Non-Darcian Mixed Convection Flow in Vertical Composite Channels with Hybrid Boundary Conditions

Document Type: Research Paper

Authors

Department of Chemical and Petroleum Engineering, Sharif University of Technology

Abstract

In this article, the effects of viscous dissipation and inertial force on the velocity and temperature distributions of the mixed convection laminar flow in a vertical channel partly filled with a saturated porous medium have been studied. In this regard, the Brinkman–Forchheimer extended Darcy model was adopted for the fluid flow in the porous region. In addition, three different viscous dissipation models with isoflux-isothermal boundary conditions were applied. To determine the velocity and temperature distributions for both the regions, the coupled non-linear governing equations were solved using two parameter perturbation and numerical methods. Moreover, the results of the numerical method were validated against those predicted by the perturbation method for small values of the dimensionless perturbation parameters. Furthermore, the results obtained for both regions were compared in terms of Grashof, Reynolds, Forchheimer, and Brinkman numbers. The predicted results clearly indicate that the type of viscous dissipation model has a significant effect on the temperature and velocity distributions.

Keywords


[4] Bejan A., “Convection Heat Transfer”, Wiley: New York, 2004.

[5] Lee D.Y., Vafai K., “Analytical Characterization and Conceptual Assessment of Solid and Fluid Temperature Differentials in Porous Media”, Int. J. Heat Mass Transfer 1999, 42, 423.

[6] Alazmi, B.; Vafai, K. “Analysis of Variants Within the Porous Media Transport Models”, ASME J. Heat Transfer 2000, 122, 303.

[7] Alazmi B., Vafai K., “Analysis of Fluid Flow and Heat Transfer Interfacial Conditions Between a Porous Medium and a Fluid Layer”, Int. J. Heat Mass Transfer 2001, 44, 1735.

[8] Kim S.J., Kim D., “Thermal Interaction at the Interface Between a Porous Medium and an Impermeable Wall”, ASME J. Heat Transfer 2001, 123, 527.

[9] Haji-Sheikh A., Vafai K., “Analysis of Flow and Heat Transfer in Porous Media Imbedded Inside Various-shaped Ducts”, Int. J. Heat Mass Transfer 2004, 47, 1889.

[10] Haji-Sheikh A., “Estimation of Average and Local Heat Transfer in Parallel Plates and Circular Ducts Filled with Porous Materials”, ASME J. Heat Transfer 2004, 126, 400.

[11] Haji-Sheikh A., “Fully Developed Heat Transfer to Fluid Flow in Rectangular Passages Filled with Porous Materials”, ASME J. Heat Transfer 2006, 128, 550.

[12] Hooman K., Merrikh A.A., “Analytical Solution of Forced Convection in a Duct of Rectangular Cross Section Saturated by a Porous Medium”, ASME J. Heat Transfer 2006, 128, 596.

[13] Nield D.A., Kuznetsov A.V., Xiong M., “Effects of Viscous Dissipation and Flow Work on Forced Convection in a Channel Filled by a Saturated Porous Medium”, Transport Porous Media 2004, 56, 351.

[14] Ranjbar-Kani A.A., Hooman K., “Viscous Dissipation Effects on Thermally Developing Forced Convection in a Porous Medium: Circular Duct with Isothermal Wall”, Int. Commun. Heat Mass Transfer 2004, 31, 897.

[15] Hooman K., Gurgenci H., “Effects of Viscous Dissipation and Boundary Conditions on Forced Convection in a Channel Occupied by a Saturated Porous Medium”, Transport Porous Media 2007, 68, 301.

[16] Hung Y.M., Tso C.P., “Temperature Variations of Forced Convection in Porous Media for Heating and Cooling Processes: Internal Heating Effect of Viscous Dissipation”, Transport Porous Media 2008, 75, 319.

[17] Umavathi J.C., Kumar J.P., Chamkha A.J., Pop I., “Mixed Convection in a Vertical PorousChannel”, Transport Porous Media 2005, 61, 315.

[18] Abu-Hijleh B.A., Al-Nimr M.A., “The Effects of the Local Inertial Term on the Fluid Flow in Channels Partially Filled With Porous Material”, Int. J. Heat Mass Transfer 2001, 4, 1565.

[19] Vafai K., Tien C.L., Boundary and Inertial Effects on Flow and Heat Transfer in Porous Media, Int. J. Heat Transfer 1981, 24, 195.

[20] Umavathi J.C., Kumar J.P., Chamkha A.J., Pop I., “Mixed Convection in a Vertical Porous Channel”, Transport Porous Media 2008, 75, 129.

[21] Barletta A., Magyari E., Pop I., Storesletten L. , “Unified Analytical Approach to the Darcy Mixed Convection with Viscous Dissipation in a Vertical Channel”, Int. J. Thermal Science 2008, 47, 408.

[22] Rajagopal K.R., Ruzicka M., Srinivasa A.R., “On the Oberbeck Approximations”, Math. Model Methods Appl. Sci. 1996, 16, 1157.

[23] Nield D.A., Bejan A., Convection in Porous Media; Springer: New York, 2006.

[24] Beckermann C., Viskanta R., Ramadhyani S., Natural Convection in Vertical Enclosures Containing Simultaneously Fluid and Porous Layers, J. Fluid Mech. 1988, 186, 257.

[25] Nield D.A., Modeling Fluid Flow in Saturated Porous Media and at Interfaces, In Transport Phenomena in Porous Media II; Ingham, D.B., Pop, I., Eds.; Pergamon: London, 2002, p 1.

[26] Al-Hadhrami A.K., Elliott L., Ingham D.B., “A New Model for Viscous Dissipation Across a Range of Permeability Values”, Transport Porous Media 2003, 53, 117.

[27] Magyari E., Rees D.A.S., Keller B., Effect of Viscous Dissipation on the Flow in Fluid Saturated Porous Media, In Handbook of Porous Media, Vafai K., Ed.; Taylor & Francis Group: New York, 2005, Chap. 9.

[28] Hajipour M., Molaei Dehkordi A., “Mixed Convection in a Vertical Channel Containing Porous and Viscous Fluid Regions with Viscous Dissipation and Inertial Effects: A Perturbation Solution”, ASME J. Heat Transfer, accepted for publication.

[29] Kumar J.P., Umavathi J.C., Biridar B.M., Mixed Convection of a Composite Porous Medium in a Vertical Channel with Asymmetric Wall Heating Conditions, J. Porous Media 2010, 13, 271.

[1] Malashetty M.S., Umavathi J.C., Prathap Kumar, J., Two Fluid Flow and Heat Transfer in an Inclined Channel Containing Porous and Fluid Layer. Heat and Mass Transfer, 2004, 40, 871.

[2] Bird R.B., Stewart W.E., Lightfoot E.N., Transport Phenomena, Wiley: New York, 2002.

[3] Tso, C.P., Mahulikar, S.P., The Use of the Brinkman Number for Single Phase Forced Convective Heat Transfer in Microchannels. Int. J. Heat Mass Transfer 1998, 41,1759.