Natural Convection Inside a Horizontal Cylinder

Natural convection of a fluid contained in an infinitely long horizontal cylinder at large Prandtl number and unit-order Grashof number is analyzed. The motion is generated by an imposed cosine wall temperature distribution which includes an arbitrary phase angle. The phase angle is a measure of the location of the wall temperature extrema. From an asymptotic ordering of the energy and vorticity transport equations for large Prandtl number it is shown that the core region, which contains fluid surrounded completely by a boundary-layer flow along the cylinder wall, may assume either of two configurations. For heating angles near the heating-from-the-side case (wall temperature extrema at the ends of the horizontal diameter) linearized forms of the boundary-layer equations are developed which yield solutions that match the core configuration not considered previously. The form of the results agrees generally with experimental evidence for heating-from-the-side.