TRANSIENT HEAT-TRANSFER FROM A SOLID SPHERE TRANSLATING AT LOW-REYNOLDS-NUMBER - PERTURBATION SOLUTION FOR LOW PECLET NUMBER

In this paper the heat transfer from a solid spherical particle transl ating at low Reynolds number is analytically examined for the limit of vanishing Peclet number. The temperature distribution within the soli d sphere is treated as fully transient while the fluid phase is consid ered to be quasisteady. The temperature field in the dispersed phase i s obtained by a singular perturbation expansion of the Acrivos-Taylor type. The time-dependence in the solid phase is handled by means of th e Laplace transform. This approach allows the temperature and heat flu x continuity conditions at the solid-liquid interface to be exactly sa tisfied. The solution in the time domain appears in the form of infini te series which have associated with them a set of eigenvalues for eve ry order of the perturbation expansion. The Nusselt number to order Pe , however, depends only on the leading order eigenvalues. An analytica l limit of the Nusselt number for large values of time is also obtaine d.