On natural convection flow of micropolar fluid

Abstract

The aim of our study, which consists of six chapters, is to study some problems on heat transfer with convection in the micropolar fluids. In the following, a brief discussion of the chapters is given. Chapter Two contains a brief overview of research works on the boundary layer flow of a micropolar fluid along a vertical plate. The literature review exposes the necessity of investigation of this problem. It also gives the step by step development of the problem. Although there are numerous studies on the boundary layer characteristics of micropolar fluid along a vertical plate, nevertheless further investigation needs to be done. In Chapte Three, an analysis is performed to study the shear stress, the couple-stress and heat transfer characteristics of a laminar mixed convection boundary layer flow of a micropolar fluid past an isothermal permeable plate. The governing nonsimilar boundary layer equations are analyzed using the (i) series solution for small 𝜉, (ii) asymptotic solution for large 𝜉 and (iii) primitive-variable formulation and the stream function formulation are being used for all 𝜉. The effects of the material parameters, such as, the vortex viscosity parameter, 𝐾, and the transpiration parameter, 𝑠, on the shear stress, the couple-stress and heat transfer have been investigated. The agreement between the solutions obtained from the stream-function formulation and the primitive-variable formulation is found to be excellent. The unsteady free convection boundary layer flow of a thermo-micropolar fluid along a vertical plate with effect of micropolar heat conduction has been investigated inChapter Four. The governing equations are transformed into a new form using a method of transformed coordinates. We then use an explicit finite difference scheme to solve the transformed equations. Here, the governing equations have been reduced to the forms that are valid for entire, small and large time regimes, by using stream-function formulation. The results obtained for the above mentioned three time regimes are compared and found in excellent agreement. Moreover, the effects of the physical parameters such as the viscosity parameter, K, and the heat conduction parameter, α*, are presented in terms of the transient shear stress, couple stress and surface heat transfer coefficient as well as transient velocity profiles, angular velocity profiles and temperature profiles.

In Chapte Five, the unsteady free convection boundary layer flow of a thermo-micropolar fluid along a vertical plate has been investigated in this paper. The temperature of the plate is assumed to be oscillating about a mean temperature, w(x), with small amplitude. The governing boundary layer equations are analyzed using straight forward finite difference method. The effects of the material parameters such as micropolar heat conduction parameter, N*, the vortex viscosity parameter, K, on the shear stress,, surface heat transfer, q, and the couple-stress, m, have been investigated. Chapter Six concerns the boundary layer characteristics of the free convection flow of a thermo-micropolar fluid from a vertical surface with the effect of stream wise sinusoidal variation of the surface temperature. The dimensionless boundary layer equations are solved using the straight forward finite difference method. Results are presented in terms of the skin friction, couple stress and heat transfer coefficients with the variation of the micropolar heat conduction parameter, the vortex viscosity parameter andthe amplitude of surface temperature. We also discussed the effects of these parameters on the streamlines, isoclines of angular velocity and isoclines of temperature.