Analytical expressions for a solution of convective heat and moisture transfer equations in the frequency domain for layered media

Analytical expressions for the solution of the differential equations in the frequency domain, describing convective heat and moisture transfer in homogeneous layered medium are obtained. The known connection between systems of differential equations of the second order and the differential matrix Riccati equation is used for the derivation of these expressions. The numerical algorithm is recursive on the number of layers, stable to the rounding errors, and each step of this numerical algorithm based on simple actions: addition, multiplication and inversion of matrices of the second order.