Date of Award


Degree Type


Degree Name

Doctor of Philosophy


Numerical techniques were developed to compute the heat transfer from a two-dimensional, thin-skinned, dome type structure heated from below.;The equations for the conservation of mass, momentum, and energy in polar cylindrical coordinates were simplified by assuming steady-state conditions, constant properties, and constant density everywhere except in the body force term of the momentum equations. The equations were then written in a stream function-vorticity form which resulted in a system of second-order, nonlinear, coupled differential equations.;A wind tunnel model was constructed to determine the sensitive parameters in determining the overall heat transfer and temperature variation of the thin skin. From the wind tunnel tests it was determined that internal heat transfer controlled the overall heat flux and that the radiation component could be as large as the convective component for appropriate conditions.;Based on the flow visualization and wind tunnel studies, the modeling effort concentrated on the internal flow. An inviscid solution was obtained by modeling the internal flow as two modified Rankine vortices and solving the inviscid energy equations. A gray body analysis was applied to the internal flow and the radiative component added to the convective heat transfer. The external heat transfer was computed from a modified cylinder heat transfer correlation. The constant dome temperature was varied until the internal and external heat fluxes were equal.;A viscous solution was obtained for the complete set of simplified equations. For low values of the Grashof Number, the resulting solution was similar to pure conduction. As the Grashof Number was increased (Gr > 1000), the isotherms became more distorted and isothermal rotating cores were formed. As the gradients at the wall became steep the solutions became unstable due to the grid spacing. Solutions were obtained for Gr (LESSTHEQ) 2 x 10('5).;It is recommended that solutions be obtained for larger values of the Grashof Number by refining the grid or the use of a boundary layer analysis. Detailed experiments should be performed to determine the effects of scale and skin thickness and material.



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