Finite-element simulation of mixed convection flow of micropolar fluid over a shrinking sheet with thermal radiation

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.