Present work formulates the unsteadily revolving fluid flow caused by a rotating porous disk in a variable viscosity fluid. Following an existing paper, the disk angular velocity is assumed to exhibit an inversely linear time dependency. Moreover, temperature dependency in fluid viscosity is incorporated in the analysis. Two different numerical approaches namely, a modified finite difference scheme and the collocation method based MATLAB package bvp4c, are employed to find self-similar solutions. Subtle fluid mechanics concepts such as radial wall stress, torque required, volumetric flow rate and heat transfer rate are analyzed for full range of unsteadiness parameter , measuring the decay rate of disk angular velocity. There exists a particular value of designated as which corresponds to zero torque (′(0) = 0) illustrating the situation of freely rotating disk. Beyond this value of , that is < , ′ (0) has a negative sign signaling that fluid's angular velocity becomes higher than that of the disk. Our emphasis is to seek how the said flow model is affected by variable fluid properties. It should be remarked here that variable viscosity/thermal conductivity considerably alters the overall drag coefficient as well as heat transfer rate.

中文翻译：

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对具有可变流体特性的减速旋转盘附近的流体流动中的传热进行建模


目前的工作阐述了由可变粘度流体中的旋转多孔盘引起的不稳定旋转流体流动。根据现有论文，假设圆盘角速度表现出反线性时间依赖性。此外，分析中还考虑了流体粘度的温度依赖性。采用两种不同的数值方法，即改进的有限差分格式和基于 MATLAB 包 bvp4c 的配置方法来寻找自相似解。分析了诸如径向壁应力、所需扭矩、体积流量和传热速率等微妙的流体力学概念，以获取全范围的非稳态参数，测量圆盘角速度的衰减率。存在指定为的特定值，其对应于零扭矩（'（0）= 0），说明了自由旋转盘的情况。超过该值（即 <），′(0) 具有负号，表示流体的角速度高于圆盘的角速度。我们的重点是寻找可变流体特性如何影响所述流动模型。这里应该指出的是，可变的粘度/导热率会显着改变整体阻力系数以及传热速率。