Hydrodynamic and thermal interaction of a periodically oscillating fluid with a porous medium lying over a thick solid plate

In this paper, the hydrodynamic and thermal interaction of a periodically oscillating compressible fluid with a layer of porous medium is analytically investigated. The velocity amplitude of the oscillating fluid is considered to be small when compared to the thermal penetration depth (a transverse length scale) of the thermal energy transport inside the porous layer. The solid wall adjacent to the bottom of the porous layer is considered to be thick and the conduction heat transfer inside that wall is included in this model. The entire problem is treated as a conjugate heat transfer thermoacoustic like problem. The governing momentum and energy equations are simplified and linearized by using a first order perturbation analysis. Such an analysis is usually used to solve the linear thermoacoustic problem in the low Mach number limit and available in the thermoacoustic literature. Analytical expressions for oscillating velocity, temperatures in the porous layer and in the solid wall, heat transfer from the solid wall to the porous medium, and the entropy generation rate are calculated and graphically presented.