Modeling and analysis of megneto-Carreau fluid with radiative heat flux: Dual solutions about critical point
Modeling and analysis of megneto-Carreau fluid with radiative heat flux: Dual solutions about critical point
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DOI：
10.1177/1687814020945477
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发表时间：
2020-07
影响因子：
2.1
通讯作者：
H. Ullah;M. Khan;T. Hayat
中科院分区：
文献类型：
--
作者：
H. Ullah;M. Khan;T. Hayat
在这篇文章中，我们的目的是分析非牛顿材料（Carreau流体）在径向收缩表面上流动的对偶解。考虑磁流体力学流体。在能量表达式的数学模型中引入了StefanBoltzmann常数和平均吸收系数的概念。质量传递进行了讨论。对于不同的相关流动变量，计算了舍伍德数、表面摩擦系数和努塞尔数的上下分支解。采用适当的变换变量，将偏微分方程组化为常微分方程组。得到了无量纲浓度、温度、速度、浓度梯度、温度梯度和速度梯度的对偶解。对于速度梯度、温度梯度和浓度梯度的情形，得到了各上下解的临界值。结果表明，浓度场和温度场对上、下分支解的速度比和温度比参数的影响是相同的。
In this article, we aim to analyze the dual solutions for the flow of non-Newtonian material (Carreau fluid) over a radially shrinking surface. Magnetohydrodynamics fluid is considered. Concept of Stefan Boltzmann constant and mean absorption coefficient is used in the mathematical modeling of energy expression. Mass transfer is discussed. The upper and lower branch solutions for the Sherwood number, skin friction coefficient, and Nusselt number are calculated for different pertinent flow variables. Appropriate transformation variables are employed for reduction of partial differential equations system into ordinary differential equations. Dual solutions are obtained for the non-dimensional concentration, temperature, velocity, gradient of concentration, gradient of temperature, and gradient of velocity. The critical values for each upper and lower solutions are obtained for the case of gradient of velocity, gradient of temperature, and gradient of concentration. It is formed that concentration and temperature fields display same impact regarding both upper and lower branch solutions for velocity ratio and temperature ratio parameters.