Thermal and concentration memory effects on the transport of heat and mass subjected to magnetic field and non-uniform free stream velocity are studied in this article. A cross-rheological model is used with governing laws that are solved numerically using the finite element method (FEM). A computer program is developed. The convergent and grid-independent solutions are computed, which are further used to analyse the impact of related parameters on flow fields. Influence of ternary, di-, and mono-nanoparticles on generalized transport of heat and mass in non-Newtonian fluids with cross-rheology. The dynamics of wall shear stress, wall heat, and mass fluxes are studied. Cross-fluid is a non-Newtonian fluid. It has shear rate-dependent viscosity. The behavior of cross-fluid rheology on velocity can be seen through a variation of the cross-fluid parameter called the Weissenberg number, and it has an increasing behavior on velocity. Cross-nanofluid is highly influenced by the magnetic field in comparison with cross-tri-nanofluid and cross-di-nanofluid.

中文翻译：

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多纳米级颗粒存在下交叉流变流体中广义传热传质的数值研究：伽辽金有限元方法

本文研究了磁场和非均匀自由流速度下热和质量传输的热和浓度记忆效应。交叉流变模型与使用有限元法 (FEM) 进行数值求解的控制定律一起使用。开发了计算机程序。计算收敛且与网格无关的解，进一步用于分析相关参数对流场的影响。三元、二元和单纳米颗粒对具有交叉流变学的非牛顿流体中的广义热和质量传递的影响。研究了壁剪应力、壁热和质量通量的动力学。交叉流体是一种非牛顿流体。它具有与剪切速率相关的粘度。跨流体流变学对速度的影响可以通过称为魏森伯格数的跨流体参数的变化看出，并且它对速度具有递增的行为。与交叉三纳米流体和交叉二纳米流体相比，交叉纳米流体受磁场的影响更大。