Hybrid solutions for thermally developing flows in channels partially filled with porous media

Abstract

A new approach based on the Generalized Integral Transform Technique is advanced to deal with convective heat transfer in partially porous channels under local thermal nonequilibrium (LTNE) formulation. A semi-infinite partially porous parallel plates channel configuration is used to illustrate the semi-analytical solution methodology. The proposed eigenfunction expansion is based on a novel coupled multilayer eigenvalue problem which results in similar accuracy and computational performance in comparison to the expansions employed in solving the formulation under the local thermal equilibrium (LTE) hypothesis. Results from the LTE and LTNE formulations are then critically compared to explore the validity of the former in the present configuration. It is observed that the LTE formulation results may significantly overestimate the Nusselt number, leading to overly optimistic heat transfer predictions. Finally, an analysis of the effect of each parameter in the difference between the temperatures in the solid and fluid phases of the porous medium and in the Nusselt number is carried out, offering guidance for the design of heat transfer devices.

Additional information

Funding

The authors are grateful for the financial support offered by the Brazilian Government agencies CNPq, CAPES (PROCAD-Defesa), and FAPERJ (Grant no. E-26/010.002590/2019).