The unified impact of thermal radiation and heat source on unsteady flow of tangent hyperbolic nanofluid through a permeable shrinking sheet

Abstract

The tangent hyperbolic nanofluid behaviour is observed in multiple practical applications and extensively used in different laboratory experiments. It motivates to focus on the two-dimensional boundary layer flow of tangent hyperbolic nanofluid past a shrinking sheet. The goal of this article is to scrutinize the mass and heat transport of an unsteady flow of non-Newtonian tangent hyperbolic nanofluid past a shrinking surface under the influences of a source of heat, thermal radiation and chemical reaction. The flow model is mathematically framed through a coupled nonlinear partial differential equations. To transform the non-linear PDEs to ODEs, we use the similarity transformations and reduced ODEs are solved by RK-IV (Runge-Kutta method of order four) with shooting technique using the computational software MATHEMATICA. The novelty which emerges from the flow pattern lies in the fact that there exist dual solutions for certain parametric domain and the range of the existing solution may be expanded by increasing the power-law index (n) and shortened by increasing the Weissenberg number (We). Another remarkable conclusion which can be drawn from the temporal stability analysis that among these two solutions, first solution is stable and realistic whereas the second solution is not physically realistic. A diversity of the parameter estimates were used to provide solution for velocity f′(η), temperature θ(η) and concentration profiles ϕ(η) of this fluid model. In addition to the above findings, there are graphs and tables with explanation for the skin friction coefficient, the Nusselt number and the Sherwood number. These characteristics of a tangent hyperbolic nanofluid are not reported yet and may be useful in the development of existing technology.