Simulation of the Heat Transfer Process of a Moving Fluid in a Plane-Parallel Channel

The paper considers a method of mathematical modeling of the heat transfer process in a moving fluid in a plane-parallel channel based on the joint use of additional boundary conditions and an additional unknown function. According to the presented method, the problem of finding a solution to a partial differential equation with respect to the temperature function is reduced to integrating an ordinary differential equation with respect to the new unknown function - the heat flow density on the surface of the area under study. An approximate analytical solution is obtained for the unsteady heat conduction problem for a plane-parallel channel under symmetric boundary conditions of the third kind. It is noted that the accuracy of the solution obtained depends on the number of approximations performed and is determined by the degree of the approximating polynomial. The graphs of the isotherm distributions, as well as speeds of their movement are built and analyzed. It is shown that isotherms occur on the channel surface with a certain initial speed, which depends on the heat transfer intensity. The method developed can be used to determine the heat flow density on the channel surface, and the error of determination in the range of the longitudinal coordinate is no more than 3% in a first approximation.