Solution to Problem on Occurrence of Natural Convection in Trapezoidal Cavities

An approach to analysis of flat linear disturbances of equilibrium for viscous fluid, gas or the liquid phase of the heat-accumulating material in cavities with a cross-section, bordered with a broken line, is developed. The approach possibilities are shown by an example of channels with a trapezoidal cross-section. A way is stipulated of building solutions to the uniform differential problem relative to the function of flow and temperature - in the form of double series of Fourier type. For determining constants, an infinite linear system of equations is derived, which is algebraic relative to R and admits the reduction. Concrete results are given, their good conformity to the known literature data is revealed.