Analysis of mathematical model of heat removal from the flat surface by the laminar moving refrigerant through conjugation porous medium

A mathematical model of convective heat transfer in a flat porous channel for the laminar flow of Newtonian medium in the form of a boundary value problem for conjugate equations of Darcy–Brinkman–Forchheymer in Darcy–Brinkman approximation and heat transfer in the Schumann's form with the second kind thermal boundary conditions is proposed. An analytical solution of the model equations to calculate the thermal and hydrodynamic fields is obtained by the method of integral transforms. It allowed to find the exact ratios for the hydrodynamic entrance region length, Fanning's hydraulic friction coefficient, identify the local characteristics of the liquid phase and a porous skeleton temperature fields depending on the porosity, as well as to evaluate the local Nusselt numbers and determine the effective heat exchange domain. The data obtained do not contradict the classical results.