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Transient Response of a Steady Vertical Flow which is Subjected to a Change in Surface Heat Flux in Porous Media

DOI: 10.1615/ICHMT.1996.TransientConvHeatTransf.500

Simon D. Harris
Rock Deformation Research, School of Earth Sciences, University of Leeds, Leeds, LS2 9JT, UK

Derek B. Ingham
Centre for CFD, Department of Applied Mathematical Studies, The University of Leeds, Leeds, LS2 9JT, UK; Energy-2050, Faculty of Engineering, University of Sheffield, Sheffield, S10 2TN, UK

Ioan Pop
Department of Applied Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania


This paper analyses the transient free convection from a vertical flat plate which is embedded in a fluid-saturated porous medium arising from a sudden change of the level of the constant uniform flux dissipation rate. From an analytical investigation of the governing boundary-layer equations, both a series solution which is valid at small values of the non-dimensional time and a solution which is valid at large times, when the transport of energy is steady, are derived. A numerical solution of the full boundary-layer equations is then obtained for the whole transient regime. Results are presented to illustrate the occurrence of transients from both small and large increases and decreases in the levels of the existing energy inputs.

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