AN APPROXIMATE ANALYTICAL SOLUTION TO THE GRAETZ PROBLEM WITH PERIODIC INLET TEMPERATURE

Unsteady heat transfer for fully developed laminar flow with a parabol ic velocity profile through a parallel-plate channel, subjected to sin usoidally varying inlet temperature is considered. A boundary conditio n which accounts for the effects of both external convection and wall thermal capacitance is considered. In this work, we develop a new appr oximate solution to this periodic Graetz problem, using a second-order Galerkin method. The present model neglects axial heat conduction alo ng the wall but takes into account the transverse temperature gradient in the wall. The effects of transverse heat conduction in the wall an d fluid-to-solid heat capacitance ratio on the behavior of the periodi c responses are investigated. Comparisons are made with a finite diffe rence solution. (C) 1997 by Elsevier Science Inc.