Solutions to a class of transport problems with radially dominant convection

For fluid systems dealing with drops and bubbles, there are many situations in which the flow is dominated by a radial field. An analysis is carried out for a general class of problems, in which the primary flow is a purely radial type in a spherical geometry and the secondary flow is a perturbation on it. In particular, the flow solutions are obtained for a particle in extensional flow, rotating particle, and a particle in a linear shear flow. In addition, the steady state heat/mass flow equations with radial convection are solved in a fairly general form for spherical boundaries. The solutions lead to a new class of polynomials for the radial functions of the separated solutions. Some of the fundamental properties of these polynomials have also been derived.