Objective:

Many methods have been used to maximize the capacity of heat transport. A constant pressure gradient or the motion of the wall can be used to increase the heat transfer rate and minimize entropy. The main goal of our investigation is to develop a mathematical model of a non-Newtonian fluid bounded within a parallel geometry. Minimization of entropy generation within the system also forms part of our objective.

Method:

Perturbation theory is applied to the nonlinear complex system of equations to obtain a series solution. The regular perturbation method is used to obtain analytical solutions to the resulting dimensionless nonlinear ordinary differential equations. A numerical scheme (the shooting method) is also used to validate the series solution obtained.

Results:

The flow and temperature of the fluid are accelerated as functions of the non-Newtonian parameter (via the power-law index). The pressure gradient parameter escalates the heat and volume flux fields. The energy loss due to entropy increases via the viscous heating parameter. A diminishing characteristic is predicted for the wall shear stress that occurs at the bottom plate versus the time-constant parameter. The Reynolds number suppresses the volume flux field.

中文翻译：

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通过加热板之间的摄动和数值方法研究熵优化的双曲正切流体（非牛顿）

目的：

已经使用许多方法来最大化热传递的能力。恒定的压力梯度或壁的运动可用于增加传热速率并使熵最小。我们研究的主要目标是建立一个以平行几何为边界的非牛顿流体的数学模型。使系统内的熵产生最小化也是我们目标的一部分。

方法：

将摄动理论应用于非线性复杂方程组以获得级数解。正则摄动法用于获得所得的无量纲非线性常微分方程的解析解。数值方案（射击方法）也用于验证获得的级数解。

结果：

流体的流量和温度作为非牛顿参数的函数加速（通过幂律指数）。压力梯度参数使热量和体积通量场升高。由于熵引起的能量损失会通过粘性加热参数而增加。预测在底板处出现的壁切应力与时间常数参数之间的递减特性。雷诺数抑制了体积通量场。