The transient heat and/or mass transfer from a fluid sphere with internal circulation into a flowing fluid are investigated. The temperature and/or concentration inside the sphere are considered uniform. Two cases are studied: the physical mass and/or heat transfer and the mass transfer accompanied by an isothermal, first-order irreversible chemical reaction in the continuous phase. Steady, creeping flow is assumed around and inside the sphere. The problem is solved by a finite difference method in the range of parameters, 10 less than or equal to Pe less than or equal to 1000, 0.01 less than or equal to H (Phi (h)) less than or equal to 100, 0.1 less than or equal to Da less than or equal to 1000. The influence of distribution coefficient (H) or volume heat capacity ratio (Phi (h)) on the transfer late and thermal wake phenomenon is analysed.