An analysis is made of transient heat transfer with transient laminar flow between heated (or cooled) parallel plates. The transient processes are caused by simultaneously changing the fluid pumping pressure and either the wall temperature or the wall heat flux. The solution is obtained for both the thermal entrance and fully developed heat-transfer regions. The slug-flow simplification is made; that is, the velocity at any instant of time is taken as uniform throughout the channel. The fluid temperature distribution, however, depends on both the axial co-ordinate and the position within the channel cross section. A few numerical examples are carried out which give some insight into various transient processes such as those occurring during a nuclear-reactor shutdown.

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