Numerical Solutions for Micropolar Transport Phenomena over a Nonlinear Stretching Sheet

Abstract

We present a numerical study for the steady, coupled, hydrodynamic, heat and mass transfer of an incompressible micropolar fluid flowing over a nonlinear stretching sheet. The governing differential equations are partially decoupled using a similarly transformation and then solved by two numerical techniques – the finite element method and the finite difference method. The dimensionless translational velocity, microrotation (angular velocity), temperature and mass distribution function are computed for the different thermophysical parameters controlling the flow regime, viz the nonlinear (stretching) parameter, b, Grashof number, G and Schmidt number, Sc. All results are shown graphically. Additionally skin friction and Nusselt number, which provide an estimate of the surface shear stress and the rate of cooling of the surface, respectively, are also computed. Excellent agreement is obtained between both numerical methods. The dimensionless translational velocity (f′) for both micropolar and Newtonian fluids is shown to decrease with an increase in nonlinear parameter b. Dimensionless microrotation (angular velocity), g, generally increases with a rise in nonlinear parameter b (in particular in the vicinity of the wall) and decreases with a rise in convective parameter, G. The effects of other parameters on the flow variables are also discussed. The flow regime has significant applications in polymer processing technology and metallurgy.

Keywords

• micropolar fluid
• nonlinear stretching sheet
• materials processing
• boundary layers
• numerical solutions
• convective heat and mass transfer