Forced convection with laminar pulsating flow in a channel or tube

A perturbation approach is used to obtain analytical expressions for the velocity, temperature distribution, and transient Nusselt number for the problem of forced convection, in a parallel-plates channel or a circular tube, produced by an applied pressure gradient that fluctuates with small amplitude harmonically in time about a non-zero mean. It is found that the fluctuating part of this Nusselt number alters in magnitude and phase as the dimensionless frequency increases. The magnitude increases from zero, goes through a peak, and then decreases to zero. The height of the peak decreases as the Prandtl number Pr increases. The phase (relative to that of the steady component) decreases from pi/2 to -pi/2. When Pr = 1 there is a weak singularity in the form of the temperature distribution, but the Nusselt number is not significantly different from the case when Pr not equal 1. (c) 2006 Elsevier Masson SAS. All rights reserved.