Steady laminar assisted mixed convection normally to a heated horizontal plate with finite length

Abstract

The flow of a fluid directed normally to a heated flat plate of finite length (two-dimensional flow) is considered in the present paper. Three cases are considered: i. both sides of the plate are heated at the same uniform temperature. ii. The upper side is heated uniformly while the lower side is insulated (upward facing plate). iii. The upper side is insulated while the lower side is uniformly heated (downward facing plate). The problem is investigated numerically with a finite volume method using the commercial code ANSYS FLUENT. The governing parameters are the Reynolds number, the Richardson number and the Prandtl number and the influence of these three parameters on the drag coefficient, the average Nusselt number and the wake length is investigated for all the considered cases. It is found that the drag coefficient, the Nusselt number and the wake length in the downward facing plate is always greater than that in the upward facing plate, for all the examined values of the Richardson, Reynolds and Prandtl number. The vertical centerline velocity above the plate and above the wake increases continuously and finally becomes identical with the velocity of a two-dimensional plume while the vertical velocity below the plate shows a maximum and then goes to zero. At very high Prandtl numbers (Pr → ∞) the buoyancy force near the plate tends to zero and the drag coefficient as well as the wake length approach asymptotically the corresponding values of pure forced convection.