Development of mathematical modeling of multi-phase flow of Casson rheological fluid: Theoretical approach

Abstract

• Multiphase flow of newtonian and casson rheological fluid. . • Magnetic and gravitational effect in a steep channel. • Exact solution is obtained through symbolic software. • Hartman number suppress the profiles of fluid and particle phases. • The dispersion of hafnium nano particles are good in newtonian fluid as compared to crystal particles. Theoretical stud of a rheological fluid suspended with two types of nanoparticles through a steep channel is presented in this article. Each suspension is formed by using the non-Newtonian Casson fluid model as the base liquid. Particulate flows are generated mainly due to the effects of gravitational force. In addition to this, the contribution of transversely applied magnetic fields is also considered. Further, the flow dynamics of Casson multiphase flows are compared with the ones suspended with the Newtonian fluid model. A closed-form solution is obtained for the mathematical modeled nonlinear partial differential equations which are transformed into a set of the ordinary differential equation. Separate expressions for volumetric flow rate and pressure gradient have been formulated, as well. Numerical results computed in the different tables show that Hafnium particles gain more momentum than crystal particles. Owing to, many engineering applications of highly thick multiphase flows, such as in chemical and textile industries, it is evident that Casson multiphase suspensions are quite suitable for coating purposes. Moreover, magnetized multiphase flows are compared with the previous investigation as the limiting case for the validation.