Williamson Nanofluid Over A Cone and Wedge: Numerical Modelling of Hydromagnetic Brownian Motion Using the Extended Darcy Model

Abstract

The originality of this experiment lies in examining how the Lorentz force and Fr affect the Williamson fluid as it moves over the cone and wedge, two very different geometries. Along with the modifiable parameters of non-isothermal settings, the effects of Soret and Dufour are also taken into account. The non-linear equations of conservation are converted into the ordinary differential equations by utilizing appropriate similarity transformations. Finally, solutions to the system of ODEs are obtained by employing a finite difference scheme known as bvp4c in MATLAB. The relative tolerance of the scheme is set to 10−6 and a grid size of 10−3. The stability and convergence of the scheme have been verified by the grid point stability test. The behaviour of momentum of molecules and their thermal and mass diffusion of the fluid, and also the velocity–gradient, temperature-gradient, and species-gradient are portrayed explicitly and deliberated in detail for the influence of numerous fluid parameters. It is found that the heat-transmission on the surface of the cone is advanced than the wedge, and the rate of transmission of heat is supreme for Newtonian fluid in comparison to Williamson fluid. In contrast to the cone, the wedge has a greater impact of Fr on velocity, temperature, and concentration. Additionally, it is discovered that the enlarged values of the Williamson parameter decrease fluid velocity while increasing temperature and concentration dispersion. By adjusting the surface suction, magnetic field strength, and permeability of the porous material, fluid velocity can also be reduced to a minimum. Fr, M, Nt, and K all increase fluid temperature, while the suction parameter decreases fluid temperature. Non-Newtonian fluid has applications in the field of lubrication in numerous devices such as micro heat exchangers, micro cooling systems, micromixers, and so on. This study has a substantial influence on numerous engineering applications that analyse energy transfer in thermal equipment, designing heat exchanger devices and engines of gas turbines.