Ferrofluid is a one-of-a-kind substance that functions both as a magnetic solid and as a liquid. In this article, waterbased Fe3O4 and Mn-ZnFe2O4 nanofluids between parallel stretchable spinning discs are considered. To carry out the study, the influence of rotational viscosity in the flow, which is due to the difference in rotation between the fluid and magnetic particles, and the applied magnetic field are examined. Additional impacts incorporated to the novelty of the model are the variable viscosity and variable thermal conductivity. The Legendre-based collocation method (LBCM) is used to solve the set of governing equations. To ensure the code validity, a comparison with analytical results is conducted and an excellent consensus is accomplished. Comparisons of the pertinent parameters on the flow profiles are displayed in tabular and graphical forms. Analyses reveal that the ferromagnetic Fe3O4 nanofluid shows higher thermal conductivity strength than the ferromagnetic Mn-ZnFe2O4 nanoparticles. This study finds its usefulness in aerospace, biotechnology, medical sciences, material sciences, and so on.

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Nanofluids generate high values of convection heat transfer coefficients, low specific heat, and density, which improve the solar thermal energy performance by making it work effectively. By utilizing nanotechnology and solar thermal radiation, the modern world is moving in the direction of new technologies. Therefore, this research is communicated to explore the significance of solar thermal energy, variable properties on non-Newtonian nanofluid flow. However, to exemplify the fluid transport features of the Casson nanofluid (CF), the Buongiorno nanofluid model was utilized. Also, the Lie-group technique is used in the framework to develop similarity variables that will be used to reduce the number of independent variables in partial differential equations (PDEs) and is solved numerically by using the weighted residual Galerkin method (WRGM). The graphical findings revealed that when the variable viscosity parameter is increased, the fluid temperature decreases, while the presence of the solar radiation parameter has the opposite impact. Additionally, when the non-Newtonian parameter approaches infinity, the Casson fluid obeys the viscosity law. The report of this study will be of benefit to thermal and chemical engineering for nanotechnology advancement. KEYWORD: Solar Thermal Energy, Nanofluids, Non-Newtonian, weighted residual Galerkin method (WRGM).