Abstract The purpose of this paper is to consider heat and mass transfer processes on two non-Newtonian fluids (Walters-B viscoelastic and Casson fluid) situated in a hot environment. This study considered concentrated fruit juice and tomato sauce as the type of Casson fluid and polymethyl methacrylate, chromatography, and ceramic processing as the type of Walters-B viscoelastic fluids. The model is governed by systems of partial differential equations. These equations were simplified with the help of appropriate similarity variables to obtain nonlinear couple fourth-order ordinary differential equations. The transformed equations were solved numerically using the spectral homotopy analysis method (SHAM). SHAM is rooted in the homotopy analysis method (HAM) and the Chebyshev spectral collocation method. SHAM is efficient and converges faster than HAM. This paper is unique because it explored variable viscosity and thermal conductivity in the presence of flow parameters such as Soret, Dufour, radiation, viscous dissipation, magnetic field, and so on. The applied magnetic field serves as an opposition to the flow and thereby slows down the motion of an electrically conducting fluid. The influence of pertinent flow parameters is extensively discussed and presented graphically. The permeability parameter is noticed to decrease the velocity profile and increase the temperature profile. The present results were found to be in good agreement with existing works in literature.

中文翻译：

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在 Soret-Dufour 影响下，变热导率和粘度对通过垂直多孔板的非牛顿流体流动的影响

摘要 本文的目的是考虑位于热环境中的两种非牛顿流体（Walters-B 粘弹性流体和 Casson 流体）的传热和传质过程。本研究将浓缩果汁和番茄酱视为 Casson 流体的类型，将聚甲基丙烯酸甲酯、色谱和陶瓷加工视为 Walters-B 粘弹性流体的类型。该模型由偏微分方程组控制。借助适当的相似变量对这些方程进行简化，得到非线性耦合的四阶常微分方程。使用光谱同伦分析方法 (SHAM) 对转换后的方程进行数值求解。SHAM 源于同伦分析法（HAM）和切比雪夫谱搭配法。SHAM 比 HAM 高效且收敛速度更快。这篇论文是独一无二的，因为它探讨了存在流动参数（如 Soret、Dufour、辐射、粘性耗散、磁场等）时的可变粘度和热导率。施加的磁场作为流动的反作用，从而减慢导电流体的运动。相关流动参数的影响被广泛讨论并以图形方式呈现。注意到渗透率参数会降低速度剖面并增加温度剖面。发现目前的结果与文献中的现有作品非常吻合。磁场等。施加的磁场作为流动的反作用，从而减慢导电流体的运动。相关流动参数的影响被广泛讨论并以图形方式呈现。注意到渗透率参数会降低速度剖面并增加温度剖面。发现目前的结果与文献中的现有作品非常吻合。磁场等。施加的磁场作为流动的反作用，从而减慢导电流体的运动。相关流动参数的影响被广泛讨论并以图形方式呈现。注意到渗透率参数会降低速度剖面并增加温度剖面。发现目前的结果与文献中的现有作品非常吻合。