An analysis is carried out to investigate the effect of thermal radiation on mixed convection flow of a msicropolar fluid over a shrinking sheet with prescribed surface heat flux. The velocity of the shrinking sheet and the surface heat flux are assumed to vary as a linear function of the distance from the origin. Using the boundary layer approximation and similarity transformations, the governing partial differential equations are transformed into a system of nonlinear coupled ordinary differential equations which are solved numerically by using a variational finite element method. The effects of suction, radiation, and buoyancy parameters on velocity, microrotation, and temperature functions are examined in detail. The skin-friction coefficient, local couple stress, and the local Nusselt number have also been computed. Under special conditions, an analytical solution is obtained only for the flow velocity, which is compared with the numerical results obtained by finite element method. An excellent agreement of the two sets of solutions is observed, which confirms the validity of the finite element method employed herein. Also, in order to check the convergence of numerical solutions, the calculations are executed by reducing the mesh size. The sensitivity of the solution as a function of suction through the permeable sheet has also been examined. The current study has important applications in industrial polymeric materials processing.

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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.

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