Analytical investigation of Couette flow in a composite channel partially filled with a porous medium and partially with a clear fluid

Convective heat transfer in porous media is a subject of growing interest. This is because of many important engineering applications of porous media. Such applications can be found in heat exchangers, energy storage units, chemical reactors, heat pipes, electronic cooling and ceramic processing. One of important and fundamental fluid flow situations in porous media is Couette flow which can occur, for example, betwen two parallel flat plates, one of which is at rest, and the other is moving in its own plane with a constant velocity, uw. Since in Couette flow velocity of the moving plate can be large, and also viscous forces in the boundary layer near the moving plate cna be significant, to obtain a correct description of the flow, it can be important to account for non-Darcian effects, namely, for the inertial (Forchheimer) and for the viscous (Brinkman) effects [1]. Investigations of heat transfer in Couette flow throgh a porous medium are limited to the case of a Brinkman-Darcy porous medium [2,3]. In an insight investigation by Nakayama [4], analytical solutions for different situations of Couette flow through an inelastic porous medium, including a porous medium described by the Brinkman-Forschheimer extension of the Darcy law, are obtained. However, results of ref. [4] are limited to the fluid flow analysis only, and no investigation of heat transfer is made in this reference. To the best of the author's knowledge, no attempt to analyze heat transfer in Couette flow through a Brinkman-Forchheimer-Darcy porous medium has yet been made. In [4] it is assumed that the channel is completely filled with a porous medium which is at rest, and there is no gap between the porous medium and the moving plate. Such a geometry can result in large friction forces between the porous matrix and the moving plate. This canlead to a damage of the porous matrix. In practical situations, it is necessary to assume that between a porous medium and a moving plate there is a gap filled with a clear fluid. Even if this gap is small, its influence on heat transfer can be significant. Accounting for this gap essentially complicates the problem, because it is necessary to analyze fluid flow and heat transfer in a composite channel, whcih is partially filled with a fluid saturated porous medium, and partially with a clear fluid. In solving this problem, correct boundary conditions at the porous medium/clear interface are important. In this research we utilize the boundary cnoditions at the interface suggested in Ochoa-Tapia and Whitaker [5,6].; The problem of fluid flow and heat transfer in Couette flow through a composite channel, which is partially filled with a fluid saturated porous medium and partially with a clear fluid, is studied. The flow in the porous region is described by the Brinkman-Forchheimer-extended Darcy equation. The analysis of heat transfer insulated fixed plate and isoflux moving plate are considered. The problem is solved under the boundary layer approximation. Analytical solutions for the flow velocity, temperature distribution, and for the Nusselt number are obtained.