Impact of the Brownian motion and thermophoretic diffusion during the radiative MHD hybrid nanofluid flow past a stretching sheet

The article aims to analyze the effects of thermophoretic and Brownian motion on steady three-dimensional magnetohydrodynamics with fully developed natural convective hybrid nanofluid flow past a bidirectionally extending sheet. We assumed the water-based copper and aluminum nanoparticles suspension under the influence of the rotational effect, nonlinear chemical reaction, thermal radiations, viscous dissipation, and heat source. The flow field is modeled with the help of the basic equations. Furthermore, the problem is reduced to ordinary differential equations (ODEs) with the similarity variables. The reduced system of ODEs is solved with the semianalytical method (homotopy analysis method). The results for the state variables are displayed through graphs tables for various pertinent parameters. The thermal profile falls with the higher values of the Brownian and thermophoresis parameters, while the concentration profile shows an opposite trend with the increasing values of the Brownian parameter. Also, the slip parameter decreases both the thermal and concentration profiles as well as the surface drag. The velocity profiles along both directions fall with the higher magnetic strength and porosity parameters. The heat source and radiations parameter enhances the thermal profile with increasing values. The study also recommends the opposite trends for the axial and transverse velocities with increasing value of the stretching ratio factor. The proposed method convergence is present through <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>ℏ</mml:mi> </mml:math> curves for the regions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>−</mml:mo> <mml:mn>2.20</mml:mn> <mml:mo>≤</mml:mo> <mml:msub> <mml:mi>ℏ</mml:mi> <mml:mi>f</mml:mi> </mml:msub> <mml:mo>≤</mml:mo> <mml:mn>0.45</mml:mn> <mml:mo>,</mml:mo> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>−</mml:mo> <mml:mn>2.25</mml:mn> <mml:mo>≤</mml:mo> <mml:msub> <mml:mi>ℏ</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mo>≤</mml:mo> <mml:mn>0.5</mml:mn> <mml:mo>,</mml:mo> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>−</mml:mo> <mml:mn>1.5</mml:mn> <mml:mo>≤</mml:mo> <mml:msub> <mml:mi>ℏ</mml:mi> <mml:mi>θ</mml:mi> </mml:msub> <mml:mo>≤</mml:mo> <mml:mn>0.25</mml:mn> <mml:mo>,</mml:mo> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>−</mml:mo> <mml:mn>1.5</mml:mn> <mml:mo>≤</mml:mo> <mml:msub> <mml:mi>ℏ</mml:mi> <mml:mi>ϕ</mml:mi> </mml:msub> <mml:mo>≤</mml:mo> <mml:mn>0.5.</mml:mn> </mml:math> The skin friction and Nusselt number are displayed through tables numerically for various values of volume fraction and other important parameters.