Buoyancy Ratio and Heat Source Effects on MHD Flow Over an Inclined Non-Linearly Stretching Sheet

Abstract

This paper numerically investigates the magnetohydrodynamic boundary layer convective flow of an electrically conducting fluid in the presence of buoyancy ratio, heat source, variable magnetic field and radiation over an inclined nonlinear stretching sheet under convective surface boundary conditions. The Rosseland approximation is adopted for thermal radiation effects and the non-uniform magnetic field applied in a transverse direction to the flow. The coupled nonlinear momentum, thermal and species concentration governing boundary layer equations are rendered into a system of third order momentum and second order energy and mass diffusion ordinary differential equations via similarity transformations with appropriate boundary conditions. The nonlinear, non-dimensional, well-posed boundary value problem is then solved with the implicit finite difference scheme known as Keller Box Method. A detailed study of the influence of the emerging dimensionless parameters governing the flow on velocity, temperature and concentration distributions is conducted. Also the evolution of skin friction coefficient, Nusselt number and Sherwood number values are depicted graphically. Numerical results are validated with some limiting cases documented in previously testified results, and good correlation is confirmed. This investigation is relevant to the delineation of space, astrophysical plasmas, polymer processing and extrusion of rubber and plastic sheets.

Heat and mass transfer in MHD stagnation‐point flow toward an inclined stretching sheet embedded in a porous medium

“…To check the correctness of the numerical method employed here, the solutions for some particular cases are put beside those of Ferdows et al, 34 Rashidi et al, 35 and Thumma et al 36 (Tables 1 and 2), and a very good agreement is observed.…”

“…The steady two‐dimensional boundary layer equations for the electrically conducting fluid flow with linear Boussinesq approximations cf 35,36 . are given by $$$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0,$$$ $$$u\frac{\partial u}{\partial x}+v\frac{\partial v}{\partial y}=\frac{{\mu }_{f}}{{\rho }_{f}}\frac{{\partial }^{2}u}{\partial {y}^{2}}+g{\beta }_{T}(T-{T}_{\infty })\cos (\alpha )+g{\beta }_{C}(C-{C}_{\infty })\cos (\alpha )-\frac{\sigma {B}^{2}(x)}{{\rho }_{f}}u-\frac{\nu u}{{K}_{p}^{^{\prime} }},$$$ $$$u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}=\frac{k}{{(\rho...$$…”

“…The steady two-dimensional boundary layer equations for the electrically conducting fluid flow with linear Boussinesq approximations cf. 35,36 are given by…”

“…They identified that the nanofluid temperature is reduced by buoyancy. Thumma and Shamshuddin 36 have elucidated the buoyancy ratio during the discussion of MHD flow on a leaning sheet taking care of heat source. Acharya et al 37 have checked the nonparallel vortex instability analyzing the free convective flow with simultaneous thermal and mass diffusion over a nonisothermal inclined flat plate and solving by the Block elimination method.…”

“…Another subtle effect is related to the numerical method. In the earlier work of Thumma and Shamshuddin, 36 Keller Box method was employed. The present solution provides consistency of the RK method and finite difference Keller‐Box method.…”