ABSTRACT
The investigation of the beginning of instability and mass/heat transport in the Rivlin-Ericksen nanoliquid layer (electrically conducting) is executed under a nonuniform time-varying magnetic-field/gravitational-field within the Hele-Shaw cell. Applied upright magnetic field/gravity involves two portions: constant portion and time-varying portion which differs sinusoidally. The heat/mass transportation in the liquid layer is examined with the help of a weakly nonlinear concept. The heat/mass transportation factor is found by originating the system of nonlinear simultaneous time-dependent ODEs for an amplitude of convection. The outcomes obtained by the inbuilt tool of Mathematica (NDSolve) are confirmed via Runge-Kutta-Fehlberg (RKF) technique. Heat/mass transportation Nusselt numbers are found in terms of several system variables, and each variable’s consequence on heat/mass transportation is described in detail. It is observed that the impact of amplitude of magnetic-field/gravity modulation, Prandtl-number is to boost heat/mass transportation while frequency of modulation, kinematic-viscoelastic parameter, Hele-Shaw number, and magnetic-number have stabilizing influence on the system.
A comparative study between magnetic field and gravity modulation is also done, and it is notable that the amount of heat/mass transportation is extra in the case of gravity modulation in comparison to magnetic-field modulation.
