Introduction
Concentration gradient often lead to mass diffusion in a mixture of two
more species (gases, liquids, plasma or solids) in an isothermal system
where species are not evenly distributed. Temperature gradient is also
another factor that can be responsible for mass diffusion as a result of
Soret effect (thermo-diffusion). Thermo-diffusion has several industrial
applications such as the optimum oil recovery from hydrocarbon
reservoirs, fabrication of semiconductor devices in molten metal and
semiconductor mixtures, separation of species such as polymers,
manipulation of macromolecules such as DNA, and engineering processed
like wire drawing, glass fibre and paper production and crystal growth\(\mathbf{[1]}\). Dufour effect is the reverse of the Soret
effect arising in a system where concentration gradient results in a
temperature change. Dufour effect may be insignificant in liquid-liquid
mixture but not when gases are involved. Blasius boundary layer
equations \(\mathbf{[2]}\) describe a steady flow of
viscous incompressible fluids about a two-dimensional flat-plate and
these equations were later generalized by Falkner and Skan to wedge
flow. Sakiadis obtained the boundary layer equations for a flow of a
quiescent ambient fluid over a moving flat surface similar to the
Blasius equations except that the boundary conditions differ\(\mathbf{[3,4]}\).
Rafael \(\mathbf{[5]}\) showed that there exist
discrepancies when both the Blasius and Sakiadis flows are compared.
Olanrewaju et al . \(\mathbf{[6]}\) reported the
effects thermal radiation, Eckert number, Prandtl number and convective
parameter on both Blasius and Sakiadis flows with a convective surface
boundary condition. Gangadhar \(\mathbf{[7]}\) extended the
work of \(\mathbf{[6]}\) by adding the effects of buoyancy
and magnetohydrodynamic on radiation and viscous dissipation for the
Blasius and Sakiadis flows with a convective surface boundary condition.
Hady et al . \(\mathbf{[8]}\) studied the effect of
porosity on the flow dynamics of both Blasius and Sakiadis flows of
nanofluid in the presence of thermal radiation under a convective
boundary condition. Mustafa et al . \(\mathbf{[9]}\)examined the effect of magnetic field parameter on Sakiadis flow of MHD
Maxwell fluid. Anjani and Suriyakumar \(\mathbf{[10]}\)furthered the work of \(\mathbf{[9]}\) by comparing both
cases of Blasius and Sakiadis MHD nanofluids flows on an inclined plate.
Krishina et al . \(\mathbf{[11]}\) investigated the
magnetohydrodynamic Blasius and Sakiadis flows with variable properties,
thermal and diffusion slip.
In all these studies, Soret–Dufour effects were not considered.
However, Makinde et al. \(\mathbf{[12]}\) examined
the hydrodynamic flow and mass diffusion of chemical species with first
and higher-order reactions of an electrically conducting fluid over a
moving vertical plate with Dufor and Soret. Animasaun and Oyem\(\mathbf{[13]}\) considered the effects of variable fluid
viscosity and thermal conductivity, Dufour and Soret on a non-Darcian
free convective heat and mass transfer fluid flow past a porous flat
surface. The influences of partial slips, Soret and Dufour on unsteady
boundary layer flow, heat and mass transfer over shrinking sheet in
copper-water nanofluid was looked into by Dzulkifli et al .\(\mathbf{[14]}\). Swamy et al .\(\left[\mathbf{15}\right]\) studies the onset of
convection, heat and mass transports in anisotropic densely packed
porous layer filled with chemically reactive binary liquid heated at the
bottom in presence of Soret and Dufour effects. Similarly, Hayatet al . \(\left[\mathbf{16}\right]\) addressed the
convective heat and mass transfer conditions in the radiative flow of
Powell-Eyring fluid past an inclined exponentially stretching surface
taking Soret and Dufour effects into account. Kafayati\(\left[\mathbf{17}\right]\) looked into entropy
generation of associated with double diffusive natural convection of
non-Newtonian power-fluids in an inclined porous cavity. Shojaeiet al . \(\left[\mathbf{18}\right]\) examined the
analytical approach of a second grade fluid flow along a stretching
cylinder and the Soret and Dufour effects. Hayat et al .\(\left[\mathbf{19}\right]\) investigated Soret and Dufour
effects on the peristaltic flow of magnetohydrodynamic (MHD)
psuedoplastic nanofluid in a tapered asymmetric channel.
In all the above mentioned studies, the interaction between
Blasius-Sakiadis flows and Soret-Dufour effects about a flat plate was
not investigated adequately. Gangadhar\(\left[\mathbf{7}\right]\) neither considered
Soret-Dufour effects and convective heat transfer but neglected the
viscous dissipation and thermal radiation parameter. In view of this,
the presented paper have extended the work of\(\mathbf{[7]}\) to include Soret (thermal-diffusion) and
Dufour (thermo-diffusion) effects as the Blasius and Sakiadis flows are
considered about a flat plate with variability properties. A similarity
transformation has been adopted to convert the governing partial
differential equations into a system of nonlinear ordinary differential
equations and the resulting boundary value problem has been solved
numerically with Runge-Kutta-Gills method with shooting technique.
Results are obtained for different values of the governing dimensionless
properties and discussed extensively.