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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.
By solving the equations of motion and energy in circular straight tube under viscoelastic fluid with fractional-order Maxwell model, the velocity distribution, temperature distribution and thermal diffusivity of oscillating tube flow are obtained. Through the analysis of the dimensionless thermal diffusivity, the dimensionless parameters affecting the axial heat transfer in viscoelastic fluid tubes are: Womersley number Wo, Deborah number De, dimensionless amplitude Δx / R and fluid Prandtl number Pr The fractional order Maxwell model also shows the resonance phenomenon existing in viscoelastic fluid flow, and the number of formant increases with the decrease of De number, and the initial frequency of resonance decreases with the decrease of De number. The position at which the peak appears is independent of Pr and the dimensionless amplitude Δx / R.