Magnetized casson SA-hybrid nanofluid flow over a permeable moving surface with thermal radiation and Joule heating effect

Here in, heat transfer characteristics of a magnetized Casson sodium alginate-alumina/copper hybrid nanofluid flowing through the permeable moving plane are investigated considering the effects of thermal radiation and Joule heating with Tiwari and Das model. The primary objective of the present study is to investigate the influence of the velocity ratio parameter on the solid volume fraction and the Casson parameter. In addition, the velocity and temperature profiles used in the current study illustrate the effects of the velocity ratio parameter R, solid volume fraction, suction effect, magnetic field, Joule heating, and thermal radiation. To apply the three-stage Lobatto IIIa with boundary value problems (bvp4c) approach to implement the appropriate similarity variables to transform the partial differential equations (PDEs) into a system of nonlinear ordinary differential equations (ODEs). It has been determined that there are two branch solutions for the velocity ratio parameter against using the Casson parameter and copper volume fraction values. Non-unique branch at R < R-ci however, no branch happens at R > R-ci. As the Eckert number and radiation grew, the rate of heat transmission surged. The increase of Casson hybrid nanofluid parameter values caused to drop the skin friction in both upper and lower branch.