A BOUNDARY LAYER SOLUTION OF A FORCED CONVECTION PROBLEM IN A COMPOSITE CHANNEL PARTLY FILLED WITH A POROUS MEDIUM

摘要

Forced convection in a composite region part of which is occupied by a clear fluid and part by a fluid saturated porous medium has recently attracted considerable attention and became a subject for numerous investigations. This interest is due to many important thermal engineering applications related to this problem. Solid matrix heat exchangers, the use of porous materials for heat transfer enhancement, fault zones in geothermal systems and solidification of binary alloys are few to mention in this respect. In this paper a problem of fully developed forced convection in a parallel-plate channel partly filled with a homogeneous porous material is considered. The flow in the porous material is described by nonlinear Brinkman-Forchheimer-extended Darcy equation. Utilizing the boundary layer approach, analytical solutions for the flow velocity, the temperature distribution, as well as for the Nusselt number are obtained. Figure 1 depicts a schematic diagram of the problem. Fully developed forced convection in a composite channel bounded by two infinite fixed plates is considered. Since the problem is symmetrical, only a half of the channel is shown in Figure 1. A porous material is attached to the walls of the channel, while the center of the channel is occupied by a clear fluid. To describe the flow in the porous region, a momentum equation which accounts for both Brinkman and Forchheimer extensions of the Darcy law is utilized. Figure 1 shows two momentum boundary layers in the porous region. The first momentum boundary layer is near the wall of the channel, while the second boundary layer is near the clear fluid/porous medium interface. Since for most practical applications of porous media the value of the Darcy number is small, in this research we proceed from the assumption that these boundary layers do not meet in the center of the porous region. It means that a part of the porous region is outside the momentum boundary layers. Providing the thickness of the porous region near the wall is sufficient, our solution is valid either for relatively small Darcy numbers, or for relatively large values of the Forchheimer coefficient, or both. This probably covers the majority of practical situations. Our solution can fail for very small thickness of the porous layer, and also when the Darcy number takes on very large values (large means of the order of unity) and the Forchheimer coefficient simultaneously takes on very small values.