SOME UNSTEADY HEAT TRANSFER PROBLEMS SOLVED BY A SIMPLE SIMILARITY TRANSFORMATION

A similarity transformation is used for solving equations of the form

This equation is reduced by means of the similarity variable to an equation with partial derivatives of the first order for 62 and to an ordinary differential equation of the second order for T. For heat transfer from solid bodies, the preceding equation is obtained when the velocity distribution can be approximated by the potential flow. Such circumstances do occur for liquid metals, because for low Prandtl numbers the thickness of the thermal boundary layer is much larger than that of the hydrodynamic boundary layer. Several cases are examined: (a) Stagnation in planar flow; (b) Flow along a planar plate in unsteady hydrodynamic conditions; (c) Flow along a curved surface in steady conditions. The time in which the steady state is achieved is evaluated.