Numerical and analytical investigation of vapor flow in a disk-shaped heat pipe incorporating secondary flow

Abstract

This paper presents a three-dimensional numerical analysis and a pseudo-three-dimensional analytical modeling of the steady incompressible vapor flow in an asymmetrical disk-shaped heat pipe heated from the top center area. The nonlinear differential elliptical equations of motion and the continuity equation were solved numerically over the entire vapor flow domain. Discretization of the governing equations was achieved using a finite element scheme based on the Galerkin method of weighted residuals. The analytical model involves the use of the boundary layer approximation and the bifurcation of the flow field on the plane to describe the velocity profile under conditions including strong flow reversal. For both numerical and analytical studies, backflow was observed at the top entrance of the condensation zone for injection Reynolds number of 50 and higher. The three-dimensional effects and the effects of the secondary flow formation are discussed in this work. The numerical and analytical results establish that the pressure variations in the angular and transverse directions for a typical disk-shaped heat pipe are small and can be neglected. A very good agreement was found between the numerical results and the analytical results. The analytical model saves tremendous computer time compared with the numerical simulation, which requires CPU times five orders of magnitude larger than those for the analytical model.