Mathematical model of heating of plane porous heat exchanger of heat surface cooling system in the starting mode

Based on the conjugate Darcy–Brinkman–Forchheymer hydrodynamic model and Schumann thermal model with boundary conditions of the second kind, a model with lumped parameters was proposed by means of geometric 2D averaging to identify the integral kinetics of the temperature fields of a porous matrix and a Newtonian coolant without phase transitions. The model was adapted for a heat-stressed surface by means of a porous compact heat exchanger with uniform porosity and permeability, obeying the modified Kozeny–Carman relation, in the form of a Cauchy problem, the solution of which was obtained in the final analytical representation for the average volume temperatures of the coolant and the porous matrix. The possibility of harmonic damped oscillations of the temperature fields and the absence of coolant overheating in the starting condition of the cooling system were shown. For the dimensionless time of establishing the stationary functioning of the porous heat exchanger, an approximate estimate was obtained correlating with the known data of computational and full-scale experiments.