Role of thermally stratified medium on a free convection flow from a rotating sphere

Abstract

Purpose

The purpose of this paper is to study the influence of thermally stratified medium on a free convection flow from a sphere, which is rotating about the vertical axis, immersed in a stably thermally stratified medium.

Design/methodology/approach

An implicit finite‐difference scheme in combination with the quasi‐linearization technique is applied to obtain the steady state non‐similar solutions of the governing boundary layer equations for flow and temperature fields.

Findings

The numerical results indicate that the heat transfer rate at the wall decreases significantly with an increasing thermal stratification parameter, but its effect on the skin friction coefficients is rather minimum. In fact, the presence of thermal stratification of the medium influences the heat transfer at wall to be in opposite direction, that is, from fluids to the wall above a certain height. The heat transfer rate increases but the skin frictions decrease with the increase of Prandtl number. In particular, the effect of buoyancy force is much more sensitive for low Prandtl number fluids (Pr = 0.7, air) than that of high Prandtl number fluids (Pr = 7, water). Also the skin friction in rotating direction is less sensitive to the buoyancy force as the buoyancy force acts in the streamwise direction for the present study of thermally stratified medium.

Research limitations/implications

The ambient temperature T_∞∞ is assumed to increase linearly with height $h$. The viscous dissipation term, which is usually small for natural convection flows, has been neglected in the energy equation. The flow is assumed to be axi‐symmetric. The Boussinesq approximation is invoked for the fluid properties to relate density changes to temperature changes, and to couple in this way the temperature field to the flow field.

Practical implications

Free convection in a thermally stratified medium occurs in many environmental processes with temperature stratification, and in industrial applications within a closed chamber with heated walls. Also, free convections associated with heat rejection systems for long‐duration deep ocean powder modules where ocean environment is stratified are examples of such type.

Originality/value

The research presented in this paper investigates the free convection flow on a sphere, which is rotating with a constant angular velocity along its vertical axis in a stably thermally stratified fluid.

Citation

Saikrishnan, P., Roy, S., Takhar, H.S. and Ravindran, R. (2010), "Role of thermally stratified medium on a free convection flow from a rotating sphere", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 20 No. 1, pp. 96-110. https://doi.org/10.1108/09615531011008145