The modeling of viscous dissipation in a saturated porous medium

Journal of Heat Transfer

Volumn 129, Issue 10, 2007, Pages 1459-1463

  Nield, D A ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Boussinesq approximation; Forced convection; Natural convection; Porous media; Pressure work; Scaling; Viscous dissipation

Indexed keywords

APPROXIMATION THEORY; FORCED CONVECTION; MATHEMATICAL MODELS; NATURAL CONVECTION; POROUS MATERIALS; VISCOUS FLOW;

BOUSSINESQ APPROXIMATION; PRESSURE FORCE; VISCOUS DISSIPATION;

HEAT TRANSFER;

APPROXIMATION THEORY; FORCED CONVECTION; HEAT TRANSFER; MATHEMATICAL MODELS; NATURAL CONVECTION; POROUS MATERIALS; VISCOUS FLOW;

EID: 36749087067     PISSN: 00221481     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2755069     Document Type: Review

References (37)

1. Nield, D. A., and Bejan, A., 2006, Convection in Porous Media, 3rd ed., Springer, New York.
2. Magyari, E., and Keller, B., 2003, "The Opposing Effect of Viscous Dissipation Allows for a Parallel Free Convection Boundary-Layer Flow Along a Cold Vertical Flat Plate," Transp. Porous Media, 51, pp. 227-230.
3. Magyari, E., and Keller, B., 2003, "Effect of Viscous Dissipation on a Quasi-Parallel Free Convection Boundary-Layer Flow Over a Vertical Plate in a Porous Medium," Transp. Porous Media, 51, pp. 231-236.
4. Magyari, E., and Keller, B., 2003, "Buoyancy Sustained by Viscous Dissipation," Transp. Porous Media, 53, pp. 105-115.
5. Magyari, E., and Keller, B., 2004, "Backward Free Convection Boundary Layers in Porous Media," Transp. Porous Media, 55, pp. 285-300.
6. Magyari, E., and Rees, D. A. S., 2006, "Effect of Viscous Dissipation on the Darcy Free Convection Boundary-Layer Flow Over a Vertical Plate With Exponential Distribution in a Porous Medium," Fluid Dyn. Res., 38, pp. 405-429.
7. Magyari, E., Pop, I., and Keller, B., 2003, "Effect of Viscous Dissipation on the Darcy Forced-Convection Flow Past a Plane Surface," J. Porous Media, 6, pp. 111-122.
8. Rees, D. A. S., Magyari, E., and Keller, B., 2003, "The Development of the Asymptotic Viscous Dissipation Profile in a Vertical Free Convective Boundary Layer Flow in a Porous Medium," Transp. Porous Media, 53, pp. 347-355.
9. Rees, D. A. S., Magyari, E., and Keller, B., 2005, "Vortex Instability of the Asymptotic Dissipation Profile in Porous Media," Transp. Porous Media, 61, pp. 1-14.
10. Nield, D. A., Kuznetsov, A. V., and Xiong, M., 2003, "Thermally Developing Forced Convection in a Porous Medium: Parallel Plate Channel With Walls at Uniform Temperature, With Axial Conduction and Viscous Dissipation Effects," Int. J. Heat Mass Transfer, 46, pp. 643-651.
11. Kuznetsov, A. V., Xiong, M., and Nield, D. A., 2003, "Thermally Developing Forced Convection in a Porous Medium: Circular Duct With Walls at Constant Temperature, With Longitudinal Conduction and Viscous Dissipation Effects," Transp. Porous Media, 53, pp. 331-345.
12. Nield, D. A., Kuznetsov, A. V., and Xiong, M., 2004, "Effects of Viscous Dissipation and Flow Work on Forced Convection in a Channel Filled by a Saturated Porous Medium," Transp. Porous Media, 56, pp. 351-367.
13. Ranjbar-Kani, A. A., and Hooman, K., 2004, "Viscous Dissipation Effects on Thermally Developing Forced Convection in a Porous Medium: Circular Duct With Isothermal Wall," Int. Commun. Heat Mass Transfer, 31, pp. 897-907.
14. Hooman, K., and Gorji-Bandry, M., 2005, "Laminar Dissipative Flow in a Porous Channel Bounded by Isothermal Parallel Plates," Appl. Math. Mech., 26, pp. 587-591.
15. Hooman, K., Pourshaghaghy, A., and Ejlali, A., 2006, "Effects of Viscous Dissipation on Thermally Developing Forced Convection in a Porous Saturated Circular Tube With an Isoflux Wall," Appl. Math. Mech., 27, pp. 683-694.
16. Hooman, K., and Gurgenti, H., 2007, "Effects of Viscous Dissipation and Boundary Conditions on Forced Convection in a Channel Occupied by a Saturated Porous Medium" Transp. Porous Media, in press.
17. Ene, H. J., and Sanchez-Palencia, E., 1982, "On Thermal Equation for Flow in Porous Media," Int. J. Eng. Sci., 20, pp. 623-630.
18. Nield, D. A., 2000, "Resolution of a Paradox Involving Viscous Dissipation and Nonlinear Drag in a Porous Medium," Transp. Porous Media, 41, pp. 349-357.
19. Narasimhan, A., and Lage, J. L., 2005, "Variable Viscosity Forced Convection in Porous Medium Channels," Handbook of Porous Media, 2nd ed., K. Vafai, ed., Taylor & Francis, New York, pp. 195-234.
20. Al-Hadhrami, A. K., Elliot, L., and Ingham, D. B., 2003, "A New Model for Viscous Dissipation in Porous Media Across a Range of Permeability Values," Transp. Porous Media, 53, pp. 117-122.
21. Nield, D. A., 2004, "Comments on 'A New Model for Viscous Dissipation in Porous Media Across a Range of Permeability Values'," Transp. Porous Media, 55, pp. 253-254.
22. Kuznetsov, A. V., Xiong, M., and Nield, D. A., 2003, "Thermally Developing Forced Convection in a Porous Medium: Circular Duct With Walls at Constant Temperature, With Longitudinal Conduction and Viscous Dissipation Effects," Transp. Porous Media, 53, pp. 331-345.
23. Gerritsen, M. G., Chen, T., and Chen, Q., 2005, private communication.
24. Bejan, A., 1984, Convection Heat Transfer, Wiley, New York.
25. Nield, D. A., 2006, "A Note on a Brinkman-Brinkman Forced Convection Problem," Transp. Porous Media, 64, pp. 185-188.
26. de Vahl Davis, G., 1983, "Natural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution," Int. J. Numer. Methods Fluids, 3, pp. 249-264.
27. Costa, V. A. F., 2006, "On Natural Convection in Enclosures Filled With Fluid-Saturated Porous Media Including Viscous Dissipation," Int. J. Heat Mass Transfer, 49, pp. 2215-2226.
28. Costa, V. A. F., 2005, "Thermodynamics of Natural Convection in Enclosures With Viscous Dissipation," Int. J. Heat Mass Transfer, 48, pp. 2333-2341.
29. Pons, M., and le Quéré, P., 2095, "An Example of Entropy Balance in Natural Convection, Part 1: The Usual Boussinesq Equations," C. R. Mec., 333, pp. 127-132.
30. Pons, M., and le Quéré, R, 2005, "An Example of Entropy Balance in Natural Convection, Part 2: The Thermodynamic Boussinesq Equations," C. R. Mec., 333, pp. 133-138.
31. Gray, D. G., and Giorgini, A., 1976, "The Validity of the Boussinesq Approximation for Liquids and Gases," Int. J. Heat Mass Transfer, 19, pp. 545-551.
32. Breugem, W. P., and Rees,. D, A. S., 2006, "A Derivation of the Volume-Averaged Boussinesq Equations for Flow in Porous Media With Viscous Dissipation," Transp. Porous Media, 63, pp. 1-12.
33. Chandrasekhar, S., 1961, Hydrodynamic and Hydromagnetic Stability, Clarendon, Oxford, p. 34.
34. Bejan, A., 1982, Entropy Generation Though Heat and Fluid Flow, Wiley, New York, pp. 35-36.
35. Bejan, A., 1988, Advanced Engineering Thermodynamics, Wiley, New York, p. 136.
36. Nield, D. A., 1982, "Onset of Convection in a Porous Layer Saturated by an Ideal Gas," Int. J. Heat Mass Transfer, 25, pp. 1605-1606.
37. Mallinson, G., Moyle, K., and Norris, S., 2004, "Volumetric, Methods for Evaluating Irreversible Energy Losses and Entropy Production With Application to Bioengineering Flows," Proceedings of the ICHMT. International Symposium on Advances in Computational Heat Transfer, Norway, Apr. 19-24, Paper No. CHT-04-262.