On the Heat Flow Through a Porous Tube Filled with Incompressible Viscous Fluid

Abstract

Abstract We studied the non-isothermal flow of an incompressible viscous fluid through a porous tube. Motivated by filtration problems, Darcy’s law was incorporated on the walls of the tube and the flow was pressure driven. The main goal was to investigate the thermodynamic part of the system, assuming that the hydrodynamic part is known. In view of the applications we wanted to model, the fluid inside the tube was supposed to be cooled (or heated) by the surrounding medium. Using asymptotic analysis with respect to the small parameter (being the ratio between the tube’s thickness and its length), we constructed the explicit second-order approximation for the temperature distribution of the fluid. Numerical examples are provided to compare the obtained solution with the one derived for a rigid tube and also to show the corrections due to higher-order terms.