On the effect of “sphericity” on forced convection
In this project, forced convection from a heated oblate spheroid will be studied in an attempt to investigate the effect of the axis ratio on the heat transfer rate. Although the problem is academically very interesting, it is quite involved in many applications such as Brownian motion, suspension rheometry, and the passage of sound waves through particulate systems. While the problem of heat transfer from a sphere is well understood, forced convection from an oblate spheroid has not received enough interest, and therefore, the effect of the axis ratio on the heat transfer rate is unknown. Consequently, in this project, the time-dependent full Navier-Stokes and energy equations will be solved using a powerful semi-analytical series truncation method where the stream function, vorticity, and the dimensionless temperature are expanded in terms of series of Associated Legendre functions. The resulting time-dependent differential equations will be solved using the Crank-Nicolson finite difference numerical scheme. The axis ratios to be considered range from 1/2 to 1 (a perfect sphere). The results for the flow and thermal fields, which are expected to be more general than those available in the literature for the perfect sphere case, will be compared with relevant published data.