Drag of a strongly heated sphere at small Reynolds numbers

Using an asymptotic small-perturbation method, the flow around a strongly heated sphere at small Reynolds numbers Re ≪ 1 is considered with account for thermal stresses in the gas in the higher-order approximations, beyond the Stokes one. It is assumed that the value of the Prandtl number Pr is arbitrary and the temperature dependence of the viscosity is described by a power law with an arbitrary exponent. In the O(Re²) and O(Re³ ln(Re)) approximations, the drag force of a heated sphere is found over a wide range of the ratios of sphere’s temperature to the gas free-stream temperature T _W /T _∞. The limits of applicability of the first (in Re) approximation are investigated, including the negative-drag effect, attributable to the action of the thermal stresses. The results are compared with numerical calculations of the flow around a hot sphere. The limits of applicability of the approximations found are examined. Similar results are obtained for the standard Navier-Stokes equations in which the thermal stresses are neglected.