Effectiveness of Cattaneo–Christov double diffusion in Sisko fluid flow with variable properties: Dual solutions

The nature and properties of generalized Newtonian fluid flows are of the most significant phenomena applicable to engineering applications. But this particular portion of research work incorporates the importance of flow, heat and mass transfer analysis of non-homogeneous Sisko fluid transport model. The flow source in this study is assumed by the stretching and shrinking velocities of the sheet. Therefore, the influence of these two velocities creates a phenomenon of multiple solutions. The effect of magnetic field is another significant physical parameter in the flow analysis and has been considered in this study. Moreover, the impacts of variable thermal conductivity, mass diffusivity and suction/injection are also incorporated. The system of conservative governing partial differential equations are converted into a dimensionless system of equations by using the suitable transformations. The new system of equations along with the corresponding transformed boundary conditions are then solved numerically with the help of collocation method in Matlab. This method is a built-in approach for the solution of nonlinear boundary value problem. In comparison with other user-defined numerical approaches, this method is little bit fast and works accurately because this method uses finite difference method for modifying weak initial guess and the CPU timing is very small as compared to other built-in approaches. The present results are shown for the existence of multiple (upper branch and lower branch) solutions for a specific range of involved physical parameters. The critical values of shrinking parameter corresponding to suction parameter and Sisko fluid parameter are computed in the certain range of ($$\chi _{{\rm c}}<\chi <0$$ ). The behaviors of various dimensionless parameters on different profiles are discussed graphically. The increase in material parameter causes a reduction in skin friction for both cases, i.e., shear-thinning as well as shear-thickening fluids. The first and second solutions of temperature and concentration profiles, respectively, show increasing and decreasing trends for an increase in temperature and concentration time relaxation parameters.