A three-dimensional boundary layer solution is presented for the natural convection in a micropolar fluid in the vicinity of an axisymmetric stagnation point on heated vertical surfaces. The effects of variable viscosity are included. The governing equations for the velocity, microrotation and temperature fields are solved numerically.
A regular parameter perturbation analysis is presented to study the effect of uniform transverse magnetic field with temperature dependent viscosity in micropolar fluids. Four different vertical flows have been analyzed: these adjacent to an isothermal surface, uniform heat flux surface, a plane plume and wall plume. Viscous dissipation, motion pressure and volumetric energy source effects are neglected. The absolute viscosity 'mi' is taken to be variable in the force momentum balance while the fluid volumetric coefficient of thermal expansion, 'beta', specific heat, Cp and thermal conductivity, k, are assumed to be constant. Numerical solutions are obtained for different values of the magnetic field, material parameters and micropolar parameters.
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A regular perturbation analysis is presented for the laminar natural convection flows of micropolar fluids with temperature dependent viscosity: a freely-rising plane plume, the flow above a horizontal line source on an adiabatic surface (a plan wall plume) and the flow adjacent to a vertical uniform flux surface. While these flows have well-known power-law similarity solutions when the fluid viscosity is taken to be constant, they are non-similar when the viscosity is considered to be a function of temperature. A flow adjacent to a vertical isothermal surface is also analyzed for comparison in order to estimate the extent of validity of the perturbation analysis. The formulation used here provides a unified treatment of variable viscosity effects on those four flows. Computed first-order perturbation quantities are presented for all four flows. The velocity, microrotation distribution, temperature and concentration profiles are shown. Numerical results are presented for the local Nusselt number and Sherwood number, wall shear stress and wall couple stress.
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The present work investigates the unsteady, imcompressible flow of a micropolar fluid between two orthogonally moving porous coaxial disks. The lower and upper disks are rotating with the same angular speed in counter directions. The flows are driven by the contraction and the rotation of the disks. An extension of the Von Kármán type similarity transformation is proposed and is applied to reduce the governing partial differential equations (PDEs) to a set of non-linear coupled ordinary differential equations (ODEs) in dimensionless form. These differential equations with appropriate boundary conditions are responsible for the flow behavior between large but finite coaxial rotating disks. The analytical solutions are obtained by employing the homotopy analysis method. The effects of some various physical parameters like the expansion ratio, the rotational Reynolds number, the permeability Reynolds number, and micropolar parameters on the velocity fields are observed in graphs and discussed in detail.
An analysis is presented for the heat transfer in a micropolar fluid boundary layer over a flat plate with uniformly distributed vectored surface mass transfer. Numerical solutions for the governing nonsimilar boundary layer equations are presented for a range of values of the material properties and Prandtl number of the fluid. The results indicate that the micropolar fluids display a reduction in drag as well as heat transfer rate when compared with Newtonian fluids.
A similarity analysis of the flow and heat transfer with magnetic field past a continuously moving semi-infinite permeable plate in a micropolar fluid is presented. The velocity, micro-rotation distribution, the temperature profiles, the skin friction and the rate of heat transfer are shown on graphs. Also the numerical values of the skin friction and the rate heat transfer are entered in tabular form.
A boundary layer solution is presented to study the mixed convection from a horizontal cylinder embedded in electrically conducting micropolar fluid. The governing conservation equations have been solved numerically. Details of the velocity, microrotation and temperature fields are presented for various material parameters. Missing values of the velocity, angular velocity and thermal functions are tabulated.
A boundary layer analysis is presented to study the effects of a transverse magnetic field on natural boundary layer flow of a micropolar fluid in a porous medium. Four different vertical flows have been analyzed, those adjacent to an isothermal surface and uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source on a vertical adiabatic surface, or wall plume. The governing equations for momentum, angular momentum and energy have been solved numerically. Missing values of the velocity, angular velocity and thermal functions are tabulated for a wide range of the material parameters, Prandtl number and magnetic parameter of the fluid. A comparison has been made with the corresponding results for Newtonian fluids. Micropolar fluids display drag reduction and reduced surface heat transfer rate in a porous medium as compared with Newtonian fluids.
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The influence of variable viscosity and a transverse magnetic field on natural convection in micropolar fluids is examined. The fluid viscosity is assumed to vary as an inverse linear function of temperature. Four different vertical flows have been analyzed, those adjacent to an isothermal surface and uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source on a vertical adiabatic surface, or wall plume. By means of similarity solutions and deviation of the velocity, temperature and micro-rotation fields as well as the skin friction, heat transfer and wall couple stress results from their constant values are determined.
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