A new class of exact solutions for three-dimensional thermal diffusion equations

Abstract

A new class of exact solutions has been obtained for three-dimensional equations of themal diffusion in a viscous incompressible liquid. This class enables the description of the temperature and concentration distribution at the boundaries of a liquid layer by a quadratic law. It has been shown that the solutions of the linearized set of thermal diffusion equations can describe the motion of a liquid at extreme points of hydrodynamic fields. A generalization of the classic Couette flow with a quadratic temperature and concentration distribution at the lower boundary has been considered as an example. The application of the presented class of solutions enables the modeling of liquid counterflows and the construction of exact solutions describing the flows of dissipative media.