基于分数阶Maxwell模型的振荡流传热特性分析

经求解基于分数阶Maxwell模型的粘弹性流体在周期性振荡压力梯度下,圆直管内的运动方程和能量方程,得到了振荡管流换热的速度分布、温度分布以及热扩散系数的解析解形式.通过对无量纲热扩散系数的分析可知,影响粘弹性流体管内振荡流轴向换热的无量纲参数有:Womersley数Wo、Deborah数De、无量纲振幅Δx/R和流体普朗特数Pr.分数阶Maxwell模型振荡流传热也存在粘弹性流体流动中存在的共振现象,且共振峰的数量随De数的减小而增加,发生共振的起始频率随De数的减小而降低.共振峰值出现的位置即频率值与Pr和无量纲振幅Δx/R无关.

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.