A non‐iterative solution of a system of ordinary differential equations arising from boundary layer theory

Using a two parameter group transformation, the ordinary differential equations describing similarity solutions for the dimensionless stream function and temperature for flow over a flat plate held at a constant temperature have been transformed from simultaneous boundary value equations to simultaneous initial value equations. The resulting initial value equations have been solved using a standard fourth order Runge Kutta method incorporated in a teaching computer package recently developed at Napier Polytechnic. The results of the solution of the initial value problem, presented in the form of the missing initial values for the dimensionless stream function and temperature, enable the usual solution curves for these variables to be reproduced easily. Also, the results have a certain pedagogical value and may be of some use in teaching fluid dynamics. Finally, constant fluid properties are assumed throughout the analysis reported here.