Bounds on Heat Transfer in a Periodic Graetz Problem

It is proven that the heat transfer coefficient and rate of decay of temperature with distance in a fully developed Graetz problem with temporally periodic inlet temperature are greater than or equal to the corresponding quantities in the corresponding steady Graetz problem. The proof is valid for arbitrary duct cross-sectional shapes and for either constant temperature, constant heat flux, or linearized radiation boundary conditions. A numerical solution of the energy equation demonstrates the validity of the theorem. The utility of the result is discussed in the context of heat exchanger design for pulsed gas lasers.