Entropy generation and heat transfer analysis of unsteady micropolar magnetized hybrid-nanofluid flow over a radially stretchable permeable rotating disk with viscous and joule dissipation effects

This study investigates the unsteady, three-dimensional radiative, micropolar hybrid nanofluid flow across the radially rotating disc in a Darcy-Forchheimer porous medium, under the influence of an applied magnetic field. The effects of viscous dissipation and Joule heating are also considered. Detailed analyses of entropy generation and the Bejan number are provided. Copper ( Cu ) and Titanium dioxide (TiO 2 ) nanoparticles are modeled mathematically using a cylindrical coordinate system with engine oil as the base fluid. Both Copper ( Cu ) and Titanium dioxide (TiO 2 ) nanoparticles are consider 50 %-50 %. The Navier-Stokes equations governing momentum, microrotation, and energy are transformed into ordinary differential equations using similarity variables. These modified equations are solved numerically using shooting approach (bvp4c). The study includes graphical representations and discussions on the impact of various controlling parameters. The considered range for the parameters are  Mn = 0.1  to  3.1,  β = 0.1  to  1.3,  π = 0.5  to  2.0, St = 0.1  to  1.3,   K 1 = S 0 = A 3 = 0.1  to  1.0, Bi = 0.1  to  0.4, Ec = 1.0  to  1.4,.  Br = 0.10  to  0.25, α 1 = 0.1  to  2.5. Results indicate that the unsteady parameter decay the velocity profile (both radial and tangential direction) and reduce the microrotation velocity in r and z direction, while enhancing the microrotational velocity in θ direction. Additionally, an increase in the stretching parameter raises the radial velocity but lowers the tangential velocity profile. The temperature profile and entropy generation increases for large values of magnetic parameter, whereas the Bejan number decreases. Similarly, tables were analyzed to illustrate the impact of varying physical parameters on the skin friction local Nusselt number. It is noted that the magnetic parameter enhance the skin friction coefficient while decline the local Nusselt number. The concentration of Copper ( Cu ) and Titanium dioxide (TiO 2 ) nanoparticles is (0-6)%.