Transient Heat Transfer for Laminar Forced Convection in the Thermal Entrance Region of Flat Ducts

An analysis is made for transient laminar heat transfer in the thermal entrance region of a flat duct (parallel plate channel) whose bounding surfaces are subjected to an arbitrary time variation of temperature or of heat flux. Initially, the system may be either in an already established steady-state heat-transfer situation, or else, the fluid and duct walls may be at the same uniform temperature. The velocity distribution in the flow is taken to be fully developed and unchanging with time. The solution for arbitrary time-dependent conditions is obtained by generalizing the thermal response to a unit step change in wall temperature or in wall heat flux. This step-function response is found by using the method of characteristics. Heat-transfer results are presented as simple analytical expressions. The time required to achieve steady state after a unit step is also given. Working formulas are summarized at the end of the paper.