Brownian motion effect on heat transfer of a three-dimensional nanofluid flow over a stretched sheet with velocity slip

Abstract

Present article provides an analytical investigation of the fluid flow and heat and mass transfer for the steady laminar MHD three-dimensional nanofluid flow over a bidirectional stretching sheet with convective surface boundary condition using optimal homotopy analysis method (OHAM) via Mathematica package BVPh2.0. In contrast to the conventional no-slip condition at the surface, Navier’s slip condition has been applied. The governing partial differential equations are transformed into a highly nonlinear coupled ordinary differential equations consisting the momentum, energy and concentration equations via appropriate similarity transformations. The current OHAM solution demonstrates very good correlation with those of the previously published studies in the especial cases. The influence of different physical parameters such as magnetic parameter (M), Prandtl number ($\Pr$), Brownian motion parameter (${\text{Nb}}$), thermophoresis parameter (${\text{Nt}}$), Lewis number (Le), velocity slip parameter (γ), stretching rate ratio parameter (λ), and Biot number (Bi) on all fluid velocity components $\left( {f^{\prime}(\eta ),\,\,g^{\prime}(\eta )} \right)$, temperature distribution $\left( {\theta \,(\eta )} \right)$ and concentration $\left( {\phi \,(\eta )} \right)$ as well as the skin friction coefficients in x and y directions $\left( {C_{\text{fx}} {\text{Re}}_{\text{x}}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} ,\,\,C_{\text{fy}} {\text{Re}}_{\text{x}}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} } \right),$ local Nusselt number $\left( {{{{\text{Nu}}_{\text{x}} } \mathord{\left/ {\vphantom {{{\text{Nu}}_{\text{x}} } {{\text{Re}}_{\text{x}}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} }}} \right. \kern-0pt} {{\text{Re}}_{\text{x}}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} }}} \right)$ and local Sherwood number $\left( {{{{\text{Sh}}_{\text{x}} } \mathord{\left/ {\vphantom {{{\text{Sh}}_{\text{x}} } {{\text{Re}}_{\text{x}}^{{\,{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} }}} \right. \kern-0pt} {{\text{Re}}_{\text{x}}^{{\,{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} }}} \right)$ are tabulated graphically and discussed in details. This study specifies that nanoparticles in the base fluid offer a potential in increasing the convective heat transfer performance of various liquids.