Heat transfer from a nano-sphere with temperature and velocity discontinuities at the interface

A singular perturbation method has been used to derive a general equation for the rate of heat transfer from a sphere at low Knudsen number. The final expression includes both velocity slip and temperature slip at the interface and applies to a general Stokesian flow regime. The asymptotic analysis was carried up to the order Pe³ln(Pe). By choosing an expression for the drag multiplier, the derived expression for the Nusselt number may be applied to solid, fluid as well as porous spheres, which are special cases of the general solutions. Comparisons with known results for these special cases indicate the accuracy and wide range of applicability of the derived general expression. The inclusion of the temperature slip at the interface makes this equation applicable to particles, bubbles and drops of nanometer sizes, in the continuum or the slip-flow regime, that is for Knudsen number Kn < 0.1. Our results show that the velocity slip at the interface does not affect significantly the overall Nusselt number, Nu. However, the temperature slip affects the heat transfer significantly. If the temperature discontinuity becomes large, the sphere becomes almost adiabatic. This indicates that, if a temperature slip is possible at the interface of nanospheres, it must be taken into account by using the derived expression for Nu. Our results at the limit of Pe = 0 are compared very well with experimental results found in the literature.