This paper presents a numerical analysis of the flow and heat transfer characteristics of mixed convection in a micropolar fluid flowing along a vertical flat plate with conduction effects. The governing non-linear equations and their associated boundary conditions are first cast into dimensionless forms by a local non-similar transformation. The resulting equations are then solved using the cubic spline collocation method and the finite difference scheme. This study examines the effects of the buoyancy parameter, the conjugate heat transfer parameter, the micropolar parameter and the Prandtl number on the flow and the thermal fields. The results show that the conjugate heat transfer parameter has a significant influence on the fluid flow and heat transfer characteristics. The buoyancy parameter reduces the solid–liquid interfacial temperature but increases the skin friction factor and the local heat transfer rate. The effect of wall conduction on the local heat transfer rate, interfacial temperature and skin friction factor is found to be more pronounced in a system with a greater buoyancy effect. Finally, compared with the case of pure forced convection, a reduction in the interfacial temperature, an increase in the skin friction factor and an increase in the local heat transfer rate are obtained in the current mixed convection case.
This paper employs linear and nonlinear stability theories to conduct a numerical characterization of thin micropolar film flows travelling down a vertical moving plate. Having applied the long-wave perturbation method to derive the generalized kinematic equations for a free film surface condition, the multiple scales method is used to solve the micropolar film flow in the cases of a stationary vertical plate, a vertical plate moving in the downward direction and a vertical plate moving in the upward direction. The numerical results indicate that both subcritical instability and supercritical stability conditions may occur in the micropolar film flow system. No obvious change in the supercritical stability condition is observed when the plate moves vertically in the upward or downward direction. The numerical results indicate that a downward motion of the vertical plate tends to enhance the stability of the film flow.
The laminar free convection flow of a micropolar fluid past an arbitrary curved surface has been analysed by using the cubic spline collocation numerical method. It is found that the flow field admits similarity solutions when the power functions for the stream-wise variations of the wall temperature m and the body shape configurations n are constants, and the sum of them is equal to unity. The solutions for the flow and heat transfer characteristics are evaluated numerically for different parameters, such as the body shape parameter n, the vortex viscosity parameter N1, the spin-gradient viscosity parameter N3 and the Prandtl number Pr. Results show that the heat transfer rate increases as the body shape parameter n or the parameter N1 decreases and the Prandtl number increases. The skin friction factor increases as the value of N1 decreases. In addition, an increase in the parameter N3 leads to an increase of the angular velocity boundary layer thickness. The model may solve industrial problems with processing of polymeric liquids, lubricants and molten plastics.
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