Solution of the laminar boundary layer of a semi-infinite flat plate given an impulsive change in velocity and temperature

The laminar boundary layer over a semi-infinite flat plate which is impulsively set in motion in an incompressible fluid and which has a simultaneous step change in surface temperature was studied. An approximate method was derived which can be used to determine the thermal boundary layer thickness as a function of the distance from the leading edge and of time. From the thermal boundary layer thickness the temperature of the fluid can be determined at any position in the boundary layer and at any time. The local Nusselt number can also be determined from the thermal boundary layer thickness.

The approximate solution was compared with exact steady-state and infinite-plate solutions of the energy equation and with a finite-difference solution of the unsteady continuity, momentum and energy equations. Agreement between the solutions was close enough to indicate that the approximate solutions for the temperature in the boundary layer and for the Nusselt number approximate the actual situation with reasonable accuracy.