Asymptotic thermal analysis of a rotating and sublimating sphere illuminated by a light source

The method of matched asymptotic expansions is applied for analysis of a generic unsteady three-dimensional (3D) thermal model of a rotating and sublimating homogeneous sphere asymmetrically illuminated by a light source and a series of approximate asymptotic models is proposed. The temperature field is described by heat conduction equation with a strongly non-linear boundary condition, accounting for the light absorption, thermal conductivity, self emission, and sublimation on the sphere surface. It is shown that properly generalized Van Dyke’s matching rule, accounting for non-linearity of the boundary condition, results in an asymptotic model, which provides accurate description of the temperature field even if the Fourier number Fo based on the sphere period of revolution is as small as 10. The asymptotic model is also capable for accurate description of the thermal boundary layer degeneration, when the angle between the rotational axis and the direction to the light source tends to zero or the effect of rotation vanishes locally. The accuracy of the asymptotic models is verified by the comparison of the computational results obtained based on the full 3D and asymptotic models. The asymptotic models are applied to study the effect of all dimensionless parameters on the total gas production rate of the sphere. It is found that in a large range of conditions the surface temperature field and gas production rate are independent of Fo, but determined by a new “rotational” parameter, which serves as measure of the sphere rotation rate.