IN A POROUS MEDIUM by Habib-Ollah SAYEHVAND a*, Ehsan KHALILI DEHKORDI a, b and Amir BASIRI PARSA a Department o Mechanical Engineering, Bu-Ali Sina University, Hamedan, Iran b Hamedan Branch, Islamic Azad University, Hamedan, Iran Original scientiic paper 1 Study the heat and mass transer in packed bed heat exchangers particularly in nuclear application is subject o many new researches. In this paper numerical analysis o orced convection heat transer rom two tandem circular cylinders embedded in a packed bed, which is made o spherical aluminum particles, is investigated in laminar low. The porous medium increases the overall heat absorbed rom two cylinders and cooling eect but increases the pressure drop, signiicantly. Also, the eect o increase the horizontal distance between two tandem circular cylinders on low pattern and heat transer is investigated. For the empty channel, the total wall heat lux in very small distances have a minimum due to generation o closed vortex region and or longer distances, by increases the distance between two tandem cylinder, the total wall heat lux increases. It is shown that or two circular cylinders embedded in the packed bed, the total wall heat luxes rom two cylinders and the luid outlet temperature increase to a maximum quantity and then decrease with negative gradient. Also, the quantities o the empty channel are too smaller than the amounts o porous medium. Key words: porous medium, packed bed, orced convection, laminar low, two tandem cylinders Fundamental and applied research in low, heat, and mass transer in porous media has received increased attention during recent decades. A complete review on heat and mass transer in porous media was perormed by Goldstein et al. [1]. Vaai [2] reported the application o porous media in biotechnology and other modern industries. The application o packed beds with regular and irregular packing, changes the heat and mass transer through the heat exchangers. There are lots o parameters, which governs the heat and mass transer in packed bed, and should be investigated. Some o them were studied in [3-5] the same as wall eects, bed perormance, temperature proiles in the bed, packing morphology, and low rates in dierent low regimes. Kaviany [6] stated that in packed beds in low Reynolds numbers, the Darcy law can be applied and it was unable to describe the lows at high Reynolds number. Thereore, many researches ocused on the non-darcian eects. Mahgoub [7] examined the non-darcian orced convection heat transer over a horizontal plate in a porous medium made by spherical particles. To consider inertia-eects, Hellstrom and Lundstrom [8] showed that the use o the 1* Corresponding author, hsayeh@basu.ac.ir

2 2118 THERMAL SCIENCE, Year 2017, Vol. 21, No. 5, pp empirically derived Ergun equation, which can describe the response o several porous media, does not reveal the real mechanisms or some lows. Results o considerable experimental researches, on unconsolidated porous media, are gathered by Vaai [9]. Yuki et al. [10] preormed particle image velocimetry to identiy the low structures in a sphere-packed pipe. Also, Orodu et al. [11] used a simple experimental set-up to validate capillary tube models o low in porous media. Numerical simulations o heat and mass transer in porous media have been developed increasingly.verma and Mewes [12] carried out the three 3-D simulation o low in packed bed o porous adsorbents using lattice Boltzmann methods. Yih-Ferng Peng et al. [13] used a nestedblock inite volume based Cartesian grid method to simulate the unsteady viscous incompressible lows. Zdravkovich [14, 15] studied the characteristic o low over cylinder and the complicated behavior o the intererence in dierent arrangement o cylinders. Tatsuno et al. [16] experimentally studied the statistically stable posture o a triangular or a square cylinder and indicated that both cylinders come to rest in a stable posture with a side perpendicular to the uniorm low. Flow over a cylinder embedded in porous medium is considered to increase the convection heat transer mainly. The problem o cooling a pipe in heat exchangers using porous medium considered in many works. In many reactors, particularly nuclear reactors, increasing the cooling rate and heat transer rom a circular cylinder which is embedded in sands is a critical problem. One o the eective ways o increase the convection heat transer is the use o porous medium instead o a single medium. Al-Sumaily et al. [17], numerically studies the time dependent orced convection heat transer rom a single circular cylinder embedded in a horizontal packed bed o spherical particles under local thermal non-equilibrium condition, using the spectral-element method. In another work Al-Sumaily et al. [18] studied the eect o porous media particle size on orced convection rom a circular cylinder without assuming local thermal equilibrium between phases. It is observed that when two cylinders horizontally or in tandem arrangement are located near each other, the regimes o heat and mass transer is dierent rom one cylinder, considerably. Kostic and Oka [19] carried out experimental investigations o the low and heat transer around two cylinders. They showed that or two cylinders in small distance, the closed vortex region or ree cavity causes that the 2 nd cylinder inluenced on the 1 st cylinder due to vortex, signiicantly and leads to a local minimum in heat transer. Dehkordi et al. [20], investigated the 2-D unsteady viscous low around two circular cylinders in a tandem arrangement in order to study the characteristics o the low in both laminar and turbulent regimes. Koda and Lien [21], considered the aerodynamic eects due to the development o 3-D low structures in the low over one and two cylinders in tandem using the lattice Boltzmann method. Shyam and Chhabra [22], studied orced convection heat transer rom two square cylinders in tandem arrangement to power-law and Newtonian luids. As the literature review indicates the low over two tandem circular cylinders in packed beds are not investigated completely and this problem should studied with more attention. In the present work, low regime o two horizontally tandem circular cylinders embedded in packed bed is mentioned and numerically solved. First the low regimes in empty and porous channel are compared. Then the streamlines, pressure gradient, orced convection heat transer and outlet temperature is derived. Also, the main objective is to discuss the eect o the distance between two cylinders on overall heat transer. Problem description Figure 1 indicates schematic o the problem. Laminar low at low Reynolds number passes over two tandem circular cylinders immersed in a horizontal packed bed o spherical

3 THERMAL SCIENCE, Year 2017, Vol. 21, No. 5, pp particles. The luid is assumed to be Newtonian and incompressible. The cylinders are isothermally heated at a constant temperature, T h, and they are cooled by the external luid with U 0, T 0. The conining horizontal walls have the same temperatures T w = T 0. The blockage ratio o the bed is D cy / H = 0.2, where D cy and H, are the cylinder diameter and the bed height, respectively. U 0 T 0 The blockage ratio o the bed is small enough to neglect the channeling eect. It is supposed that the porous medium is homogenous and isotropic. There is no heat generation in the porous medium. Also, the radiation is neglected and local thermal equilibrium between the two phases is regarded. Mathematical ormulation The 2-D governing equations are average-volume continuity, Darcy-Forchheimer momentum and local thermodynamic equilibrium (LTE) energy equation which are presented in vectorial orm as the ollowing [6, 17, 18 and 23]: u' =0 (1) u' 1 F 2 u' u' u' u' u' u' P t K K T ( Cp) m ( Cp) ' T Ke T t u (3) The operator... used or the local average o a quantity and or velocity is calculated by: ' u v (2) 2 2 u (4) Due to interaction o solid and luid the mean energy capacity is used in eq. (3) that can be calculated by: ( C ) ( C ) (1 )( C ) (5) p m p p s Using the ollowing dimensionless variables, transorm the previous equations into dimensionless orm:, ' 0 x, y x y u, ', T u T, P P (6) D 2 cy u Th T0 u So the eqs. (1)-(3) change to the ollowing relations: u' 0 2 u 1 F 1 2 ( u) u u u u u P t Re D D Re L u D cy T h L Cylinder1 Cylinder2 D a a D 0 T W = T 0 T W = T 0 Figure 1. Schematic o the two tandem cylinder embedded in packed bed L d H (7) (8)

4 2120 THERMAL SCIENCE, Year 2017, Vol. 21, No. 5, pp K t C ReDPr C k u (9) where C = ε + (1 ε)(k r / α r ) and k r and α r are the solid/luid thermal conductivity and diusivity ratios, k s / k and α s / α, respectively. The Reynolds, Darcy, Prandtl, and Biot numbers are deined, respectively: Re ud, Da D ha, Pr, and Bi (10) 2 0 cy K cy s s D 2 Dcy ks Duallien [24], suggested the ollowing relation or the speciic surace area: a s 6(1 ) (11) d p Wakao et al. [25], introduced the interacial heat transer coeicient: 0.6 k u d 1/3 p h 2Pr (12) s d Ergun [26] suggested relations or the permeability and geometric unction: 3 2 d p 1.75 K, F 2 150(1 ) and the eective thermal conductivity is deined as k,e,(x,y) = k st + k d(x,y) [27], oered the semitheoretical model or stagnant conductivity: 1 B 1 B 2 kst 2 1 B1 B1 1 1 ln( B) k 1B 2 1B (14) 10/9 1 1, B 1.25 K r Wakao and Kaguei [28], based on experimental correlations in longitudinal and lateral directions deine the dispersion conductivity which is the result o tortuous path around particles: k dx u d p k dy u d p 0.5Pr, 0.1Pr (15) k k and the solid eective thermal conductivity is k s,e = (1 ε) k s. It is assumed that the luid and solid phases share the same temperature as the isothermal surace o the cylinder. In other words, thermal equilibrium is imposed at the heated boundary. To evaluate the heat transer the time-mean average Nusselt number along the heated cylinder or solid and luid phases is used with the ollowing relation: Nu cy cy cy cy, Nus k ks (13) h D h D (16)

5 THERMAL SCIENCE, Year 2017, Vol. 21, No. 5, pp The viscous resistance in a packed bed is equal to [29]: 2 150(1 ) Rv (17) d that d p is the diameter o particles in packed bed and is sphericity o particles. The inertial resistance is calculated with [29]: (1 ) 6 S p Ri, 3 d d V p p p p S p and V p are the surace area and the volume o the particle, respectively. For spherical particles sphericity is equal to 1.0. So the total pressure drop is equal to: Numerical solution d p Ri Re u u d 2 The computational domains are made based on the results o [16, 17]. The governing equations are numerically solved using the inite volume method. The convection and diusion luxes on the aces o control volume are interpolated with high order upwind and central dierences. Figure 3 indicated the computational domain which is made with triangular grids as ig. 2 and iner grid near solid walls was generated. The independency o results to grid resolution, at dierent grids are examined or D cy / d p = 10, ε = The variation o mean luid Nusselt number, which is chosen as a control parameter, vs. dierent grid number is shown in ig. 3. It seems that i the domain includes at least nodes, the grid impendency is obtained and the dierence between the results less than 0.1%. For validation o the present numerical method, irst the problem o two tandem cylinder, is solved and in ig. 4 present streamlines are compered o the experimental results o [15, 16, 19]. Second, the problem o low over a cylinder, which is embedded in a porous medium, is considered. Figure 5 shows the variation o mean luid Nusselt number vs. dierent Peclet number around one cylinder embedded in a packed bed o aluminum particles and compared with the results o previous works [30, 31]. It is observed that the results o experimental, analytical, and present numerical work are in a good accordance. l 2 Figure 2. Generated mesh, using iner meshes near and behind the cylinders 40 Nu (18) (19) Number o nodes Figure 3. Mean luid Nusselt number around cylinder 1 vs. number o nodes, in porous channel with Pr = 5.49, Pe = 150

6 2122 THERMAL SCIENCE, Year 2017, Vol. 21, No. 5, pp (a) (a) Experimental [30] Analytical [31] Numerical present work 20 L / D cy = 3 (b) (b) Experimental L / D cy = 2.25 Numerical Figure 4. Flow past two tandem cylinders at Re = 0.02; comparison the results o numerical present work and the experimental results [15, 16, 19] Pe = 5 Pe = 50 Pe = 250 Pe = 500 (a) Empty (b) Packed bed Figure 6. Flow streamlines in empty and porous channel vs. Peclet number at L/Dyc, Pr = 5.49 Q t [kwm 2 ) Total wall heat lux in packed bed Total wall heat lux in water Figure 7. Comparison o total wall heat lux in empty and porous channel vs. horizontal distances between two cylinders, Pr = 5.49, Pe = Pe Figure 5. Mean luid Nusselt number vs. Peclet number or a cylinder embedded in porous channel Dcy = 0.012, Pr = 5.49 Results and discussion Figure 6 compares the low streamlines around two tandem cylinders in = 1 with Pr = 5.49 in dierent velocities. In the column (a) by increase the velocity, due to separation a wake region is seen and growth by increment in velocity so that it can cover two cylinders and a closed vortex region may generated. But in the column (b), the channel illed with solid aluminum particles. Due to interaction o luid and solid particles, the low velocity can not increase, thereore the separation does not happen. So the low pattern in porous has no signiicant changes in dierent velocities and there is no closed vortex region here. All the comparisons in the ollowing igures are perormed in very low Reynolds numbers and in long distances between two cylinders, so that the two cylinders are not located in closed vortex region in empty channels. Figure 7 compares the total wall heat lux o two cylinders in pure water and water passes through packed bed o aluminum particles and when the water passes through the packed bed the heat transer increase, considerably. The maximum heat rom cylinders in porous is Q max = kw/m 2 and in empty channel is Q max = kw/m 2. So by using porous channel the heat transer about three times increased and this is the main reason o using the porous channels, especially in compact nuclear heat exchangers in which the limitations o distances and time are

7 THERMAL SCIENCE, Year 2017, Vol. 21, No. 5, pp too important. In the packed bed, the total wall heat lux has a signiicant increment with increasing the distance o two cylinders up to = 3 and ater this distance the trend o wall heat lux changes. In ig. 8 the luid mean Nusselt number vs. horizontal distance between the two cylinder is drawn and it is obvious that in = 3 there is a local maximum. But in the empty channel, the total wall heat lux has a mild increment with increasing the distance o two cylinders. Another eect o using packed bed is the change in the pressure contours and pressure gradient. 37 Nu d p /d l [kgm 2 s 2 ] Pressure gradient around cylinder 1 in packed bed Pressure gradient around cylinder 1 in water Figure 8. Mean luid Nusselt number in packed bed vs. the horizontal distance o two cylinders, Pr = 5.49, Pe = 150 Figure 9. Comparison o the pressure gradient around cylinder 1 in empty and porous channel, vs. the horizontal distance o two cylinders, Pr = 5.49, Pe = 150 Figure 9 compares the pressure gradient around cylinder 1, in empty and porous channels. As it is expected, with increase the solid particles, the interaction between the solid and luid molecules causes signiicant pressure drop in luid low. Figure 10 compares the pressure contour lines in empty and porous channels. Due to increase the porous particles, the pressure contours around two cylinder changes to uniorm state, especially in the distance between two cylinders the dierence between empty and porous channel is notable. Figure 11 indicates the luid non-dimensional outlet temperature in water and cylinders embedded in porous medium. The luid outlet temperature in porous medium is greater than water. Figure 12 shows the variation o the luid and solid mean Nusselt number around cylinder 1 when the water passing through the porous channel. The solid Empty Packed bed Figure 10. Comparison o the Pressure Contours in empty and porous channel at L/Dcy = 3 and Pr = 5.49, Pe = 150

8 2124 THERMAL SCIENCE, Year 2017, Vol. 21, No. 5, pp θ 0.12 particles absorb a part o heat orm the cylinder. The share o luid particles is greater than the solid particles. The physical explanation o the dierence between empty and porous channels is presented. First it should be noted that in porous medium solid particles change the streamlines, pressure gradient and pressure contours to a more uniorm state, so the regime o the luid changes extremely. There is no wake between the two cylinders and behind the second cylinders. While the low uniormly and slowly passes the channel, it better absorb the heat rom the wall cylinders and solid particles. Second, due to interaction between solid particles and two cylinder walls, they absorb the heat rom the cylinders because aluminum has very high thermal conductivity coeicient. Third, due to the interaction o luid and solid particles in the packed bed, the absorbed heat rom the solid particles easily transer to luid particles. Now, i the air passes the channel with the same geometry and porous materials, the same trends are seen. Figure 13 compares the total wall heat luxes o two tandem circular cylinders in empty and porous channel with Pr = The same as water, it is seen that or the porous medium, the maximum heat transer is obtained at = 3. The comparison o igs. 7 and 13 shows that, the quantities o max heat luxes or the air are lower than water because air has lower heat capacity, density and Prandtl number. That means increase the Prandtl number o luid in the packed bed resulted in an increase in the total heat luxes, signiicantly. Nu Outlet non-dimensional temp. in packed bed Outlet non-dimensional temp. in water Figure 11. Comparison o the luid non-dimensional outlet temperature vs. the horizontal distance o two cylinders, Pr = 5.49, Pe = 150 Fluid mean Nusselt number Solid particles mean Nusselt number Q t [kwm 2 ] Total wall heat lux in packed bed Total wall heat lux in air Figure 12. Mean Nusselt number o the luid and solid particles in packed bed vs. the horizontal distance o two cylinders, Pr = 5.49, Pe = 150 Figure 13. Total wall heat lux in empty and porous channel vs. the horizontal distance o two cylinders Pr = 0.715, Pe = 150 Figure 14, clearly shows the total wall heat lux in porous channel has a local maximum at = 3. When the laminar low reaches to irst cylinder, luid particles absorbs amount o heat rom cylinder. Ater passing the irst cylinder, in the distance between two

9 THERMAL SCIENCE, Year 2017, Vol. 21, No. 5, pp cylinders, the interaction o luid-solid particles causes a heat transer and reduction in temperature. Vice versa, increase the distance causes the loss in heat transer because o the growth o the pressure drop and reduction o the velocity. So, it should be an optimum point or this distance and as ig. 14 shows, it takes place in = 3. It can be an applicable matter in packed bed piping. But in empty channel the trend o the total heat transer is dierent. It is seen that in empty channel there is a mild increment in total heat transer with increasing the distance between the cylinders. Figure 15 comparison o the streamlines in empty channel vs. the horizontal distance o two cylinders, Pr = 0.715, Pe = 150. It shows the streamlines o air in empty vs. the variation o horizontal distance between two cylinders. Here, with increase the distances between two cylinder the wake ater the cylinder 1 is diminishes and the streamlines o low behind the cylinder 1 attached to each other and the wakes behind it disappears, so the low can absorb the second cylinder wall heat luxes easily and thereore the overall heat lux and outlet temperature increases and especially the total wall heat lux has a continuous increment with increasing the horizontal distance, although its quantity is more lower than which belong to porous channel Q t [kwm 2 ] = = = = 4 Figure 14. Total wall heat lux in porous channel vs. the horizontal distance o two cylinders, Pr = 0.715, Pe = 150 Figure 15. Comparison o the stream lines in empty channel vs. the horizontal distance o two cylinders, Pr = 0.715, Pe = 150 Figure 16 shows the pressure gradients around the irst and second cylinders are dierent, signiicantly. The pressure gradient around the irst cylinder is much higher than the pressure gradient around the second cylinder. The pressure gradient around the second cylinder increased with increase the distance o two cylinders. Figure 17 shows the dierence between the pressure gradient in pure air and packed bed around cylinder 1. The quantities or air are lower than the pressure gradients or the water. Figure 18 indicates the non-dimensional outlet temperature in empty and porous medium. The outlet temperature in packed bed is greater than empty channel considerably. Also, the air outlet temperature is lower than the water outlet temperature in both empty air and air passes through packed bed. Figure 19 shows the contour lines o temperature or air passing the porous channel contains the two embedded tandem cylinders vs. the distance between the cylinders. With increase the horizontal distance between cylinders, the isotherm lines between two cylinders becomes uniorm. The physical explanation which presented or the empty and porous channel when the air is the working luid is the same as what presented previously or the water.

10 2126 THERMAL SCIENCE, Year 2017, Vol. 21, No. 5, pp Pressure gradient around cylinder 1 in air Pressure gradient around cylinder 2 in air 10 4 Pressure gradient around cylinder 1 in packed bed Pressure gradient around cylinder 2 in air d p /d l [kgm 2 s 2 ] d p /d l [kgm 2 s 2 ] Figure 16. Pressure gradient around two tandem cylinder in empty channel vs. the horizontal distance o two cylinders, Pr = 0.715, Pe = θ 0.12 Outlet non-dimensional temp. in packed bed Outlet non-dimensional temp. in air Figure 17. Comparison o the pressure gradient around cylinder 1 in empty and porous channel vs. the horizontal distance o two cylinders, Pr = 0.715, Pe = = = = Figure 18. Comparison o the luid non-dimensional outlet temperature in empty and porous channel vs. the horizontal distance o two cylinders, Pr = 0.715, Pe = 150 = 4 Figure 19. Temperature contours in porous channel vs. the horizontal distance o two cylinders, Pr = 0.715, Pe = 150 Conclusions In the present work, orced convection heat transer rom two tandem circular cylinders embedded in a porous medium is investigated. The porous channel included the aluminum spherical particles and it is shown the presence o porous medium, enhances the overall heat transer. At the same time, change the pressure contours and increases the pressure drop in the channel signiicantly. Comparison o the pressure gradients in empty and porous channels indicates that the length o the porous channel should be as much as shorter due to high pressure

11 THERMAL SCIENCE, Year 2017, Vol. 21, No. 5, pp gradient. The horizontal distance between two tandem cylinders is a main actor that changes the total wall heat luxes rom two tandem cylinders in porous medium and at the distance about three times o cylinder diameter in laminar low, the maximum o heat absorption rom two cylinders is obtained. Increasing the distance more than this quantity, causes reduction in overall wall heat lux. The outlet temperature o the luid in porous channel is greater that the empty channel. In empty channel there is a very low increase in heat transer absorbed rom two cylinders with increment the distance. Nomenclature as speciic interacial area, [m 1 ] Cp speciic heat capacity, [Jkg 1 K 1 ] dp particle diameter, [m] Dcy cylinder diameter, [m] Da Darcy number, (= k/dcy 2 ) F geometric unction hs interacial heat transer coeicient, [Wm 2 K 1 ] H channel height, [m] K permeability, [= ε 3 d 2 p / 150(1 ε) 2 ], [m 2 ] k thermal conductivity, [Wm 1 K 1 ] kr solid/luid thermal conductivity ratio, kr = ks /k L horizontal distance between two cylinder, [m] Nu time mean average Nusselt number P luid pressure, [Nm 2 ] P dimensionless luid pressure Pr Prandtl number, (= ν /α) Qt total wall heat lux, [Wm 2 ] ReD Reynolds number, (= u0ρdcy / µ) Ri inertial resistance Rv viscous resistance t time, [s] t dimensionless time T temperature, [K] Th cylinder wall temperature, [K] ' vectorial luid velocity, [ms 1 ] dimensionless vectorial velocity, (= u /u0) u horizontal velocity component, [ms 1 ] u dimensionless horizontal velocity component u0 inlet horizontal luid velocity, [ms 1 ] v vertical velocity component, [ms 1 ] v dimensionless vertical velocity component x, y horizontal and vertical co-ordinates, [m] x, y dimensionless horizontal and vertical coordinates Greek symbols α thermal diusivity, [m 2 s 1 ] αr solid-to-luid thermal diusivity ratio, (= αs / α ) ε porosity θ dimensionless temperature, [= (T T0) / (Th T0)] µ luid dynamic viscosity, [kgm 1 s 1 ] ρ luid density, [kgm 3 ] sphericity o particles Subscripts e eective luid s solid Reerences [1] Goldstein, R. J., et al., Heat Transer A Review o 2004 Literature, Int. J. o Heat and Mass Transer, 53, (2010), 21-22, pp [2] Vaai, K., Porous Media-Application in Biological Systems and Biotechnology, Taylor and Francis, Oxord, UK, 2011 [3] Kwapinski, W., et. al., Modeling o the Wall Eect in Packed Bed Adsorption, Chemical Engineering and Technology, 27 (2004), 11, pp [4] Thomeo, J. C., Grace, J. R., Heat Transer in Packed Beds: Experimental Evaluation o One-Phase Water Flow, Brazilian J. o Chemical Engineering, 21 (2004), 1, pp [5] Teplitskii, Y. S., Heat Exchange in a Tube Flled with Granular Bed, J. o Engineering Physics and Thermophysics, 77 (2004), 1, pp [6] Kaviany, M., Principles o Heat Transer in Porous Media, 2 nd ed., Springer, New York, USA, 1998 [7] Mahgoub, S. E., Forced Convection Heat Transer Over a Flat Plate in a Porous Medium, Ain Shams Engineering Journal, 4, (2013), 4, pp [8] Hellstrom, J. G. I., Lundstrom, T. S., Flow through Porous Media at Moderate Reynolds Number, Proceedings, Int. Scientiic Colloquium Modeling or Material Processing, Riga, 2006

12 2128 THERMAL SCIENCE, Year 2017, Vol. 21, No. 5, pp [9] Vaai, K., Handbook o Porous Media, 2 ed ed., Taylor and Francis, New York, USA, 2005 [10] Yuki, K., et al., Flow Visualization and Heat Transer Characteristics or Sphere-Packed Pipes, J. o Thermophysics and Heat Transer, 22 (2008), 4, pp [11] Orodu, O. D., et al., Experimental Study o Darcy and Non-Darcy Flow in Porous Media, Int. J. o Engineering and Technology, 2 (2012), 2, pp [12] Verma, N., Mewes, D., Lattice Boltzmann Methods or Simulation o Micro and Macro-Transport in a Packed Bed o Porous Adsorbents under Non-Isothermal Condition, Computers and Mathematics with Applications, 58 (2009), 5, pp [13] Peng, Y.-F., et al., Nested Cartesian Grid Method in Incompressible Viscous Fluid Flow, J. o Computational Physics, 229 (2010), 19, pp [14] Zdravkovich, M. M., Flow around Circular Cylinders, Vol. 1: Fundamentals, Oxord Science Publications, Oxord, UK, 1997 [15] Zdravkovich, M. M., Flow around Circular Cylinders, Vol. 2: Applications, Oxord Science Publications, Oxord, UK, 2002 [16] Tatsuno, M., et al., On the Stable Posture o a Triangular or a Square Cylinder about Its Central Axis in a Uniorm Flow., Fluid Dyn. Res., 6 (1990), 3-4, pp [17] Al-Sumaily, G. F., et al., Analysis o Forced Convection Heat Transer rom a Circular Cylinder Embedded in a Porous Medium, Int. J. o Thermal Sciences, 51 (2012), Jan., pp [18] Al-Sumaily, G. F., et al., The Eect o Porous Media Particle Size on Forced Convection rom a Circular Cylinder without Assuming Local Thermal Equilibrium between Phases, Int. J. o Heat and Mass Transer, 55 (2012), 13-14, pp [19] Kostic, Z. G., Oka, S. N., Fluid Flow and Heat Transer with Two Cylinders in Cross Flow, J. o Heat and Mass Transer, 15 (1972), 2, pp [20] Dehkordi, B. G., et al., Numerical Simulation o Flow over Two Circular Cylinders in Tandem Arrangement, J. o Hydrodynamics, 23 (2011), 1, pp [21] Koda, Y., Lien, F.-S., Aerodynamic Eects o the Early Three-Dimensional Instabilities in the Flow over One and Two Circular Cylinders in Tandem Predicted by the Lattice Boltzmann Method, Computers & Fluids, 74 (2013), Mar., pp [22] Shyam, R., Chhabra, R. P., Eect o Prandtl Number on Heat Transer rom Tandem Square Cylinders Immersed in Power-Law Fluids in the Low Reynolds Number Regime, International Journal o Heat and Mass Transer, 57 (2013), 2, pp [23] Nield, D. A., Bejan, A., Convection in Porous Media, 3 rd ed., Springer Science, Business Media, New York, USA, 2006 [24] Dullien, F. A., Media Fluid Transport and Pore Structure, Academic Press, New York, USA, 1979 [25] Wakao, N., et al., Eect o Fluid Dispersion Coeicients on Particle-to-Fluid Heat Transer Coeicients in Packed Beds-Correlation o Nusselt Numbers, Chem. Eng. Sci., 34 (1979), 3, pp [26] Ergun, S., Fluid Flow through Packed Columns, Chem. Eng. Prog. 48 (1952), 2, pp [27] Zehner, P., Schluender, E. U., Thermal Conductivity o Granular Materials at Moderate Temperatures, Chem. Ing. Tech., 42 (1970), 14, pp [28] Wakao, N., Kaguei, S., Heat and Mass Transer in Packed Beds, Gordon and Breach, Philadelphia, Penn., USA, 1982 [29] ***, ANSYS Fluent Tutorial Guide, Release 15.0, (10), 2013, pp [30] Nasr, K., et al., Experimental Investigation on Forced Convection Heat Transer rom a Cylinder Embedded in a Packed Bed, J. Heat Transer 116 (1994), 1, pp [31] Cheng, P., Mixed Convection about a Horizontal Cylinder and a Sphere in a Fluid Saturated Porous Medium, Int. J. Heat Mass Transer 25, (1982), 8, pp Paper submitted: March 7, 2015 Paper revised: April 20, 2015 Paper accepted: May 19, Society o Thermal Engineers o Serbia. Published by the Vinča Institute o Nuclear Sciences, Belgrade, Serbia. This is an open access article distributed under the CC BY-NC-ND 4.0 terms and conditions.