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

ISSN 印刷: 2152-5102
ISSN オンライン: 2152-5110

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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

要約

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.

参考

  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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