Steady and transient film boiling on a sphere in forced convection

A theoretical study of film boiling on a sphere in forced convection is given. First of all the steady state is analyzed, that is, the assumption is made that the sphere temperature is maintained constant. Subcooling is included in the model. Simple analytical solutions are obtained for the vapour film thickness and local Nusselt number in two limiting cases, corresponding roughly to large and small subcooling. The usefulness of these two results is enhanced by two factors: the range not covered by either limiting case is rather small, and the parameters occurring in the solutions do not depend explicitly on the sphere radius or its velocity. Next it is shown that (in the parameter regime appropriate to the experiments so far reported) the transients in the vapour and coolant are negligible and therefore a quasi-steady approximation is valid in those regions. Thus the steady-state theory already obtained can be used to formulate the unsteady heat-transfer problem for the sphere. The solution of this problem is given.