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Analytical solutions for unsteady free convection in porous media

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Abstract

Analytic solutions for two of the similarity cases identified by Johnson and Cheng (1978) for the unsteady free-convection boundary-layer flow over an impermeable vertical flat plate adjacent to a fluid saturated porous medium are given in the present paper. These are the solutions corresponding to an exponential (e sup a 2 t sup) and a power-law (t m) variation of the surface temperature, respectively. They represent exact solutions for doubly infinite plates and approximate solutions for semi-infinite plates. In the latter cases their validity is restricted to the so-called `conduction regime' of the flow. It is shown that in the power law case, physical solutions only exist in the range m>−1 of the temperature exponent and they can be expressed in terms of Kummer's confluent hypergeometric functions. For m ≥ 0 exponentially decaying unique solutions were found, while in the range −1<m<0 both exponentially and algebraically decaying multiple solutions occur. The origin of the multiple solutions as well as the feasibility conditions of all the above mentioned solutions is discussed in detail.

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Author notes

  1. I. Pop

    Present address: Faculty of Mathematics, University of Cluj, R-3400, Cluj, CP 253, Romania

Authors and Affiliations

  1. Chair of Physics of Buildings, Institute of Building Technology, Swiss Federal Institute of Technology (ETH) Zürich, CH-8093, Zürich, Switzerland

    E. Magyari & B. Keller

  2. Department of Aerodynamics and Fluid Mechanics, Brandenburg Technical University Cottbus, Universitätsplatz 3, D-030044, Cottbus, Germany

    I. Pop

Authors
  1. E. Magyari
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  2. I. Pop
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  3. B. Keller
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Magyari, E., Pop, I. & Keller, B. Analytical solutions for unsteady free convection in porous media. Journal of Engineering Mathematics 48, 93–104 (2004). https://doi.org/10.1023/B:ENGI.0000011914.16863.06

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  • DOI: https://doi.org/10.1023/B:ENGI.0000011914.16863.06

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