A Universal Model of Heat Transfer in Systems with Penetration Cooling

Penetration cooling is one of the most intensive methods of regulation of heat transfer, which is explained by the highly developed contact (wetted) surface within a porous matrix and by the significant effect of heat flux reduction upon the injection of coolant into the boundary layer. However, there are serious difficulties in performing theoretical analysis of heat transfer within permeable matrices with filtration of coolant because of the absence of a universally accepted approach to the choice of geometric scale of pore channels and criterion relations for the calculation of the coefficient of internal heat transfer, as well as because of the indeterminacy of the boundary conditions on the internal and external surfaces for the coolant temperature. In this paper, all of these problems are coordinated from a unified standpoint, which enables one to formulate a universal model of heat transfer in permeable envelopes. The results of systematic calculations by the suggested mathematical model are used to reveal and optimize the most important parameters of the system of heat shielding designed for the blades of high-temperature rims of gas turbines.