Conjugate problems of unsteady heat and mass conduction under varying external conditions

A closed system of algebraic and ordinary differential equations that enables one to simply and with a high degree of accuracy solve unsteady problems of heat conduction and diffusion extraction of a substance from solids of standard shapes - a plate, a cylinder, and a sphere - under varying external conditions is proposed. The method of solution is based on a unified universal dependence that describes with a high degree of accuracy the distribution of temperatures or concentrations of the substance in the above solids and on equations that determine variations in characteristics involved in this dependence with time and space as the solids move.