With their extraordinary ability to conduct heat and their promise to increase heat transfer efficiency, nanofluids have emerged as a major player in the field of fluid technology today. This manuscript delves into the dynamic behavior of time-dependent complex Oldroyd-B nanofluids as they traverse between parallel plates within a porous media. Intriguingly, the study introduces captivating elements, including magnetic fields, convection, diffusion, heat source effects, and chemical reactions, which augment the uniqueness of the research. The designed model exhibits the potential to uncover the inherent characteristics and memory effects of viscoelastic nanofluids, pioneering the utilization of non-integer Caputo fractional derivatives to address this challenge. To tackle the complexities of this problem, we employ a combination of finite difference and finite element methods for the discretization of the governing flow equations. This enables us to flawlessly compute key parameters such as the Nusselt number, Sherwood number, and Skin friction coefficient for the complex fractional viscoelastic model. Our rigorous approach also involves the validation of the numerical scheme for convergence and the provision of error estimates. Our research delves into the realm of heat and mass transfer phenomena in porous media, specifically focusing on the intricate interplay between complex fluid dynamics and nanoparticle suspension. The results are given graphically, providing a picture of the importance of certain fractional and dimensionless physical characteristics. Notably, the flow simulations' application and importance are deepened by the inclusion of chemical processes, especially when considering the chemical sector.

中文翻译：

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使用 Oldroyd-B 复杂纳米流体流动和热源增强多孔介质中的传热和传质


凭借其非凡的导热能力和提高传热效率的承诺，纳米流体已成为当今流体技术领域的主要参与者。该手稿深入研究了时间依赖性复杂 Oldroyd-B 纳米流体在多孔介质内的平行板之间穿过时的动态行为。有趣的是，该研究引入了引人入胜的元素，包括磁场、对流、扩散、热源效应和化学反应，这增强了研究的独特性。设计的模型展示了揭示粘弹性纳米流体的固有特性和记忆效应的潜力，开创性地利用非整数卡普托分数导数来应对这一挑战。为了解决这个问题的复杂性，我们采用有限差分和有限元方法的组合来离散控制流动方程。这使我们能够完美地计算复杂分数粘弹性模型的关键参数，例如努塞尔数、舍伍德数和表层摩擦系数。我们严格的方法还涉及验证数值方案的收敛性和提供误差估计。我们的研究深入研究多孔介质中的传热和传质现象领域，特别关注复杂流体动力学和纳米颗粒悬浮液之间复杂的相互作用。结果以图形方式给出，提供了某些分数和无量纲物理特性的重要性的图片。值得注意的是，流动模拟的应用和重要性因化学过程的纳入而加深，特别是在考虑化学领域时。