Numerical Investigation of Multiple Solutions for Caputo Fractional-Order-Two Dimensional Magnetohydrodynamic Unsteady Flow of Generalized Viscous Fluid over a Shrinking Sheet Using the Adams-Type Predictor-Corrector Method

Abstract

In this paper, magnetohydrodynamic (MHD) flow over a shrinking sheet and heat transfer with viscous dissipation has been studied. The governing equations of the considered problem are transformed into ordinary differential equations using similarity transformation. The resultant equations are converted into a system of fractional differential boundary layer equations by employing a Caputo derivative which is then solved numerically using the Adams-type predictor-corrector method (APCM). The results show the existence of two ranges of solutions, namely, dual solutions and no solution. Moreover, the results indicate that dual solutions exist for a certain range of specific parameters which are in line with the results of some previously published work. It is also observed that the velocity boundary layer decreases as the suction and magnetic parameters increase.

Influence of undulating wall heat and mass flux on MHD natural convection boundary layer flow from a vertical wall

“…Their remarkable result was that the velocity field can be expressed as an upraising function of the electric field and unsteadiness parameter whereas the temperature distribution as the Biot number and radiation parameter. MHD micropolar fluid flows over an exponentially shrinking sheet were simulated by Lund et al [17][18][19] considering different boundary conditions and solution procedures to investigate the stability of the different solutions. In all studies, they concluded that only the first solution is stable.…”

Recent Trends in Coatings and Thin Film: Modeling and Application

“…The magnetohydrodynamic flow over a shrinking sheet and heat transfer with viscous dissipation has been studied in [15]. The governing equations of the considered problem are transformed into ordinary differential equations while using similarity transformation.…”

Fractional View Analysis of Third Order Kortewege-De Vries Equations, Using a New Analytical Technique

“…The KDV equation used to model long waves, tides, solitary waves, and wave propagating in a shallow canal. A partial differential Kortewege-De Vries equation of third order is also applied to study the non-linear model of water waves in superficial canal certain namely canal [3], in the time when wave in water was of important concentration in applications in navigational design and also for the awareness of flood and tides [4,5]. The applications in numerous areas of physics, applied science and other scientific applications, therefore the excessive amount of investigation as a research work has been capitalized in the study of KDV equations [6][7][8][9][10].…”