Finite Element Solution of Unsteady Mixed Convection Flow of Micropolar Fluid over a Porous Shrinking Sheet

Abstract

The objective of this investigation is to analyze the effect of unsteadiness on the mixed convection boundary layer flow of micropolar fluid over a permeable shrinking sheet in the presence of viscous dissipation. At the sheet a variable distribution of suction is assumed. The unsteadiness in the flow and temperature fields is caused by the time dependence of the shrinking velocity and surface temperature. With the aid of similarity transformations, the governing partial differential equations are transformed into a set of nonlinear ordinary differential equations, which are solved numerically, using variational finite element method. The influence of important physical parameters, namely, suction parameter, unsteadiness parameter, buoyancy parameter and Eckert number on the velocity, microrotation, and temperature functions is investigated and analyzed with the help of their graphical representations. Additionally skin friction and the rate of heat transfer have also been computed. Under special conditions, an exact solution for the flow velocity is compared with the numerical results obtained by finite element method. An excellent agreement is observed for the two sets of solutions. Furthermore, to verify the convergence of numerical results, calculations are conducted with increasing number of elements.

Dual solutions for unsteady mixed convection flow of MHD micropolar fluid over a stretching/shrinking sheet with non-uniform heat source/sink

“…In injection case it takes reverse action and shown fall in velocity and temperature profiles. This agrees with the result obtained by Gupta et al [10]. Physically an increase in the unsteadiness parameter increases the heat loss by the sheet in injection case.…”

“…In this study we analyzed the unsteady mixed convection flow of micropolar fluid past a stretching or shrinking sheet by considering the additional assumptions like Magneticfield, Stretching sheet, injection, diffusion, chemical reaction and the space and temperature dependent heat generation/absorption (non uniform heat source/sink) along with the different numerical technique. We presented dual solutions for suction and injection cases and compared the results of the present study with the existed results of Gupta et al [10]. Under some special conditions, present results have an excellent agreement with the results of Gupta et al [10].…”

“…We presented dual solutions for suction and injection cases and compared the results of the present study with the existed results of Gupta et al [10]. Under some special conditions, present results have an excellent agreement with the results of Gupta et al [10].…”

“…Zaimi and Ishak [9] illustrated stagnation-point flow and heat transfer behavior of micropolar fluid over a nonlinearly stretching/shrinking sheet. Recently, unsteady mixed convection flow of a micropolar fluid over a permeable shrinking sheet by using finite element analysis was discussed by Gupta et al [10]. Ashraf and Batool [11] analyzed MHD flow and heat transfer behavior of a micropolar fluid over a stretchable disk.…”

“…Present problem is the extension study of Gupta et al [10]. In this study we analyzed the unsteady mixed convection flow of micropolar fluid past a stretching or shrinking sheet by considering the additional assumptions like Magneticfield, Stretching sheet, injection, diffusion, chemical reaction and the space and temperature dependent heat generation/absorption (non uniform heat source/sink) along with the different numerical technique.…”