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 π/2 to −π/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≠1.