Modelling unsteady waveform Williamson fluid flow near a permeable radioactive surface

Abstract

The unsteady heat and mass transfer waveform flow in an electrical conducting Williamson fluid past a permeable stretching surface is studied. Rosseland approximation is implemented to accomplish the nonlinear solar effects. Few years back, Zheng et al. (2013) studied a two dimensional waveform stretched surface model for Newtonian fluid. Now if the fluid is not Newtonian (Williamson) and stretched linearly having waveform velocity Uw = cx sin ωt in x− direction, then there exists oscillation frequency near the stretched surface depending on the unsteady dimensionless parameter. A distant change in physical phenomena is assumed in the form of chemical reaction. The governing problem is transformed into the dimensionless partial differential system by using similarity transformation technique. For numerical solutions, an explicit finite difference scheme is executed under some restrictions. The figures of the Sherwood and Nusselt numbers as well as the concentration, velocity and temperature distributions for non-dimensional parameters are presented. Infinite number of singularities occur for different values of dimensionless time constant appearing in drag relation. That's why the drag impact is written in tabulated form for some constant value τ = π/2. A good agreement is noticed when the numerical results of drag force is compared with previous literature. It is found that unsteadiness parameter, Williamson parameter, magnetic field and electric filed shows decline behavior in fluid particles motion. The temperature of the fluid reduces for large values of Prandtl number but inverse behavior is noticed for radiation parameter. Moreover, concentration profile shows reduction due to large values of Schmidt number but inverse impact is achieved for chemical reaction parameter.