Abstract
The mixed convection boundary-layer flow on a horizontal impermeable surface embedded in a saturated porous medium and driven by a local heat source is considered. Similarity solutions are obtained for specific outer flow variations and these are shown to have a solution only for parameter values greater than some critical value. When this is not the case the solution develops a singularity at a finite distance from the leading edge. The nature of this singularity is also discussed.
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References
Bejan, A., Convective heat transfer in porous media, In: S. Kakac, R. K. Shah and W. Aung (eds), Handbook of Single-Phase Convective Heat Transfer, Chapter 16, Wiley, New York, 1987.
Nield, D. A. and Bejan, A.: Convection in Porous Media., Springer, New York, 1992.
Nakayama, A., PC-Aided Numerical Heat Transfer and Convective Flow, CRC Press, Tokyo, 1995.
Kimura, S., Kiwata, T., Okajima, A. and Pop, I.: Conjugate natural convection in porous media, In: Adv. Water Res., special issue: Adv. Heat Transfer in Porous Media 1997 (in press).
Cheng, P. and Chang, I. D., Buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces, Int. J. Heat Mass Transfer 19(1976), 1267-1272
Merkin, J. H. and Zhang, G., On the similarity solutions for free convection in a saturated porous medium adjacent to impermeable horizontal surfaces, Warme-und Staffubertr. 25(1990), 179- 184.
Higuera, F. J. and Weidman, P. D., Natural convection beneath a downward facing heated plate in a porous medium, Eur. J. Mech. B/Fluids 14(1995), 29-40.
Chaudhary, M. A., Merkin, J. H. and Pop, I., Natural convection from a horizontal permeable surface in a porous medium-numerical and asymptotic solutions, Transport in Porous Media 22(1996), 327-3440.
Cheng, P., Similarity solutions for mixed convection from horizontal impermeable surfaces in saturated porous media, Int. J. Heat Mass Transfer 20(1977), 893-898.
Prasad, V., Lai, F.-C. and Kulacki, F. A., Mixed convection in horizontal porous layers heated from below, J. Heat Transfer 110(1988), 395-402.
Lai, F.-C. and Kulacki, F. A., The influence of surface mass flux on mixed convection from horizontal surfaces in a porous medium-variable surface heat flux, Int. J. Heat Mass Transfer 33(1990), 576-579.
Aldos, J. K., Chen, T. S. and Armaly, B. F., Non-similarity solutions for mixed convection from horizontal surfaces in a porous medium-variable surface heat flux, Int. J. Heat Mass Transfer 36(1993), 463-470.
Aldos, T. K., Chen, T. S. and Armaly, B. F., Non-similarity solutions for mixed convection from horizontal surfaces in a porous medium-variable wall temperature, Int. J. Heat Mass Transfer 36(1993), 471-477.
Daniels, P. G., A singularity in thermal boundary-layer flow on a horizontal surface, J. Fluid Mech. 242(1992), 419-440.
Merkin, J. H., Free convection above a uniformly heated horizontal circular disk, Int. J. Heat Mass Transfer 28(1985), 1157-1163.
Merkin, J. H., Free convection above a heated horizontal circular disk, J. Appl. Math. Phys. (ZAMP) 34(1983), 596-608.
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Merkin, J.H., Pop, I. Mixed Convection on a Horizontal Surface Embedded in a Porous Medium: the Structure of a Singularity. Transport in Porous Media 29, 355–364 (1997). https://doi.org/10.1023/A:1006556111769
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DOI: https://doi.org/10.1023/A:1006556111769