AM  Vol.2 No.8 , August 2011
Free Convection Flow between Vertical Plates Moving in Opposite Direction and Partially Filled with Porous Medium
ABSTRACT
The laminar fully developed free-convection flow in a channel bounded by two vertical plates, partially filled with porous matrix and partially with a clear fluid, has been discussed when both the plates are moving in opposite direction. Two regions are coupled, by equating the velocity and shear stress at the interface. The momentum transfer in porous medium has been described by the Brinkman-extended Darcy model. The affect of Darcy number on flow velocity has been discussed in fluid region, interface region and porous medium with the help of graphs. Analytic method has been adopted to obtain the expressions of velocity and temperature. The skin-friction component has also been determined and presented with the help of tables.

Cite this paper
nullU. Gupta, A. Jha and R. Chaudhary, "Free Convection Flow between Vertical Plates Moving in Opposite Direction and Partially Filled with Porous Medium," Applied Mathematics, Vol. 2 No. 8, 2011, pp. 935-941. doi: 10.4236/am.2011.28128.
References
[1]   G. S. Beavers and D. D. Joseph, “Boundary Condition at a Naturally Permeable Wall,” The Journal of Fluid Mechanics, Vol. 30, 1967, pp. 197-207. doi:10.1017/S0022112067001375

[2]   G. I. Taylor, “A Model for the Boundary Conditions of a Porous Material Part 1,” The Journal of Fluid Mechanics, Vol. 49, No. 2, 1971, pp. 319-326. doi:10.1017/S0022112071002088

[3]   S. Richardson, “A Model for the Boundary Conditions of a Porous Material Part 2,” The Journal of Fluid Mechanics, Vol. 49, No. 2, 1971, pp. 327-336. doi:10.1017/S002211207100209X

[4]   K. Vafai and S. J. Kim, “Fluid Mechanics of the Interface Region between a Porous Medium and a Fluid Layer: An Alexact Solution,” International Journal of Heat Fluid Flow, Vol. 11, No. 3, 1990, pp. 254-256. doi:10.1016/0142-727X(90)90045-D

[5]   K. Vafai and S. J. Kim, “On the Limitation of the Brinkman-Forchheimer-Extended Darcy Equation,” International Journal of Heat Fluid Flow, Vol. 16, 1995, pp. 11-15. doi:10.1016/0142-727X(94)00002-T

[6]   A. V. Kuznetsov, “Thermal Nonequilibrium Forced Convection in Porous Media,” In: D. B. Inghan and I. Pop, Eds., Transport Phenomena in Porous Media, Elsevier, Oxford, 1998, pp. 103-129.

[7]   B. Alazmi and K. Vafai, “Analysis of Fluid Flow and Heat Transfer Interfacial Conditions between a Porous Medium and a Fluid Layer,” International Journal of Heat Mass Transfer, Vol. 44, No. 9, 2001, pp. 1735-1749. doi:10.1016/S0017-9310(00)00217-9

[8]   J. J. Valencia-Lopez and J. A. Ochoa-Tapia, “A Study of Buoyancy-Driven Flow in a Confined Fluid Overlying a Porous Layer,” International Journal of Heat Mass Transfer, Vol. 44, No. 24, 2001, pp. 4725-4736. doi:10.1016/S0017-9310(01)00105-3

[9]   D. A. Nield and A. Bejan, “Convection in Porous Media,” New York, Springer-Verlag, 2006.

[10]   M. Kaviany, “Principles of Heat Transfer in Porous Media,” Springer-Verlag, New York, 1991.

[11]   K. Vafai and C. L. Tien, “Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media,” International Journal of Heat Mass Transfer, Vol. 24, No. 2, 1981, pp. 195-203. doi:10.1016/0017-9310(81)90027-2

[12]   M. Kaviany, “Laminar Flow through a Porous Channel Bounded by Isothermal Parallel Plates,” International Journal of Heat Mass Transfer, Vol. 28, No. 4, 1985, pp. 851-858.

[13]   N. Rudriah and S. T. Nagraj, “Natural Convection through Vertical Porous Stratum,” International Journal of Engineering Science, Vol. 15, 1977, pp. 589-600. doi:10.1016/0020-7225(77)90055-6

[14]   C. Backermann, R. Viskanta and S. Ramadhyani, “Natural Convection in Vertical Enclosures Containing Simultaneously Fluid and Porous Layers,” The Journal of Fluid Mechanics, Vol. 186, 1988, pp. 257-284. doi:10.1017/S0022112088000138

[15]   A. Khalili, I. S. Shivakumara and S. P. Suma, “Convective Instability in Superposed Fluid and Porous Layers with Vertical Throughflow,” Transactions on Porous Media, Vol. 51, 2003, pp. 1-18. doi:10.1023/A:1021246000885

[16]   T. Paul, B. K. Jha and A. K. Singh, “Free- Convection between Vertical Walls Partially Filled with Porous Medium,” Heat and Mass Transfer, Vol. 33, No. 5-6, 1998, pp. 515-519. doi:10.1007/s002310050223

[17]   A. K. Singh, T. Paul and G. R. Thorpe, “Natural Convection Due to Heat and Mass Transfer in a Composite System,” Heat and Mass Transfer, Vol. 35, 1999, pp. 39-48. doi:10.1007/s002310050296

[18]   H. P. G. Darcy, “Les Fontaines Publiques de la villa de Dijon,” Dalmont, Paris, 1856.

 
 
Top