Natural Convection in a Cavity Partially Filled with a Vertical Porous Medium

Abstract:

The shear stress jump boundary condition that must be imposed at an interface between a porous medium and a free fluid in an enclosure is investigated. Two-domain approach is founded and finite element method is used to solve the problem. Three stress jump coefficients 0, 1, -1 are analyzed for different Rayleigh number, permeability and thickness of porous layer. Variation of Maximum stream function and Nusselt number show stronger convection and heat transfer when the stress jump coefficient is positive. There is little distinctive in flow and heat transfer when the value of coefficient is equal to 0 and -1.

• Periodical: Advanced Materials Research (Volume 321)
• Pages: 15-18
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.321.15
• Online since: August 2011
• Authors: Fang Liu, Bao Ming Chen
• Keywords: Interfacial Boundary Condition, Natural Convection, Porous/fluid Domain, Stress Jump

References

[1] G. S. Beavers, D.D. Joseph, Boundary Conditions at a Naturally Permeable Wall[J], J. Fluid Mech, 30(1), 197–207, (1967).

DOI: 10.1017/s0022112067001375

[2] J. A. Ochoa-Tapia, S. Whitaker, Momentum Transfer at the Boundary Between a Porous Medium and a Homogeneous Fluid-I. Theoretical Development[J], Int. J. Heat Mass Transfer, 38(4), 2635-2646, (1995).

DOI: 10.1016/0017-9310(94)00346-w

[3] J. A. Ochoa-Tapia, S. Whitaker, Momentum Transfer at the Boundary between a Porous Medium and a Homogeneous Fluid-II. Comparison with Experiment[J], Int. J. Heat Mass Transfer, 38(14), 2647-2655, (1995).

DOI: 10.1016/0017-9310(94)00347-x

[4] M. Khakpour, K. Vafai, Analysis of Transport Phenomena within PEM Fuel Cells–An Analytical Solution[J], Int. J. Heat Mass Transfer, 51(15-16), 3712–3723, (2008).

DOI: 10.1016/j.ijheatmasstransfer.2007.12.013

[5] A. C. Baytas, A. F. Baytas, D. B. Ingham, I. Pop, Double Diffusive Natural Convection in an Enclosure Filled with a Step Type Porous Layer: Non-Darcy Flow[J], International Journal of Thermal Sciences, 48(4), 665–673, (2009).

DOI: 10.1016/j.ijthermalsci.2008.06.001

[6] H. C. Chan, W. C. Huang, J. M. Leu, C. J. Lai, Macroscopic Modeling of Turbulent Flow over a Porous Medium[J], Int. J. Heat and Fluid Flow, 28(5), 1157–1166, (2007).

DOI: 10.1016/j.ijheatfluidflow.2006.10.005

[7] C. Deng, D. M. Martinez, Viscous Flow in a Channel Partially Filled with a Porous Medium and Withwall Suction[J], Chemical Engineering Science, 60(2), 329–336, (2005).

DOI: 10.1016/j.ces.2004.08.010

[8] H. Tan, K. M. Pillai, Finite Element Implementation of Stress-jump and Stress-continuity Conditions at Porous-medium[J], Clear-fluid Interface, Computers & Fluids, 38(6), 1118-1131, (2009).

DOI: 10.1016/j.compfluid.2008.11.006

[9] M. Mishra, A. R. Rao, Peristaltic Transport in a Channel with a Porous Peripheral Layer: Model of a Flow in Gastrointestinal Tract[J], Journal of Biomechanics, 38(4), 779–789, (2005).

DOI: 10.1016/j.jbiomech.2004.05.017

[10] X. B. Chen, P. Yu, Y. Sui, S. H. Winots, H. T. Low, Natural convection in a cavity filled with porous layers on the top and bottom walls[J], Transp Porous Med, 78:, 259-276, (2009).

DOI: 10.1007/s11242-008-9300-2