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.
Highlights
In numerous industrial transport processes, convective heat and mass transfer takes place simultaneously
It can be seen that the skin friction coefficient −f (0)′′, increases with increase in s, nonlinear parameter and Prandtl number while it decreases with buoyancy parameter (G)
Comparison between the finite element and finite difference solutions is illustrated in Table 3, where for s = 0.5, P r = 7, b = 0.5, Sc = 1.0, G = 0.5 we have compared profiles of h, g and θ with η coordinate
Summary
In numerous industrial transport processes, convective heat and mass transfer takes place simultaneously. Phenomena involving stretching sheets feature widely in for example, aerospace component production metal casting [1]. In such processes metals or alloys are heated until molten, poured into a mould or die, and liquid metal is subsequently stretched to achieve the desired product. With further cooling and the loss of latent heat of fusion, the atoms of the metallic alloy lose energy and are bound tightly together in a regular structure. The mechanical properties of the final product depend to a great extent on the heat and mass transfer phenomena, the cooling rate, surface mass transfer rate etc. Much numerical research has been conducted in metal sheet flows including studies by Lait et al [2], Goldschmit et al who examined viscoplastic metal flows [3], Goldschmit [4] who provides a finite element methodology for general metal flow forming, and more recently by Cavaliere et al [5]
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