Stokes-type conjugate heat transfer and thermoelasticity analysis of a hollow spherical particle in a slip flow

Conjugate heat transfer around a spherical particle submerged in a viscous heat-conducting fluid at very low Reynolds numbers is analytically investigated. The cases of spherically symmetric and axisymmetric temperature fields are solved. The temperature jump condition of dilute gas dynamics is assumed. The induced thermal stresses in the sphere in the case of spherical symmetry are analytically solved as well. The effect of temperature jump, heat conductivity ratio between the solid and fluid media, the heat generation and the inner radius of the sphere on the temperature, displacement, radial stress and circumferential stresses are studied. Furthermore, an exact correlation is proposed between the Reynolds, Knudsen and Nusselt numbers as well as the drag coefficient of the sphere, which is valid for slip flow at the Stokes limit. Whether it is accurate at higher Reynolds numbers would need further research.