Perturbation method for the motion of crystal solid particles in Couette–Poiseuille flow of non‐Newtonian fluid

Abstract The study of fluid–particle mixture flows with heat transfer have attracted considerable attention from researchers owing to their wide‐ranging applications in science, engineering, and technology. The present work focuses on analyzing the motion of solid particles within three fundamental flow configurations of a Tangent‐hyperbolic fluid confined between two infinite parallel plates under the influence of an external magnetic field. The mixture flow is analyzed by incorporating the stress tensor of the Tangent‐hyperbolic fluid, and two distinct two‐phase models are formulated based on the continuity, momentum, and energy equations together with the relevant boundary conditions. To simplify the governing system and highlight the influence of physical parameters, the equations are transformed into a dimensionless form through the introduction of suitable nondimensional variables. The regular perturbation technique is then applied to derive approximate analytical solutions for the problem. The computational analysis shows that increasing the concentration of rigid solid particles in the carrier fluid enhances the flow characteristics in both plane Poiseuille and generalized Couette flow configurations. It is also observed that the Power‐law index plays a significant role in elevating the temperature distribution and improving the heat transfer rate across all considered flow cases. Among them, the pressure‐driven plane Poiseuille flow exhibits the highest rate of heat transfer. The heat transfer behavior of hydromagnetic mixture flow containing suspended crystal particles in a Tangent‐hyperbolic fluid between infinite parallel plates, considering three distinct fundamental flow configurations, has not been previously addressed in the literature. This unexplored aspect constitutes the research gap targeted in the present study. This theoretical work can be useful in understanding the three fundamental fluid‐particle suspension flows of Tangent‐hyperbolic fluid in two‐parallel infinite plates when the magnetic field is applied uniformly. Further, this study will also help how the heat transfer rate is affected by the motion of crystal nanoparticles and moving plates with and without pressure gradient.