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An analytical investigation of pressure-driven flow and heat transfer of a Sisko fluid flowing through parallel plates with viscous dissipation
Sādhanā ( IF 1.6 ) Pub Date : 2020-07-02 , DOI: 10.1007/s12046-020-01413-2
Sumanta Chaudhuri , Sushil Kumar Rathore

Pressure driven flow of a Sisko fluid through rectangular parallel plates, having different wall temperatures is investigated considering the effect of viscous dissipation. The nonlinear momentum and energy conservation equations are solved employing homotopy perturbation method (HPM) and analytical solutions for the velocity, flow rate and temperature distributions are obtained. The analytical solution of pressure-driven flow and heat transfer characteristics of Sisko fluids flowing through parallel plates, taking into account viscous dissipation effect, has not been addressed earlier. For a special case of a typical Sisko fluid, the HPM solution exhibits an excellent agreement with the exact solution. Effects of various parameters such as Sisko fluid parameter, non-Newtonian index and Brinkman numbers on the variation of velocity and temperature are discussed. Further, temperature distribution in flow of Sisko fluids through parallel plates with both the plates maintained at same temperature is also obtained by a suitable substitution in the expression for temperature distribution. It is observed that the velocity decreases significantly with an increase in Sisko fluid parameter. Temperature of the fluid decreases with an increase in Sisko fluid parameter and displays an increasing trend with an increase in Brinkman number. Results of the present study are useful for designing thermal systems handling polymer flows. For the typical case of two plates having same temperature, the maximum temperature is observed to occur at the centre, which is attributed to the effect of viscous dissipation acting as an internal source. The theoretical framework developed and analytical solution provided for the problem under consideration may be taken as benchmark result for validation of future work.



中文翻译:

通过粘性耗散流经平行板的Sisko流体的压力驱动流动和传热的分析研究

考虑到粘性耗散的影响,研究了通过壁面温度不同的矩形平行板通过Sisko流体的压力驱动流。利用同伦摄动法(HPM)求解了非线性动量和能量守恒方程,并获得了速度,流量和温度分布的解析解。考虑到粘性耗散效应,Sisko流体流经平行板的压力驱动的流动和传热特性的解析解尚未解决。对于典型的希斯科(Sisko)流体的特殊情况,HPM解决方案与精确解决方案具有极好的一致性。各种参数的影响,例如Sisko流体参数,讨论了非牛顿指数和Brinkman数对速度和温度变化的影响。此外,通过适当地代入温度分布的表达式,还可以得到通过两块板都保持相同温度的,通过平行板的西斯科流体流动中的温度分布。观察到,速度随着Sisko流体参数的增加而显着降低。流体温度随着Sisko流体参数的增加而降低,并随着Brinkman数的增加而显示出增加的趋势。本研究的结果对于设计处理聚合物流的热系统很有用。对于两块板温度相同的典型情况,观察到最高温度发生在中心,这归因于粘性耗散作为内部来源的影响。为考虑中的问题开发的理论框架和提供的分析解决方案可以作为验证未来工作的基准结果。

更新日期:2020-07-02
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