Theoretical analysis of heat transfer in oscillating flows with fractional Maxwell model

By solving the momentum and energy equations of the oscillating flow with the fractional Maxwell model, which is driven by a sinusoidally varying pressure gradient, the general analytical solutions of the velocity profile, the temperature profile and the enhanced thermal diffusivity were obtained. Based upon the analysis of the enhanced thermal diffusivity, it is found that the parameters influenced the enhanced heat transfer for the problem are the Womersley number Wo, the Deborah number De, the dimensionless amplitude Δx/R and the Prandtl number of the fluid Pr. The heat transfer with fractional Maxwell model exhibits resonance phenomena similar to the flow of the viscoelastic fluid. And the number of the resonance peaks increases with the decrease of De, the frequency of the first peak decreases with the decrease of De. In addition, the frequencies where the resonance occurs are not concerned with the Pr and Δx/R.