Numerical simulation of nanofluid flow between two parallel disks using 3-stage Lobatto III-A formula

The development of nanofluid technology has become a key research area in physics, mathematics, engineering, and materials science. Nowadays, in many industrial applications, nanofluids are widely used to enhance thermophysical properties such as thermal diffusivity, thermal conductivity, and convective heat transfer. Scientists and engineers have established interests in the direction of flow problems developed via disk-shaped bodies. There are various logics to discuss flow phenomenon due to rotating bodies, but its applications include in thermal power engineering system, gas turbine rotors, air cleaning machines, aerodynamics, etc. Nowadays manufacturing industries have inaugurated to select liquid based on heat transfer properties. Therefore, this article focuses on studying the laminar incompressible nanofluid between two parallel disks. Mathematical formulations of the law of conservation of mass, momentum, and heat transfer are investigated numerically. By using suitable similarities, the flow equations are converted into nonlinear ordinary differential equations. The resulting equations were solved numerically via MATLAB software. The effects of physical parameters of interest, such as Reynolds number, magnetic factor, Brownian parameter, and thermophoresis parameter on normal velocity, streamwise velocity, temperature, and concentration profiles are computed and presented using the graphs. The results revealed that the energy profile significantly rises, and the profile moves closer to the upper disk by enhancing the Brownian motion and thermophoresis parameter. The dynamics behind this is that by increasing the Brownian motion, the boundary layer wideness increases which increases the temperature. Moreover, streamwise velocity increases for large values of Reynolds number. Besides, the thermophoresis profile increases for large values of the thermophoresis factor. It could be observed that shear stress at nonporous/porous disk is adjusted by selecting a suitable value of injection velocity at the porous disk. Also, normal velocity decreases by increasing the parameter M.