Development and analysis of models of heat transfer in compact porous heat exchangers of aero space control systems

The paper presents a study of thermal and hydraulic characteristics of porous heat exchangers in conditions of intensive heat dissipation from compact surfaces. We present a mathematical model of convective heat transfer in a porous heat exchange element for conjugate Darcy-Brinkman-Forchheimer equations with boundary conditions of the second kind. An accurate solution of hydrodynamic and thermal problems is obtained analytically by integral transformation. We obtained dependences for determining the velocity field, the length of the initial hydrodynamic area, the Fanning hydraulic friction head, the local temperature of the porous matrix and the liquid cooler, the local Nusselt numbers. We assessed the influence of porosity, permeability, Darcy and Reynolds numbers on the thermal and hydraulic condition of a compact porous heat exchanger. Reasonable ranges of thermal and hydraulic characteristics of the heat exchangers being developed are established. Critical operating modes of heat exchangers are specified. The data obtained agree well with the classical results. We developed an engineering methodology differing from the existing ones by its invariance. The methodology makes it possible to determine the design characteristics of compact porous heat-exchange elements of aerospace control systems.