Transient power variation in surface conditions in heat conduction for plates

Transient temperature solutions in plates are derived for heating conditions varying as time to an integer power at a surface. The powers include 0, 1, 2 and 3; the last of which is useful for cubic splines. Boundary conditions of the first, second and third kinds are treated at both surfaces with the non-homogeneity at x = 0. As the power increases by one, an additional quasi-steady summation term appears in the analytical solution. Algebraic forms for these summations are derived in a systematic way. Extensive tables are given along with an example.