Numerical analysis of variable property heat transfer to a single sphere in high temperature surroundings

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Abstract
A theoretical study has been conducted to investigate the effects of large temperature differences on the rate of pure heat transfer from a very hot gas to stationary spheres.In the numerical analysis, the momentum and energy equations for variable property flow past a sphere were solved simultaneously, using finite difference techniques. Results were obtained for Reynolds numbers up to 50 and surface temperature to gas temperature ratios varying between 0.25 and unity. These ranges cover most of the conditions commonly encountered in heterogeneous plasmas, transferred arc, and other high temperature chemical engineering processes. The flow behavior, drag coefficients, and Nusselt number were calculated for each case.The constant property solutions were in excellent agreement with numerical and experimental results reported in the literature, thus justifying the validity of the model and of the underlying assumptions. In general, the effect of variable properties was to drastically increase the flow velocity, vorticity, and temperature and vorticity gradients near the surface.A generalized heat transfer correlation was derived which, in addition to constant property conditions, included the effect of large variations in the physical properties of the fluid as a result of large temperature differences.