Multiple solutions of Cu-C₆H₉NaO₇ and Ag-C₆H₉NaO₇ nanofluids flow over nonlinear shrinking surface

Abstract

Model of Casson nanofluid flow over a nonlinear shrinking surface is considered. Model of Tiwari and Das is applied to nanofluid comprising of sodium alginate with copper and silver. The governing nonlinear equations incorporating the effects of the viscous dissipation are transformed into boundary value problems (BVPs) of ordinary differential equations (ODEs) by using appropriate similarity transformations. The resulting equations are converted into initial value problems (IVPs) using the shooting method which are then solved by Runge-Kutta method of fourth order. In order to determine the stability of the dual solutions obtained, stability analysis is performed and discovered that the first (second) solution is stable (unstable) and physically realizable (unrealizable). Both the thickness of the thermal boundary layer as well as temperature increase when the Casson parameter (β) is increased in the second solution.

Keywords

Cu-C₆H₉NaO₇ / Ag-C₆H₉NaO₇ / shrinking surface / dual solution / stability analysis / nanofluid

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