rabolic equations govern many of the transient engineering problems. Space integration using finite element or finite difference methods changes the parabolic partial differential equation into an ordinary differential equation. Time integration schemes are needed to solve the later equation. In order to accurately perform the later integration a proper time step must be provided. Time step estimates based on a stability criteria has been prescribed in the literature. The following paper presents time step estimates that satisfy stability as well as accuracy criteria. These estimates were correlated to the Froude and Courant Numbers. The later criteria were found to be over conservative for some integration schemes. Suggestions as to which time scheme is the best to use is also presented.