The thermal boundary layer over a semi-infinite flat plate is investigated. For time t < 0 there is the Blasius boundary layer and no thermal boundary layer. At t = 0, a temperature boundary layer is initiated without altering the velocity and the subsequent temperature boundary layer is studied for all time. The resulting linear, singular parabolic partial differential equation is solved using an efficient numerical method. Numerical results for several values of the Prandtl number are compared with analytical and numerical results obtained by previous authors. Because of the large interest shown recently in impulsive problems which result in the solution of singular parabolic equations the method is extended to study some of these problems. In two of the examples considered the governing equations are nonlinear.

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