Theoretical analysis of heat transfer in oscillating flows with fractional Maxwell model
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摘要: 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.
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关键词:
- 分数阶Maxwell模型 /
- 振荡流 /
- 传热 /
- 粘弹性流体 /
- 管流
Abstract: 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.-
Key words:
- fractional Maxwell model /
- oscillating flow /
- heat transfer /
- viscoelastic fluid /
- pipe flow
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[1] Rahaman K D,Ramkissoon H.Unsteady axial viscoelastic pipe flows [J].J Non-Newtonian Fluid Mech,1995,57:27-38 [2] Andrienko Y A,Siginer D A,Yanovsky Yu G.Resonance behavior of viscoelastic fluids in Poiseuille flow and application to flow enhancement [J].Int J Non-Linear Mech,2000,35:95-102 [3] Tsiklauri D,Beresney I.Enhancement in dynamic response of a viscoelastic fluid flowing through a longitudinally vibrating tube [J].Phys Rev E,2001,63:046304 [4] Watson E.Diffusion in oscillatory pipe flow [J].J Fluid Mech,1983,133:233-244 [5] Kurzweg U H.Enhanced heat conduction in fluids subjected to sinusoidal oscillations [J].J Heat Transfer,1985,107:459-462 [6] 赵令德,朱谷君,曹玉璋,等.毛细管束中层流粘性振荡流强化传热的若干问题[J].北京航空航天大学学报,1991,17(2):57-66 Zhao Lingde,Zhu Gujun,Cao Yuzhang,et al.Some aspects of enhanced heat transfer in laminar oscillatory viscous flows within capillary bundle [J].Journal of Beijing University of Aeronautics and Astronautics,1991,17(2):57-66 (in Chinese) [7] 赵令德,朱谷君,曹玉璋,等.振荡管流换热的理论解[J].力学学报,1992,24(5):614-619 Zhao Lingde,Zhu Gujun,Cao Yuzhang,et al.Theoretical solution on heat transfer in oscillatory pipe flow [J].Chinese Journal of Theoretical and Applied Mechanics,1992,24(5):614-619 (in Chinese) [8] Lambert A A,Cuevas S,del Río J A.Enhanced heat transfer using oscillatory flows in solar collectors [J].Solar Energy J,2006,80:1296-1302 [9] Lambert A A,Cuevas S,del Río J A,et al.Heat transfer enhancement in oscillatory flows of Newtonian and viscoelastic fluids[J].International Journal of Heat and Mass Transfer,2009,52:5472-5478 [10] Hayat T,Nadeem S,Asghar S.Periodic unidirectional flows of a viscoelastic fluid with the fractional Maxwell model [J].Appl Math Comput,2004,151:153-161 [11] Jia J H,Hua H X.Study of oscillating flow of viscoelastic fluid with the fractional Maxwell method [J].ASME Trans J Fluids Eng,2008,130:1-4 [12] Yin Y B,Zhu K Q.Oscillating flow of a viscoelastic fluid in a pipe with the fractional Maxwell model [J].Applied Mathematics and Computation,2006,173:231-242 [13] Yan B H,Yu L,Yang Y H.Study of oscillating flow in rolling motion with the fractional derivative Maxwell model [J].Progress in Nuclear Energy,2011,53:132-138 [14] Chatwin P C.On the longitudinal dispersion of passive contaminant in oscillatory flows in tubes [J].J Fluid Mech,1975,71(3):513-527 -
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