Soret and Dufour effects on convective heat and mass transfer in stagnation-point flow towards a shrinking surface

A mathematical model is presented to study the Soret and Dufour effects on the convective heat and mass transfer in stagnation-point flow of viscous incompressible fluid towards a shrinking surface. Suitable similarity transformations are used to convert the governing partial differential equations into self-similarity ordinary differential equations that are then numerically solved by shooting method. Dual solutions for temperature and concentration are obtained in the presence of Soret and Dufour effects. Graphical representations of the heat and mass transfer coefficients, the dimensionless thermal and solute profiles for various values of Prandtl number, Lewis number, Soret number and Dufour number are demonstrated. With Soret number the mass transfer coefficient which is related to mass transfer rate increases for both solutions and the heat transfer coefficient (related to heat transfer rate) for both solutions becomes larger with Dufour number. The Prandtl number causes reduction in heat and the mass transfer coefficients and similarly with the Lewis number mass transfer coefficient decreases. Also, double crossing over is found in dual dimensionless temperature profiles for increasing Soret number and in dual dimensionless concentration profiles for the increase in Dufour number. Due to the larger values of Dufour number the thermal boundary layer increases and for Prandtl number increment it decreases; whereas, the solute boundary layer thickness reduces with increasing values of Prandtl number and Lewis number.