In this paper, the two-phase flow of non-Newtonian fluid is investigated. The main source of the flow is metachronal waves which are caused by the back and forth motion of cilia attached to the opposite walls of the channel. Magnetohydrodynamics (MHD) of Casson fluid experience the effects of transverse magnetic fields incorporated with the slippery walls of the channel. Thermal effects are examined by taking Roseland’s approximation and application of thermal radiation into account. The heat transfer through the multiphase flow of non-Newtonian fluid is further, compared with Newtonian bi-phase flow. Since the main objective of the current study is to analyze heat transfer through an MHD multiphase flow of Casson fluid. The two-phase heated flow of non-Newtonian fluid is driven by cilia motion results in nonlinear and coupled differential equations which are transformed and subsequently, integrated subject to slip boundary conditions. A closed-form solution is eventually obtained form that effectively describes the flow dynamics of multiphase flow. A comprehensive parametric study is carried out which highlights the significant contribution of pertinent parameters of the heat transfer of Casson multiphase flow. It is inferred that lubricated walls and magnetic fields hamper the movement of multiphase flow. It is noted that a sufficient amount of additional thermal energy moves into the system, due to the Eckert number and Prandtl number. While thermal radiation acts differently by expunging the heat transfer. Moreover, Casson multiphase flow is a more suitable source of heat transfer than Newtonian multiphase flow.

中文翻译：

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润滑壁作用下异时波诱导的MHD液-粒悬浮对比研究

本文研究了非牛顿流体的两相流动。流动的主要来源是异时波，它是由附着在通道相对壁上的纤毛来回运动引起的。Casson 流体的磁流体动力学 (MHD) 经历了与通道的光滑壁相结合的横向磁场的影响。通过考虑 Roseland 的近似和热辐射的应用来检查热效应。与牛顿双相流相比，通过非牛顿流体多相流的传热更远。由于当前研究的主要目标是分析通过卡松流体的 MHD 多相流的热传递。非牛顿流体的两相加热流由纤毛运动驱动，产生非线性和耦合的微分方程，这些方程被转换并随后在滑移边界条件下积分。最终得到一个封闭形式的解，它有效地描述了多相流的流动动力学。进行了一项全面的参数研究，突出了 Casson 多相流传热的相关参数的重要贡献。据推断，润滑壁和磁场阻碍了多相流的运动。值得注意的是，由于埃克特数和普朗特数，足够量的额外热能进入系统。而热辐射通过消除热传递起到不同的作用。而且，