Abstract
This paper presents an analytical and numerical study of transient free convection from a horizontal surface that is embedded in a fluid-saturated porous medium. It is assumed that for time \(\bar \tau < 0\) steady state velocity and temperature fields are obtained in the boundary-layer which occurs due to a uniform flux dissipation rate q 1′′ on the surface. Then, at \(\bar \tau = 0\) the heat flux on the surface is suddenly changed to q 2′′ and maintained at this value for \(\bar \tau > 0\). Firstly, solutions which are valid for small and large \(\bar \tau \) are obtained. The full boundary-layer equations are then integrated step-by-step for the transient regime from the initial unsteady state (\(\bar \tau = 0\)) until such times at which this forward marching approach is no longer well posed. Beyond this time no valid solutions could be obtained which matched the final solution from the forward integration to the steady state profiles at large times \(\bar \tau \to \infty \).
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Harris, S.D., Ingham, D.B. & Pop, I. Transient Free Convection from a Horizontal Surface in a Porous Medium Subjected to a Sudden Change in Surface Heat Flux. Transport in Porous Media 39, 97–117 (2000). https://doi.org/10.1023/A:1006697816838
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DOI: https://doi.org/10.1023/A:1006697816838