A self-similar unsteady flow with conjugated heat transfer

In this paper an exact analytical self-similar solution of the thermo-fluid dynamic field arising in an impulsively accelerated flow over a flat plate is proposed. The plate is considered of infinite thickness and the thermal field is computed both in the fluid and in the solid with the temperature and the heat flux unknown at the solid–fluid interface (conjugated heat transfer). The values of the initial temperatures in the solid and in the fluid are different constants. The solution, obtained in the incompressible case, is extended to compressible flows by the Stewartson–Dorodnitsin transformation. The influence of the non-dimensional parameters governing the phenomenon is discussed with particular emphasis to the simple expressions of the interface temperature and heat flux.