Natural Convection inside a Horizontal Circular Cylinder

摘要

The work analyzes the natural convection of a fluid contained in an infinitely long horizontal cylinder at large Prandtl number and unit order Grashof number. The motion is generated by an imposed cosine wall temperature distribution which includes an arbitrary phase angle. This phase angle may be varied to allow for cases ranging from heating-from-the-side to heating-from-below to be investigated. From an asymptotic ordering of the governing energy and vorticity transport equations for large Prandtl number, it is shown that the core region, which contains the fluid surrounded completely by a boundary-layer flow along the cylinder wall, may assume either of two configurations. The choice of the core configuration is shown to depend upon the nature of the streamlines therein. Solutions obtained from linearized forms of the full governing equations agree with the core temperature and velocity fields which were observed experimentally for heating angles sufficiently away from the heating-from-the-side case. Also, the influence of various linearizations is studied. For heating angles near the heating-from-the-side case, a linearized form of the boundary layer equations is developed which allows the solutions to match with the second possible core configuration. The form of the results agrees generally with experimental evidence for heating-from-the-side. (Author)