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Computational study of solid-liquid supercritical flow of 4th-grade fluid through magnetized surface

This paper offers a comparative investigation of the multiphase flow of Newtonian and non-Newtonian dispersions passing through an inclined channel. Couette and Generalized Couette flow models are taken into account. A fourth-grade fluid is taken as non-Newtonian fluid, as well as base fluid. The stress tensor of fourth-grade fluid is used to formulate the problem. The relative motion between fluid and the upper plate is considered, while the relative motion between fluid and lower plate is mistreated. Crystal and Hafnium nano-sized particles are utilized to prepare dispersions. An external magnetic field is applied to the multiphase flows of dispersions in the channel and at the same time, the impact of gravitational force is also examined which has great mastery on flows. The governing equations for two-phase flows problem are determined by using Naiver-Stokes equations of continuity and momentum. Partial differential equations are reduced into ordinary differential equations by using appropriate transformations. The perturbation method is used to find out analytical solutions to these ordinary differential equations. Exact and approximation solutions are obtained by using MATHEMATICA Software. The impacts of salient parameters on each type of flow for velocity profile are discussed graphically. Furthermore, the comparison of velocity profiles of multiphase flows of dispersions is also presented in tabular forms. The variation in the magnitude of the fourth-grade non-Newtonian dimensionless parameter has great importance in non-Newtonian dispersions. The outcomes dispose of that the two-phase flows of Newtonian fluids suspended with crystal and hafnium particles are better one than the bi-phase flows of fourth-grade dispersions. Moreover, the Newtonian fluids suspended with hafnium particles are more consequential than the Newtonian fluids suspended with crystal particles. Similarly, the same behavior is observed in fourth-grade non-Newtonian dispersions. Then it is concluded that hafnium particles are a better option than crystal particles. These amalgams are very useful in every field of life, especially medicine as nanofluid drug delivery. In addition to this, no comparative analysis between Newtonian and fourth-grade non-Newtonian bi-phase flows has so far been reported in the existing literature.