Numerical evaluation of heat transfer from a spherical dimple in a flat plate: Development of appropriate boundary conditions

Abstract

ABSTRACT A numerical investigation has been performed as to the feasibility of using spherical indentations in a flat plate for enhancing heat transfer in the laminar regime. An attempt to validate the calculation procedure resulted in a significant difference with previously published results, in which the inlet boundary condition was stated to be the Polhausen distribution. An investigation of the disparity lead to a study of the effects of various boundary conditions on the development of laminar boundary layers on an infinitesimally thin flat plate. In two-dimensions, regions appear in which velocities are greater than the free stream velocity (overshoot), unless the Blasius distribution is used to predict the inlet velocity in both directions. Surprisingly, although regions of overshoot occur when areas upstream and downstream of the plate are included in calculating the flow near the plate, the velocity distribution within the boundary layer is well represented by the Blasius profile for most of the plate. Outside the boundary layer the velocity distribution depends on the position and the length of the plate. Calculations in three dimensions using inlet boundary conditions developed from the two-dimensional study indicate that a single dimple does not enhance heat transfer.