Heat Exchange in a Cylindrical Channel with Stabilized Laminar Fluid Flow

Abstract

Based on the determination of the temperature perturbation front and additional boundary conditions, an approximate analytical solution is obtained for the stationary heat exchange problem when fluid flows in a cylindrical channel with a constant parabolic velocity profile (the Gretz–Nusselt problem), which allows us to investigate the temperature distribution in the fluid in a wide range of distances from the pipe inlet, including small and very small distances. Based on the data of numerical calculations of temperature change at a certain value of the spatial variable using the solution obtained by solving the inverse heat conduction problem, the Peclet number was found (in the case where it is unknown in the solution obtained), from which we can determine the velocity profile and the flow rate of the liquid. Graphs of the distribution of isotherms and the their velocities in space over time are plotted.