Abstract
A numerical investigation of unsteady magnetohydrodynamic mixed convective boundary layer flow of a nanofluid over an exponentially stretching sheet in porous media, is presented. The transformed, non-similar conservations equations are solved using a robust, explicit, finite difference method (EFDM). A detailed stability and convergence analysis is also conducted. The regime is shown to be controlled by a number of emerging thermophysical parameters i.e. combined porous and hydromagnetic parameter (R), thermal Grashof number (G r ), species Grashof number (G m ), viscosity ratio parameter (Λ), dimensionless porous media inertial parameter (∇), Eckert number (E c ), Lewis number (L e ), Brownian motion parameter (Nb) and thermophoresis parameter (Nt). The flow is found to be accelerated with increasing thermal and species Grashof numbers and also increasing Brownian motion and thermophoresis effects. However, flow is decelerated with increasing viscosity ratio and combined porous and hydromagnetic parameters. Temperatures are enhanced with increasing Brownian motion and thermophoresis as are concentration values. With progression in time the flow is accelerated and temperatures and concentrations are increased. EFDM solutions are validated with an optimized variational iteration method. The present study finds applications in magnetic nanomaterials processing.
Highlights
Magnetohydrodynamic (MHD) boundary layer flows with heat and mass transfer from a continuously stretching surface with a given temperature distribution moving in an otherwise quiescent fluid medium have stimulated considerable interest in recent years
Non-dimensional velocity, temperature and species concentration are computed for different values of combined porous and hydromagnetic parameter (R), thermal Grashof number(Gr), species Grashof number (Gm), viscosity ratio parameter (K), dimensionless porous media inertial parameter (r), Eckert number (Ec), Lewis number (Le), Brownian motion parameter (Nb), Fig. 3 Thermal Grashof number ðGrÞ effect on velocity profiles
A distinct velocity shoot arises for all profiles near the sheet surface (Y = 0) and this is accentuated with increasing thermal Grashof number
Summary
Magnetohydrodynamic (MHD) boundary layer flows with heat and mass transfer from a continuously stretching surface with a given temperature distribution moving in an otherwise quiescent fluid medium have stimulated considerable interest in recent years. Rana et al (2013) studied using a finite element technique, the transient magnetohydrodynamic boundary layer flow in an incompressible rotating nanofluid over a stretching continuous sheet, showing that both Brownian motion and thermophoresis enhance wall mass transfer rates (Sherwood number). In the present article we simulate the transient MHD dissipative mixed convective boundary layer nanofluid flow over an exponentially stretching sheet adjacent to a non-Darcian porous medium. Ð4Þ where u and v are the velocities in the x- and y-directions, respectively, t is time, q is the fluid density, m the kinematic viscosity, m~ the reference kinematic viscosity, K the permeability of the porous regime, cp the specific heat at constant pressure, T and C the fluid temperature and concentration in the boundary layer, cÃe2 is the inertia parameter, a is the thermal diffusivity, ðqcÞp is effective heat capacity of the nanofluid, ðqcÞf is heat capacity of the fluid, DB is the species diffusivity and DT is the thermotemperature gradient and the second and third terms on the left hand side represent the convective heat transfer terms. Introducing the following nondimensional variables; X xU0 x eL; Y yU0 x
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