Abstract
In this research work, we consider a thermal energy system with a different controlling effects which impact the entire system. These controlling effects include the variable thermo-physical properties of Carreau fluid flow causing change in internal energy (viscous dissipation) of the permeable thermal conversion problem. The disturbance in fluid's motion is created by applying magnetic dipole. After converting the thermal system from partial differential into ordinary differential, the developed system is solved by using midpoint method in combination with bisection. The thermal energy extrusion system consists of velocity and temperature fields. The related controlling parameters include variable thermal conductivity parameter, Darcy-Forchheimer parameter, Eckert number, mixed convection parameter, variable viscosity parameter, ferrohydrodynamic interaction variable, Weissenberg number, curie temperature and Prandtl number. The sketched results provides good thermal effects on entire system for small and large values of these parameters. Carreau fluid model is performed to analyse the properties of shear thinning and thickening. It is noticed that velocity distribution reduces for large values of Williamson parameter, ferrohydrodynamic interaction variable, porosity parameter and variable viscosity parameter but opposite behavior is achieved for large values of Darcy-Forchheimer parameter. The temperature profile shows great impact by emerging parameters appearing on it. The small parameter and Eckert number shows enhancement in temperature distribution, but large reduction is noticed in temperature distribution for greater values of Prandtl number and curie parameter. Comparison of current thermal system is calculated for limited values of these parameters.