Convective heat transfer in unsteady laminar parallel flows

In laminar, fully developed pipe and channel flows that undergo transients from a known initial state, exact analytical solutions for the momentary velocity field as functionals of the flow rate can be determined from the Navier-Stokes equations, for arbitrary flow unsteadiness [Phys. Fluids 12, 518 (2000)]. For laminar, fully developed duct flows with uniform wall heating that undergo large flow transients, the companion thermal energy equation can be approximated in a form that may also be solved analytically, yielding solutions for the instantaneous temperature field for arbitrary time unsteadiness in both the flow and the wall heat flux. Expressions for Nusselt numbers in convective heat transfer in duct flows with arbitrary temporal flow and heat flux unsteadiness can then be found, which illustrate how the flow and heat flux transient histories determine whether the unsteadiness enhances or reduces the overall heat-transfer effectiveness. These expressions are used to show how significant enhancements or reductions in the average Nusselt number can be achieved in duct flow by applying appropriate temporal flow control. (c) 2006 American Institute of Physics.