Abstract
In this article, the magnetohydrodynamic (MHD) flow of Casson nanofluid with thermal radiation over an unsteady shrinking surface is investigated. The equation of momentum is derived from the Navier–Stokes model for non-Newtonian fluid where components of the viscous terms are symmetric. The effect of Stefan blowing with partial slip conditions of velocity, concentration, and temperature on the velocity, concentration, and temperature distributions is also taken into account. The modeled equations of partial differential equations (PDEs) are transformed into the equivalent boundary value problems (BVPs) of ordinary differential equations (ODEs) by employing similarity transformations. These similarity transformations can be obtained by using symmetry analysis. The resultant BVPs are reduced into initial value problems (IVPs) by using the shooting method and then solved by using the fourth-order Runge–Kutta (RK) technique. The numerical results reveal that dual solutions exist in some ranges of different physical parameters such as unsteadiness and suction/injection parameters. The thickness of the velocity boundary layer is enhanced in the second solution by increasing the magnetic and velocity slip factor effect in the boundary layer. Increment in the Prandtl number and Brownian motion parameter is caused by a reduction of the thickness of the thermal boundary layer and temperature. Moreover, stability analysis performed by employing the three-stage Lobatto IIIA formula in the BVP4C solver with the help of MATLAB software reveals that only the first solution is stable and physically realizable.
Highlights
In the past few decades, non-Newtonian fluids have attracted the interest of scientists, researchers, and mathematicians due to their significant applications in various industrial sectors
To the best of our knowledge, no such study on the unsteady flow of Casson nanofluid with the effect of Stefan blowing and partial slip conditions for multiple solutions has been reported in the literature
We need to introduce a new dimensionless time variable τ in order to perform a stability analysis of the solution where τ corresponds to the initial value problems (IVPs)
Summary
In the past few decades, non-Newtonian fluids have attracted the interest of scientists, researchers, and mathematicians due to their significant applications in various industrial sectors. To the best of our knowledge, no such study on the unsteady flow of Casson nanofluid with the effect of Stefan blowing and partial slip conditions for multiple solutions has been reported in the literature. The non-Newtonian problems of Casson fluid boundary layer flow over a shrinking surface have numerous applications in manufacturing processes and industry, in the metal and plastic industries. Shahzad et al [27] considered the MHD flow of Casson fluid with a thermal radiation effect They found only one solution using the homotropy analysis method. To the best of our knowledge, there have been no investigations focusing on the MHD flow of Casson nanofluids on a shrinking sheet with the Stefan blowing effect.
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