Transient Convective Heat Transfer in Porous Media

Ruben D’Rose (), Mark Willemsz and David Smeulders
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Ruben D’Rose: Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Mark Willemsz: Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
David Smeulders: Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Mathematics, 2023, vol. 11, issue 21, 1-12

Abstract: In this study, several methods to analyze convective heat transfer in a porous medium are presented and discussed. First, the method of Fourier was used to obtain solutions for reduced temperatures θ s and θ f . The results showed an exponentially decaying propagating temperature front. Then, we discuss the method of integration that was presented earlier by Schumann. This method makes use of a transformation of variables. Thirdly, the system of partial differential equations was directly solved with the Finite Difference method, of which the result showed good agreement with the Fourier solutions. For the chosen Δ τ and Δ ξ , the maximum error for θ f = 3.7 % . The maximum error for θ s for the first ξ and first τ is large (36%) but decays rapidly. The problem was extended by adding a linear heat source term to the solid. Again, making use of the change in variables, analytical solutions were derived for the solid and fluid phases, and corrections to the previous literature were suggested. Finally, results obtained from a numerical model were compared to the analytical solutions, which again showed good agreement (maximum error of 6%).

Keywords: mathematical model; numerical method; heat transfer (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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