This study presents a mathematical model for layered non-miscible liquid flow in an inclined channel subject to a pulsatile pressure gradient. The Casson hybrid nanofluid (hnf) is sandwiched between the layers of Newtonian ternary hybrid nanofluid (t-hnf) and nanofluid (nf). Additionally, the impact of temperature-dependent viscosity is taken into consideration. Multiwall carbon nanotubes, molybdenum disulfide, and silver are considered nanoparticles, with water and kerosene oil as base fluids. The governing partial differential equations are transformed into coupled non-linear ordinary differential equations (ODEs) using the perturbation technique. The resulting ODEs are solved numerically using MATHEMATICA software with the help of the shooting technique associated with the Runge-Kutta fourth-order scheme. The behaviors of numerous sundry parameters against velocity, temperature, concentration, and shear stress are depicted graphically and in tabular form. The outcomes of the study reveal that if the viscosity is held constant, then the fluid’s velocity is initially low and gradually increases as the viscosity variation parameter rises. The velocity of fluid flow is higher when a Newtonian fluid occupies the middle region of the channel than when Casson fluid does. The increase in the nanoparticle shape factor, at both boundaries, results in an increase in the rate of heat transfer.
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