This study investigates the flow and heat transfer characteristics of a second‐grade fluid over a flat surface with variable heat flux. Utilizing a mathematical model based on distributed order fractional derivatives, we offer a more precise representation of non‐Newtonian fluid behavior. The associated highly nonlinear equations are tackled numerically through an innovative amalgamation of the finite difference scheme and the technique. Our investigation thoroughly evaluates the influence of several critical parameters on the fluid's motion and thermal characteristics. Notably, the magnetic parameter significantly inhibits the fluid's velocity, illustrating the impact of magnetic forces. Additionally, the power law parameter leads to a decrease in both velocity and temperature profiles, highlighting its influence on fluid dynamics. Furthermore, changes in the Reynold number and the second‐grade fluid parameter are observed to cause a substantial increase in skin friction, by approximately 40% to 50%. These simulation results provide valuable insights into the complex interaction between fluid flow and heat transfer characteristics, enhancing our understanding of such systems in industrial applications.

中文翻译：

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使用分布式分数阶导数和 Cattaneo 热通量模型进行 MHD 流体流动分析的先进数值模拟技术

本研究研究了具有可变热通量的二级流体在平坦表面上的流动和传热特性。利用基于分布阶分数导数的数学模型，我们提供了非牛顿流体行为的更精确的表示。通过有限差分格式和技术的创新结合，可以在数值上解决相关的高度非线性方程。我们的研究彻底评估了几个关键参数对流体运动和热特性的影响。值得注意的是，磁性参数显着抑制流体的速度，说明了磁力的影响。此外，幂律参数会导致速度和温度曲线下降，突出其对流体动力学的影响。此外，据观察，雷诺数和二级流体参数的变化会导致表面摩擦力大幅增加，大约增加 40% 至 50%。这些模拟结果为流体流动和传热特性之间的复杂相互作用提供了宝贵的见解，增强了我们对工业应用中此类系统的理解。