Radiative porosity sodium alginate hybrid nanofluid flow over an exponential stretching/shrinking surface: Dual solutions

Abstract

An investigation into the effects that porous medium, magnetic fields, thermal radiation, and viscous dissipation have on SA-hybrid nanofluid was the focus of a numerical study that was carried out for a dual branches solution that featured an exponentially stretching and shrinking layer. The principal goal of this study is to explore the behavior of coefficient skin friction and heat transfer with the permeability parameter for the suction aspect, as well as the behavior of solid volume fraction against the stretching/shrinking effect. The impact of the permeability parameter, magnetic, shrinkage parameter, and viscous dissipation on the temperature profile and velocity of sodium alginate-hybrid nanofluid flow are also incorporated in the present investigation. The governing equations in the form of partial differential equations (PDEs) are transformed into the form of ordinary differential equations (ODEs), implementing a similarity variable having exponential similarity. The ODE system is numerically solved using the Three-stage Labatto III-A technique included in the bvp4c solver with the MATLAB program. Two branches’ solutions are obtained when the pertinent parameters are varied over defined ranges. Non unique solutions are obtained when the critical point reaches suction greater or equal to suction critical points and shrinking paramter greater or equal to shrinking paramter critical points for suction and shrinkage effects respectively. In addition, the upper branch has a significant increase in reduced skin friction and heat transfer when the permeability parameter is raised, whereas the lower branch experiences a decrease. The heat transfer rate diminutions in the upper branch solution and increases in the lower branch solution as the solid volume percentage of copper increases. Temperature profiles decrease as permeability parameter values improve. As Eckert's value increases, the temperature profile also improves.