Transient convective heating and prediction of temperature rise times on surfaces and edges

The problem of predicting surface temperatures of solids subjected to transient convective heating is analyzed; both smooth wall and corner edge geometries are considered. Exact solutions are obtained which characterize the temperature rise near the surface and elucidate the boundary layer nature of the problem. These can also be inverted to predict the time required to reach a given critical temperature. It is shown that the time required at a corner edge is always less than a quarter of that at a smooth surface. Extending the analysis further, the rise time at the vertex point of a cube is seen to be less than a ninth of that for a smooth wall.