Transient Convective Heat Transfer in Porous Media

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 theta s and theta 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 Delta tau and Delta xi, the maximum error for theta f=3.7%. The maximum error for theta s for the first xi and first tau 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%).

Automated summary

This study presents and discusses several methods for analyzing convective heat transfer in a porous medium. The Fourier method, integration method, and finite difference method were used to obtain temperature solutions. The results were compared to a numerical model, showing good agreement between them.