Free convection from a sphere in a slightlythermally stratified fluid
Abstract
The steady, axisymmetric flow of a vertically stratified viscous fluid over a fixed sphere is considered in a uniform gravity field. Analytical solutions are obtained by the singular perturbation technique valid for small (modified) Grashof numbers. Two cases are considered, viz. when the sphere is either thermally insulated or when its surface temperature is maintained constant equal to that of the fluid occupying the diametral plane. Streamlines are shown graphically in an axial plane for the flow near the sphere. It is found that for the thermally insulated sphere, the flow is like the one about a stationary sphere in a rotating fluid, i.e., the inflow near the equator changes into an outflow at the poles, the transition occurring at an angle of 54.5 deg measured from the poles. For the isothermal sphere, the streamlines are similar to those of a uniformly spinning sphere in a fluid at rest.
 Publication:

International Journal of Heat and Mass Transfer
 Pub Date:
 November 1977
 DOI:
 10.1016/00179310(77)901247
 Bibcode:
 1977IJHMT..20.1155S
 Keywords:

 Convective Heat Transfer;
 Free Convection;
 Rotating Fluids;
 Rotating Spheres;
 Stratified Flow;
 Viscous Flow;
 Grashof Number;
 Gravitational Fields;
 Isotherms;
 Perturbation Theory;
 Streamlining;
 Surface Temperature;
 Thermal Insulation;
 Fluid Mechanics and Heat Transfer