Variational solution of the problem of unsteady-state convective heat transfer in the channel (Q1111421)

With the use of a convolution-type functional, the variational description is given for the process of unsteady-state convective heat transfer in channels of complex cross-section with an arbitrary dependence of the velocity vector, thermophysical characteristics of the medium, volumetric heat generation source and of the parameters of boundary conditions on space and time. Based on the Galerkin-Kantorovich method involving the reduction to ordinary differential equations, a corresponding system of Euler equations is written out, the solution of which (analytical or numerical) is necessary to determine the temperature field in each specific case. An example is provided to illustrate a numerical solution of the problem stated.