Heat Transfer in a Cylindrical Channel with Stabilized Laminar Fluid Flow
Based on the joint use of the method of separation of Fourier variables and the method of collocations, an approximate analytical solution of the heat exchange problem for the flow of fluid in a flat channel was obtained. The purpose of the research: the development of a method for solving the boundary value problem of heat transfer with a stabilized laminar fluid flow in a flat channel, which allows obtaining approximate analytical solutions that are simple in form. Research objectives: development of a method for mathematical modeling of heat transfer processes in moving fluids, described by differential equations with separable variables. The hypothesis of the study: an increase in the number of collocation points - the points at which the Sturm - Liouville differential equation is precisely satisfied, makes it possible to increase the accuracy of determining the temperature function, including for small values of the longitudinal variable. The paper presents the results of calculations of temperature fields in a liquid; an analysis of the discrepancy of the initial differential equation was performed depending on the number of collocation points.