Analytical Solution to the Problem of Convective Heat Transfer in a Porous Rectangular Channel for Thermal Boundary Conditions of the Second Genus

Abstract

In the three-dimensional statement, we consider the Brinkman equation together with the equation of heterogeneous heat transfer for an unidirectional ow of the Newtonian uid under laminar regime through horizontal porous channel having a constant rectangular cross-section with known thermal ows at the boundary and small values of the Darcy numbers. Due to the linearity of the formulated system of model equations, we obtain analytical solution of the system using the Laplace and Fourier integral transformation. The obtained solution allows to estimate the length of the input hydrodynamic section, the coecient of hydraulic resistance, and the local Nusselt numbers. The results obtained for the hydrodynamic subproblem with a large porosity and thermal subproblem with a stationary temperature eld agree with the classical data.