Study of Thermal Exchange with Liquid Flowing in a Cylindrical Channel

Abstract

This article considers the sequence for obtaining the approximate analytical solution for the non-stationary problem of heat exchange in liquids moving in cylindrical conduit (the Graetz-Nusselt problem). The solution was obtained based on Fourier's variable separation method with involving the additional boundary conditions. The physical sense of the additional boundary conditions consists in complying with the original differential equation in the boundary point of the transverse space variable (in the conduit center). It is demonstrated that the proposed approach allows obtaining simple-form approximate analytical solutions with the accuracy being sufficient for engineering applications. Therefore, in the range of $\mathbf{x}\pmb{\geq 0.01}$, the deviation between the obtained results and the accurate solution already in the fourth approximation is not higher than 3%. It is noted that considerable calculation differences occur in obtaining the accurate analytical solutions for small values of longitudinal coordinate.