A locally modified single-phase model for analyzing magnetohydrodynamic boundary layer flow and heat transfer of nanofluids over nonlinearly stretching sheet with chemical reaction

The problem of boundary layer flow and heat transfer of nanofluids over nonlinear stretching
of a flat sheet in the presence of a magnetic field and chemical reaction is investigated numerically.
In this paper, a new locally modified single-phase model for the analysis is introduced.
In this model, the effective viscosity, density and thermal conductivity of the solid-liquid mixtures
(nanofluids) which are commonly utilized in the homogenous single-phase model, are
locally combined with the prevalent single-phase model. Similarity transformation is used to
convert the governing equations into three coupled nonlinear ordinary differential equations.
These equations depend on five local functions of the nanoparticle volume fraction viz., local
viscosity ratio, magnetic, Prandtl, Brownian motion and thermophoresis functions. The equations
are solved using Newton’s method and a block tridiagonal matrix solver. The results
are compared to the prevalent single-phase model. In addition, the effect of important governing
parameters on the velocity, temperature, volume fraction distribution and the heat
and mass transfer rates are examined.