Theoretical Solutions of Heat Transfer in the Hydrodynamic Entrance Length of Double Pipes

Abstract

In the industrial heat-exchangers, there are many cases of unsteady heat transfer in the hydrodynamic entry length with temperature distributions of pipe-walls along the axial direction of double pipes and the pressure-drop from the inlet to the outlet, and in the atomic reactors (LMFR), the heat generates from the inside of the fluid. Therefore, in these cases, the research of unsteady heat transfer generating heat from the inside of the fluid is necessary. In this paper, theoretical solutions of the unsteady heat transfer in the hydrodynamic entrance length of vertical double pipes are made. In these solutions, such cases of unsteady heat transfer in the hydrodynamic entry length of vertical double pipes are treated that the heat generates from the inside of the fluid, free convection and laminar flow coexist at the same time, the pressure drops from the inlet to the outlet, and arbitrary temperature distributions of pipe-walls vary in the axial direction. In the solutions, the finite Hankel transform, the finite Fourier transform, the Laplace transform and Bessel functions are used. But, there is not a case of such an experiment. Theoretical solutions are reduced to the steady heat transfer and compared with experiments.