The problem represents the transient evolution of the temperature field near the surface of a body (a 2D cylinder section) immersed into a fluid flowing into a channel. The body surface is exchanging heat with the surrounding fluid. This is a well-known problem in the design and sizing of heat exchangers used for many industrial, civil and, more recently, biomedical applications.
The problem is described by the coupling of an unsteady heat transfer phenomenon by conduction (diffusion) into a body and by convection-conduction phenomena inside the field where the fluid is flowing. There is a coupling between diffusion (conduction) and convection phenomena. The convective field is given by a potential solution (see, for example, RL Panton's Incompressible Flows, Wiley-Interscience, John Wiley and Sons, New York, NY).