Transient and non-Darcian effects on natural convection flow in a vertical channel partially filled with porous medium: Analysis with Forchheimer-Brinkman extended Darcy model

International Journal of Heat and Mass Transfer

Volumn 54, Issue 5-6, 2011, Pages 1111-1120

  Singh, Atul Kumar ^a   Agnihotri, Pratibha ^a   Singh, N P ^b   Singh, Ajay Kumar ^c  

^a VSSD College Kanpur   (India)

^b Rama Institute of Engineering and Technology   (India)

^c C L Jain College   (India)

Author keywords

Natural convection; Porous medium; Transient and non Darcian effects; Vertical channel

Indexed keywords

APPROXIMATE SOLUTION; CHANNEL WALL; DARCY MODEL; DARCY NUMBER; KINEMATIC VISCOSITY; LAMINAR NATURAL CONVECTION; MOMENTUM EQUATION; NATURAL CONVECTION FLOW; NUMERICAL VALUES; PHYSICAL PARAMETERS; POROUS MEDIUM; RATE OF HEAT TRANSFER; THERMAL CONDUCTIVITY RATIO; THERMAL ENERGY EQUATION; VELOCITY FIELD; VERTICAL CHANNELS;

HEAT FLUX; MIXED CONVECTION; PERTURBATION TECHNIQUES; POROUS MATERIALS;

NATURAL CONVECTION;

EID: 78650605525     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2010.11.011     Document Type: Article

References (47)

1. H.I. Ene, and D. Polisevski Thermal Flow in Porous Media 1987 D. Reidel Dordrecht, The Netherlands
2. D.A. Nield, and A. Bejan Convection in Porous Media 1998 Springer New York
3. A. Bejan Heat Transfer 1993 John Wiley & Sons Inc. New York
4. A. Nakayama PC-Aided Numerical Heat Transfer and Convective Flow 1995 CRC Press Tokyo
5. M. Kaviany Principles of Heat Transfer in Porous Media second ed. 1995 Springer New York
6. H. Darcy Les Fontaines Publiques de la Ville de Dijon 1856 Victor Dalmont Paris
7. S. Irmay On the theoretical derivation of Darcy and Forchheimer formulas Eos, Trans. AGU 39 1958 702 707
8. G.S. Beavers, and D.D. Joseph Boundary conditions at a naturally permeable wall J. Fluid Mech. 30 1967 192 203
9. G.I. Taylor A model for the boundary condition of a porous material, Part-I J. Fluid Mech. 49 1971 319 326
10. S. Richardson A model for the boundary condition of a porous material. Part-II J. Fluid Mech. 49 1971 327 336
11. G. Neale, and W. Nader Practical significance of Brinkman's extension of Darcy law: coupled parallel flows within a channel and a boundary porous medium Can. J. Chem. Eng. 52 1974 475 478
12. C.W. Somerton, and I. Catton On the stability of superposed porous and fluid layers ASME J. Heat Transfer 104 1982 160 165
13. P. Cheng, and I. Pop Transient free convection about a vertical flat plate imbedded in a porous medium Int. J. Eng. Sci. 22 1984 253 264
14. D. Poulikakos, and M. Kazmierczak Forced convection in a duct partially filled with a porous material ASME J. Heat Transfer 109 1987 653 662
15. K.J. Renken, and D. Poulikakos Experiment and analysis of forced convective heat transport in a packed bed of spheres Int. J. Heat Mass Transfer 31 1988 1399 1408
16. B.C. Chandrasekhera, and P. Nagaraju Composite heat transfer in the case of a steady laminar flow of a gray fluid with small optical density past a horizontal plate embedded in a saturated porous medium Warme-Stoffubertrag. 19 1988 343 352
17. K. Vafai, and S.J. Kim Forced convection in a channel filled with a porous medium: An exact solution ASME J. Heat Transfer 111 1989 1103 1106
18. K. Vafai, and S.J. Kim Analysis of surface enhancement by a porous substrate ASME J. Heat Transfer 112 1990 700 706
19. A. Nakayama, T. Kokudai, and H. Koyama Forchheimer free convection over a non-isothermal body of arbitrary shape in a saturated porous medium ASME J. Heat Transfer 112 1990 511 515
20. N. Kladias, and V. Prasad Flow transitions in buoyancy-induced non-Darcy convection in a porous medium heated from below ASME J. Heat Transfer 112 1990 675 684
21. N. Kladias, and V. Prasad Experimental verification of Darcy-Brinkman-Forchheimer model for natural convection in porous media AIAA J. Thermophys. Heat Transfer 5 1991 560 576
22. D.W. Ruth, and H. Ma On the derivation of the Forchheimer equation by means of averaging theorem Transport Porous Media 7 1992 255 264
23. H. Ma, and D.W. Ruth The microscopic analysis of high Forchheimer number in porous media Transport Porous Media 13 1993 139 160
24. A.V. Shenoy Darcy-Forchheimer natural, forced and mixed convection heat transfer in non-Newtonian power law fluid-saturated porous medium Transport Porous Media 11 1993 219 241
25. K. Vafai, and S.J. Kim On the limitations of the Brinkman-Forchheimer Darcy equation Int. J. Heat Fluid Flow. 16 1995 11 15
26. P.M. Knupp, and J.L. Lage Generalization of the Forchheimer-extended Darcy flow model to the tensor permeability case via a variational principle J. Fluid Mech. 299 1995 97 104
27. D.R. Marpu Forchheimer and Brinkman extended Darcy flow model on natural convection in a vertical cylindrical porous medium Acta Mech. 109 1995 41 48
28. A.K. Singh, and G. Thorpe Natural convection in a confined fluid overlying a porous layer: a comparison study of different models Ind. J. Pure Appl. Math. 23 1995 81 95
29. D.A. Nield The effect of temperature-dependent viscosity on the onset of convection in a saturated porous medium ASME J. Heat Transfer 118 1996 803 805
30. A.V. Kuzentsov Influence of the stress jump condition at the porous medium/clear fluid interface on a flow at a porous wall Int. Comm. Heat Mass Transfer 24 1997 401 410
31. A. Nakayama A unified treatment of Darcy-Forcheimer boundary layer flows D.B. Ingham, I. Pop, Transport Phenomena in Porous Media 1998 Elsevier 179 204
32. T. Paul, A.K. Singh, and G.R. Thorpe Transient natural convection flow in a vertical channel partially filled with a porous medium Math. Eng. 7 1999 441 455
33. M.S. Malashetty, J.C. Umavathi, and J.P. Kumar Two fluid flow and heat transfer in an inclined channel containing porous and fluid layers Heat Mass Transfer 40 2004 871 876
34. Y.C. Chen Non-Darcy flow stability of mixed convection in a vertical channel filled with a porous medium Int. J. Heat Mass Transfer 47 2004 1257 1266
35. K.C. Leong, and L.W. Jin Heat transfer of oscillating and steady flows in a channel filled with porous medium Int. Comm. Heat Mass Transfer 31 2004 63 72
36. Ajay Kumar Singh, and H.S. Takhar Free convection flow of two immiscible viscous liquids through parallel permeable beds: use of Brinkman model Int. J. Fluid Mech. Res. 32 2005 635 660
37. H. Beji, and P. Gobin The effect of thermal dispersion on natural dispersion heat transfer in porous media Numer. Heat Transfer 23A 1992 483 500
38. D. Mishra, and A. Sarkar A comparative study of porous media models in a differentially heated square cavity using a finite element method Int. J. Numer. Methods Heat Fluid Flow 5 1995 735 752
39. S. Whitaker The Forchheimer equation: a theoretical development Transport Porous Media 25 1996 27 61
40. S. Ergun Fluid flow through packed columns Chem. Eng. Prog. 48 1952 89 94
41. A.K. Singh, H.R. Gholami, and V.M. Soundalgekar Transient free-convection flow between two vertical parallel plates Heat Mass Transfer 31 1996 329 332
42. T. Paul, B.K. Jha, and A.K. Singh Free convection between vertical walls partially field with porous medium Heat Mass Transfer 33 1998 515 519
43. K. Vafai, and R. Thiyagaraja Analysis of flow and heat transfer at the interface region of the porous medium Int. J. Heat Mass Transfer 30 1987 1391 1405
44. A. Amiri, and K. Vafai Analysis of dispersion effects and non-thermal equilibrium, non-Darcian, variable porosity incompressible flow through porous media Int. J. Heat Mass Transfer 37 1994 939 954
45. A. Amiri, K. Vafai, and T.M. Kuzay Effects of boundary conditions on non-Darcian heat transfer through porous media and experimental comparisons Numer. Heat Transfer. Part A 27 1995 651 664
46. K. Vafai Hand Book of Porous Media 2000 Marcel Deckker New York
47. K. Vafai Hand Book of Porous Media second ed. 2005 Taylor and Francis New York