School of Mathematics and Statistics,Beijing Institute of Technology, Beijing 100081, China; Department of Mathematics and Statistics, Hazara University, Mansehra 21300, Pakistan.
School of Mathematics and Statistics,Beijing Institute of Technology, Beijing 100081, China; Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif, Azad Kashmir 12010, Pakistan.
Comput Methods Programs Biomed. 2020 Jul;190:105363. doi: 10.1016/j.cmpb.2020.105363. Epub 2020 Jan 28.
Background In this research communication, entropy optimized Darcy-Forchheimer flow with magnetohydrodynamic over a stretched surface is considered. Here Molybdenum disulfide (MOS) and Silicon dioxide (SiO) are taken as a nanoparticles and Propylene glycol as a continuous phase liquid. Electrically conducting fluid is considered and flow is generated via stretched surface of sheet. The total entropy rate which is depends on four types of irreversibilities i.e., heat transfer, porosity, fluid friction and dissipation) is calculated via second law of thermodynamics. The energy expression is mathematically modeled and discussed subject to heat generation/absorption, dissipation, thermal radiation and Joule heating. Furthermore, temperature dependent viscosity is accounted. Method The nonlinear PDE's (partial differential equations) are first changed to ODE's (ordinary differential equations) through implementation of appropriate similarity variables (transformations). The numerical results of ordinary ones are computed via Built-In-Shooting method. The results for the flow field, temperature, skin friction, Nusselt number and entropy generation are discussed against various sundry flow parameters graphically. Results Salient characteristics of sundry flow parameters on the entropy generation rate, velocity, Bejan number, gradients of velocity, gradient of temperature and temperature are examined and display graphically. The results are computed for both nanoparticles. From obtained results it is observed that temperature field increases versus higher thermal Biot number for both nanoparticles. It is also observed that the thermal field is more in presence of Molybdenum disulfide as compared to Silicon dioxide, because the thermal conductivity of Molybdenum disulfide is higher than Silicon dioxide. Entropy generation and Bejan number show contrast impact versus higher estimations of Brinkman number versus both nanoparticles.
背景 在本研究通讯中，考虑了熵优化的达西-Forchheimer 流动与磁流体动力学在拉伸表面上的流动。这里选择二硫化钼 (MOS) 和二氧化硅 (SiO) 作为纳米粒子，丙二醇作为连续相液体。考虑到导电流体，通过薄板的拉伸表面产生流动。总熵率取决于传热、多孔性、流体摩擦和耗散等四种不可逆性，并通过热力学第二定律进行计算。能量表达式通过热生成/吸收、耗散、热辐射和焦耳加热进行数学建模和讨论。此外，还考虑了温度相关的粘度。
方法 通过实施适当的相似性变量（变换），将非线性 PDE（偏微分方程）首先转换为 ODE（常微分方程）。通过内置射击法计算普通 ODE 的数值结果。以各种不同的流动参数为变量，对流动场、温度、摩擦系数、努塞尔数和熵产生进行了讨论。
结果 以图表形式检查并显示了各种不同流动参数对熵产生率、速度、贝努力数、速度梯度、温度梯度和温度的影响。计算了两种纳米粒子的结果。从得到的结果中可以观察到，对于两种纳米粒子，温度场随着更高的热 Biot 数而增加。还观察到，在二硫化钼存在的情况下，热场比二氧化硅更大，因为二硫化钼的热导率比二氧化硅更高。熵产生和 Bejan 数显示出与 Brinkman 数的更高估计值的对比影响，对于两种纳米粒子都是如此。
