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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Imprimir: 2152-5102
ISSN On-line: 2152-5110

Volumes:
Volume 46, 2019 Volume 45, 2018 Volume 44, 2017 Volume 43, 2016 Volume 42, 2015 Volume 41, 2014 Volume 40, 2013 Volume 39, 2012 Volume 38, 2011 Volume 37, 2010 Volume 36, 2009 Volume 35, 2008 Volume 34, 2007 Volume 33, 2006 Volume 32, 2005 Volume 31, 2004 Volume 30, 2003 Volume 29, 2002 Volume 28, 2001 Volume 27, 2000 Volume 26, 1999 Volume 25, 1998 Volume 24, 1997 Volume 23, 1996 Volume 22, 1995

International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v37.i1.30
pages 31-41

The Onset of Heat Transfer in Multiple Layers

Salah Abd El-Aziem El-Kholy
Department of Mathematics, Faculty of Science, Menoufia University Shebin El-Kom, Egypt
Rama Subba Reddy Gorla
Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44115 USA; Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA; Department of Mechanical & Civil Engineering, Purdue University Northwest, Westville, IN 46391, USA

RESUMO

The onset of convection in a system consisting of a horizontal fluid layer and a layer of porous media saturated with the same fluid, with heating from below, are considered. The two surfaces are rigid. A solution is obtained under parallel flow assumption for constant-flux thermal boundary conditions for which the onset of cellular convection occurs. The critical Rayleigh number and Nusselt number depend on the depth ratio η, the thermal conductivity ratio k, and the Darcy number Da. Results are given for a range of values of each of the governing parameters. The results are compared to limiting cases of the problem for standard terrestrial conditions or microgravity and are found to be in good agreement.

Referências

  1. Horton, F. T. and Rogers, C. W., Convection Currents in a Porous Medium.

  2. Lapwood, E. R., Convection of a Fluid in a Porous Medium.

  3. Cheng, P., Heat Transfer in Geothermal Systems.

  4. Caltagirone, J. P., Convection in a Porous Medium.

  5. Nield,D. A., Onset of Convection in a Fluid Layer Overlying a Layer of a Porous Layer.

  6. Nield, D. A., The Boundary Correction for the Rayleigh-Darcy Problem: Limitations of the Brinkman Equation.

  7. Pillastsis, G., Tasilm, M. E., and Narusawa, U., Thermal Instability of a Fluid-Saturated Porous Medium Bounded by Thin Fluid Layers.

  8. Vasseur, P., Wang, C. H., and Sen, M., Thermal Instability and Natural Convection in a Fluid Layer Over a Porous Substrate.

  9. Nield, D. A. and Bejan, A., Convection in Porous Media.

  10. Cheng, P., Similarity Solutions for Mixed Convection from Horizontal Impermeable Surfaces in Saturated Porous Media.

  11. Combarnous, M. A. and Bories, S. A., Hydrothermal Convection in Saturated Porous Media.

  12. Horne, R. N. and Caltagirone, J.-P., On the Evolution of Thermal Disturbances during Natural Convection in a Porous Medium.

  13. Springer, J., Shape-Derived Anisotropy Directions in Quadrangle and Brick Finite Elements.


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