Numerical analysis of MHD Darcy–Forchheimer Williamson hybrid nanofluid flow with brownian and thermophoretic effects

This study explores the thermal and mass transportation phenomena in blood-based magnetohydrodynamic Darcy–Forchheimer Williamson hybrid nanofluid motion over an extendable boundary within a porous matrix, combining thermophoretic effects and Brownian movement dynamics. The magnetic field effects, Joule thermal dissipation and internal heat generation due to viscous dissipation mechanisms are considered. The governing nonlinear partial differential equations are first converted to ordinary differential equation systems through the use of similarity transformation methods and then they have been solved using numerical computation by employing bvp4c solver based upon MATLAB program. The analysis is on the effect of governing parameters which are critical to flow behavior. The work also examines transport phenomena parameters like surface friction coefficients, heat and mass transfer rates. Numerical findings show that the values of hybrid nanofluid temperature distributions show increasing trend as a result of an increase in the thermophoretic and Brownian motion parameters respectively, on the other hand species concentration tends to be enhanced under stronger thermophoresis but it is diminished as compared to strong Brownian effect. The velocity profiles are found to increase with the rise of stretching effects, magnetic field strength and buoyancy forces where it shows decaying behavior for larger values of Darcy–Forchheimer resistance and Williamson fluid parameters. The novelty of the work lies in analysing the MHD Darcy–Forchheimer flow of a Williamson hybrid nanofluid while simultaneously incorporating Brownian motion, thermophoresis, Joule heating, viscous dissipation, and chemical reaction in a porous medium. This is the first such formulation, and it reveals new thermal, concentration, and velocity behaviours compared to conventional nanofluid models. The results also reveal new velocity, temperature and concentration behavior compared to available simple models. The working fluid has a noticeable increase in mass transfer with the increase of Schmidt numbers, leading to an increment of Sherwood number up to 48.10%. Similarly increasing the dimensionless chemical reaction parameter (Kr:0.1 to 1.00) raises the Sherwood number and overall enhancement in mass transfer becomes 30.79%.