MHD stagnation point flow of Casson hybrid nanofluid with bioconvection for biomedical skin patch applications

Abstract

This study investigates the magnetohydrodynamic (MHD) stagnation point flow of a Casson hybrid nanofluid across a stretchable surface, with applications in biomedical fields such as thermal management in skin patches. The research addresses the critical need for efficient heat and mass transfer in medical applications by utilizing a hybrid nanofluid composed of magnesium oxide $\left(MgO\right)$ and silicon dioxide $\left(Si{O}_2\right)$ nanoparticles dispersed in blood as the base fluid. These nanoparticles are chosen for their biocompatibility, cost-effectiveness, and ability to enhance heat and mass transfer properties. The study incorporates the CattaneoChristov double diffusion model alongside the bioconvection phenomenon and effects of magnetic strength, thermal radiation, viscous dissipation, and chemical reactions. The governing partial differential equations (PDEs) are transformed into nonlinear ordinary differential equations (ODEs) using similarity transformations and solved numerically using the BVP4C algorithm with a three-stage Lobatto method. The following dimensionless parameter ranges are considered: Casson parameter $\left(\beta \right)$ from 1 to 7, magnetic strength $\left(M\right)$ from 0.01 to 0.18, Eckert number $\left(\text{Ec}\right)$ from 0.5 to 2, radiation parameter $\left(\text{Rd}\right)$ from 0.3 to 1.2, Schmidt number $\left(Sc\right)$ from 1 to 2.5, and chemical reaction parameter $\left(\kappa \right)$ from 0.5 to 0.8. Key findings demonstrate that the temperature distribution increases with the $\text{Ec}$, while the velocity profile decreases with higher $\beta$ values. The study also highlights that hybrid nanofluids significantly reduce drag force by 34–39 % for Casson parameter values ($\beta$ =1, 3, 5). Additionally, the Nusselt number shows a substantial enhancement of 50–72 % for specific ranges of the Brinkman number ($\text{Br}$ = 1–3) and radiation parameter ($\text{Rd}$ = 0.3–0.9), with a maximum increase of 72.69 %. Response surface methodology and sensitivity analysis are conducted to quantify the sensitivity caused by input data such as the $\beta ,\text{Ec},$ and $\kappa$. The results demonstrate that the coefficient of determination for skin friction coefficient and Nusselt number are 94.75 % and 97.23 %, respectively. This is an indication that we have obtained the best-fit empirical correlations. The sensitivity analysis results showed that the skin friction coefficient and Nusselt number are highly sensitive to the chemical reaction parameter.