Numerical investigation of MHD boundary layer flow of Maxwell nanofluid over a nonlinear stretching sheet employing the Buongiorno model

The steady two-dimensional boundary-layer flow, heat transfer, and nanoparticle mass transfer properties of a Maxwell nanofluid across a nonlinearly stretching sheet under the influence of a transverse magnetic field are investigated numerically in this work. The analysis takes into account fluid elasticity, magnetohydrodynamic effects, and transport mechanisms for nanoparticles based on Buongiorno’s nanofluid model, which takes thermophoretic diffusion and Brownian motion into account. A linked system of ordinary differential equations is formed from the governing nonlinear partial differential equations by using appropriate similarity transformations. Combined with the Runge–Kutta–Fehlberg (RK-45) method, the Shooting method is used to solve these equations numerically. The effects on the velocity, temperature, and nanoparticle concentration distributions of the magnetic parameter M, viscoelastic (Maxwell) parameter K, nonlinear stretching parameter n, Prandtl number Pr, Brownian motion parameter \(N_\textrm{b}\) $N_{\text{b}}$ , thermophoresis parameter \(N_\textrm{t}\) $N_{\text{t}}$ , and Lewis number Le are investigated in a comprehensive parametric study. The momentum boundary layer is found to be dramatically altered by increasing magnetic and elastic effects, but thermophoresis and Brownian motion have competing roles in heat and concentration transport. Mass diffusion is highly regulated by the Prandtl number, and heat diffusion by the Lewis number. Excellent agreement with previously published results is achieved, with the present numerical values matching the existing data up to four decimal places, validating the accuracy and reliability of the proposed shooting approach. The results of this study provide important insight on how to improve mass and heat transport properties in viscoelastic nanofluids. Furthermore, it is expected that the findings will be helpful in the design and optimization of advanced thermal systems with possible uses in energy systems, polymer processing, magnetic materials, improved cooling technologies, and other technical and industrial processes.