Micropolar fluids are used in lubrication theory, thrust bearing technologies, cervical flows, lubricants, paint rheology, and the polymer industry. This study develops the numerical simulation of the magneto-Darcy flow of a polarized nanoliquid with Joule heating and viscous heating mechanisms on an exponentially elongated surface. The effects of linearized Rosseland radiation and temperature-dependent heat generation are considered. The flow is generated by an exponential form of elongation of a flexible sheet. The porous matrix and nanoparticle effects are characterized by the Darcy expression and the two-component Buongiorno model correspondingly. The resulting partial differential systems are solved numerically using the Runge–Kutta-based shooting technique to interpret the importance of key parameters in physical quantities. A direct comparison is made to validate the results. Our results demonstrated that arbitrary movement of the nanoparticles significantly advances the temperature profile by reducing the concentration of nanoparticles. Both Joule heating and viscous heating mechanisms improve the structure of the thermal boundary layer. The porous matrix reduces the velocity of the nanoliquid and thus the width of the velocity boundary layer is reduced.

微极性流体用于润滑理论、推力轴承技术、颈流、润滑剂、涂料流变学和聚合物工业。本研究利用焦耳加热和粘性加热机制在指数拉长的表面上对极化纳米液体的磁达西流进行数值模拟。考虑了线性化 Rosseland 辐射和与温度相关的发热的影响。流动是由柔性片材的指数形式的伸长率产生的。多孔基体和纳米粒子效应的特点是相应的 Darcy 表达式和双组分 Buongiorno 模型。所得偏微分系统使用基于 Runge-Kutta 的射击技术进行数值求解，以解释物理量中关键参数的重要性。进行直接比较以验证结果。我们的结果表明，纳米颗粒的任意运动通过降低纳米颗粒的浓度显着提高了温度曲线。焦耳加热和粘性加热机制都改善了热边界层的结构。多孔基质降低了纳米液体的速度，从而降低了速度边界层的宽度。