The variable nature of the thermal conductivity of nanofluid with respect to temperature plays an important role in many engineering and industrial applications including solar collectors and thermoelectricity. Thus, the foremost motivation of this article is to investigate the effects of thermal conductivity and electric conductivity due to variable temperature on the flow of Williamson nanofluid. The flow is considered between two stretchable rotating disks. The mathematical modeling and analysis have been made in the presence of magnetohydrodynamic and thermal radiation. The governing differential equations of the problem are transformed into non-dimensional differential equations by using similarity transformations. The transformed differential equations are thus solved by a finite difference method. The behaviors of velocity, temperature and concentration profiles due to various parameters are discussed. For magnetic parameter, the radial and tangential velocities have showed decreasing behavior, while converse behavior is observed for axial velocity. The temperature profile shows increasing behavior due to an increase in the Weissenberg number, heat generation parameter and Eckert number, while it declines by increasing electric conductivity parameter. The nanoparticle concentration profile declines due to an increase in the Lewis number and Reynolds number.

中文翻译：

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可变热导率和电导率对威廉姆森纳米流体在两个平行圆盘之间流动的影响

纳米流体的热导率随温度变化的性质在许多工程和工业应用中发挥着重要作用，包括太阳能集热器和热电。因此，本文的首要动机是研究由于温度变化引起的热导率和电导率对威廉姆森纳米流体流动的影响。在两个可拉伸的旋转圆盘之间考虑流动。在存在磁流体动力学和热辐射的情况下进行了数学建模和分析。通过相似变换将问题的控制微分方程转化为无量纲微分方程。变换后的微分方程因此通过有限差分法求解。速度的行为，讨论了由各种参数引起的温度和浓度曲线。对于磁参数，径向和切向速度表现出降低的行为，而对于轴向速度则观察到相反的行为。由于魏森伯格数、发热参数和埃克特数的增加，温度曲线显示出增加的行为，而随着电导率参数的增加而下降。由于路易斯数和雷诺数的增加，纳米粒子浓度分布下降。发热参数和埃克特数，随着电导率参数的增加而下降。由于路易斯数和雷诺数的增加，纳米粒子浓度分布下降。发热参数和埃克特数，随着电导率参数的增加而下降。由于路易斯数和雷诺数的增加，纳米粒子浓度分布下降。