Taguchi and ANOVA optimizations on thermal enhancement of the Casson fluid with tri-hybrid nanofluid due to hemispherical surface

The current model aims to simulate the characteristics of the Casson fluid with slip effects and a heat source on a hemispherical surface. Trihybrid nanofluid contains aluminum oxide, $$\:SiC$$ and $$\:C{o}_{3}{O}_{4}$$ in the base fluid (ethylene glycol). The activation energy, thermal and the Lorentz force are considered. Taking into account the Casson fluid and the trihybrid nanofluid enhances the uniqueness of the model. Additionally, the current study explores the insights of heat transfer efficiency, agricultural productivity, cooling of electronic equipment, solar collectors and climate variation. The study formulates a mathematical model using partial differential equations and converts it into dimensionless form using suitable variables. The resulting model is simulated by the finite element method. Moreover, Taguchi and ANOVA methods are used on the Nusselt number. Increasing the magnetic number and the Casson number decreases the velocity field and the momentum boundary-layer thickness. The velocity field and thickness (momentum boundary layer) have decreased when slip flow number ( $$\:{\beta\:}^{*}$$ ) and $$\:{\lambda\:}_{T}$$ are increased. The temperature profile increases by approximately 16% when the radiation parameter is increased from 0.3 to 1.5, while the tri-hybrid nanofluid experiences a 20% higher temperature profile than the hybrid nanofluid. The heat transfer rate for the tri-hybrid nanofluid is enhanced by 28.63% compared to the hybrid nanofluid in the case of the magnetic field.