Approximate Solution to a Class of Transient Forced Convection Problems

Abstract

Approximate solutions using integral methods and the method of characteristics are found for the case of laminar, low speed, constant property, two-dimensional planar boundary layer type flow over a body which is initially at the constant temperature of the fluid passing over it and then, suddenly, has its surface temperature changed to a new constant value or has a constant heat flux imposed at the surface. The free stream velocity is variable with position along the body and the entire velocity field is assumed to be in the steady state. Response curves for surface heat flux or of surface temperature as a function of position and time are presented for power law variations of free stream velocity (the “wedge” type flows) and also for one particular nonsimilar (nonwedge) case. The relative ease with which the nonsimilar cases can be handled is thought to make the approach, advanced herein, a useful tool for the engineer to attack other nonsimilar cases. It was also found that the use of an “equivalent” wedge variable gives reasonably satisfactory results for the nonsimilar case chosen. Hence the application of the equivalent wedge methods is valid for transient forced convection problems just as it is, as is well known, for steady-state forced convection.