Transient Convective Heat Transfer in Planar Stagnation Flows With Time-Varying Surface Heat Flux and Temperature

Impinging flows are used in a variety of applications where effective and localized heat transfer is mandated by short residence times or by space constraints, as in cooling materials moving along a conveyor or removing heat dissipated within microelectronic circuitry. A wide selection of heat transfer correlations is available for steady-state conditions. However, instantaneous heat transfer coefficients can differ significantly from steady-state values when temporal variations occur in the surface heat flux or surface temperature. Under these conditions, the temperatures of fluid layers near the surface are affected preferentially due to their proximity to the temporal variation. A theoretical model is formulated to assess the importance of a time-varying surface heat flux or temperature on convective heat transfer in a steady, planar stagnation flow. A governing equation for the transient heat transfer response is formulated analytically from the boundary layer equations for momentum and energy conservation in the fluid. Numerical solutions to the governing equation are determined for ramp and sinusoidal changes in the surface heat flux or temperature. Results indicate that the time response is chiefly governed by the velocity gradient in the free stream and to a lesser extent by the Prandtl number. Departures from steady-state Nusselt numbers are larger for more rapid transients and smaller or comparable in size to the magnitude of the imposed variation at the surface.