Temperature and heat transfer history of a solid body in a forced convection flow

Consideration is given to problems of unsteady forced convection heat transfer in the presence of either time-invariant or time-dependent surface temperatures. The transient is initiated when a solid body is exposed to a fluid having a temperature different from its own. In the first part of the paper, a solution method is developed for determining the surface heat transfer for the case of steady, uniform surface temperature. Then, attention is turned to the determination of the temperature history of non-internally-heated bodies of high thermal conductance, which lose heat by convection to the fluid environment. A numerical scheme for deducing results for the temperature history is described, while analytical expressions appropriate to the initial and quasi-steady stages of the transient are presented. Detailed consideration is given to the case of a sphere in a low Péclet number flow, for which an exact solution for the temperature history is worked out. The results from the numerical scheme are found to be in excellent agreement with those from the exact solution, while the expressions for the initial and quasi-steady stages, when taken together, serve to establish the general behavior of the solution over the entire transient period.