Mixed convection in vertical internal flow of a micropolar fluid

The theory of micropolar fluids due to Eringen is used to formulate a set of equations for the flow and heat transfer characteristics of the combined convection micropolar flow in vertical channels. It is found that the microstructure and substructure parameters have significant effects on the flow and thermal fields. By making the Newtonian solvent more and more micropolar, it is possible to obtain drag reduction as well as reduced heat transfer characteristics.     

Analysis of forced convection micropolar boundary layer about a permeable sphere

The heat transfer characteristics and local skin friction for forced convection flow of micropolar fluid over an isothermal or a constant-heat-flux surface of sphere with surface mass transfer have been studied. The problem was formulated by applying a suitable variables transformation and the solutions were obtained by an implicit finite difference method. Numerical results were carried out for a wide range of mass transfer parameters as the Prandtl number at 0.7 or 7 with several values of material parameters of the micropolar fluid. The variations of the local friction factor and local Nusselt number are plotted and discussed.     

Mixed convection in micropolar fluid flow over a horizontal plate with surface mass transfer

Combined free and forced convection in the boundary layer flow of a micropolar fluid over a horizontal surface is studied. Buoyancy effects on the flow and temperature fields are discussed. The influence of uniform mass transfer from the surface is also considered. Wall friction and heat transfer results are presented for various cases representing the relative effects of blowing or suction as compared to the combined effects of buoyancy and mass transfer.     

Penetrative convection in a micropolar fluid

This work investigates stationary penetrative convection in an incompressible micropolar fluid heated from above and with its lower boundary at a fixed temperature. Linear, energy and conditional stability results are obtained for a series of upper surface temperatures and values for the micropolar parameter. The conditional energy analysis strongly suggests that the micropolar parameter should be small for optimal results.     

Mixed convection boundary layer flow of a micropolar fluid along vertical cylinders and needles

An analysis is presented to investigate the effects of buoyancy and curvature on convection along vertical cylinders and needles placed in a micropolar fluid. The governing equations for momentum, angular momentum and energy are solved numerically by finite difference scheme. The heat transfer results are presented for a range of values of the buoyancy parameters, the curvature parameter and the material parameters of the fluid. The effect of the microrotation boundary conditions on heat transfer is discussed.     

Free convection about a vertical frustum of a cone in a micropolar fluid

The paper studies the problem of free convection about a vertical frustum of a cone in a micropolar fluid. It is assumed that the flow is steady, and the surface temperature of the frustum of the cone is constant. Another assumption is that the angles of the frustum of the cone are large enough so that the transverse curvature effects are negligible. Under these assumptions, the governing boundary layer equations subjected to appropriate boundary conditions are first written in a non-dimensional form. These equations are then transformed into a set of non-similar partial differential equations of parabolic type, which is amenable to a direct numerical solution, using a very efficient method known as Keller-box method. Numerical solutions are obtained for a range values of the micropolar parameter Δ varying between Δ = 0 (Newtonian fluid) to Δ = 2 and Prandtl number Pr is varied from 0.1 to 10. Flow and heat transfer characteristics are determined and are given in tables and also shown on graphs. The obtained results are also compared with those known from the open literature and it is found that they are in excellent agreement.     

Rayleigh-Benard convection in a micropolar ferromagnetic fluid

The problem of Rayleigh-Benard convection in a micropolar ferromagnetic fluid layer permeated by a uniform, vertical magnetic field is investigated analytically with free-free, isothermal, spin-vanishing, magnetic boundaries. The influence of the various micropolar and magnetization parameters on the onset of stationary convection has been analysed. It is observed that the micropolar ferromagnetic fluid layer heated from below is more stable as compared with the classical Newtonian ferromagnetic fluid. The nature of influence of the magnetization parameters on convection in the micropolar ferromagnetic fluid is similar to that in the case of Newtonian ferromagnetic fluids. The influence of the micropolar parameters on convection in the ferromagnetic case is akin to its role in the non-magnetic fluid case. The critical wave number is found to be insensitive to the changes in the micropolar fluid parameters, but sensitive to the magnetization parameters.     

Longitudinal oscillations of a sphere in a micropolar fluid

Summary A general expression for the force exerted on a sphere excuting longitudinal oscillations, with small amplitude, in an incompressible micropolar fluid is obtained. This is accomplished by using direct integral consequences of the full field and the constitutive equations written in cartesian coordinates. The results which are independent of any boundary conditions are then applied to calculate the hydrodynamic force experienced by a sphere moving with rectilinear oscillating velocityu(t)=(u _oe^it, 0, 0) in an unbounded micropolar fluid. As a special case, a general expression for the drag in a similar viscous flow is also derived.     

Uniform suction/blowing effect on forced convection about a wedge: Uniform heat flux

Summary The effect of constant suction/blowing on steady two-dimensional laminar forced flow about a uniform heat flux wedge is numerically analyzed. The nonlinear boundary-layer equations were transformed and the resulting differential equations were solved by an implicit finite difference scheme (Keller box method). Numerical results for the velocity distribution, the temperature distribution, the local skin friction coefficient and the local Nusselt number are presented for various values of Prandtl number Pr, pressure gradient parameterm and suction/blowing parameter . In general, it has been found that the local skin friction coeffcient and the local Nusselt number increase owing to suction of fluid. This trend reversed for blowing of fluid. In addition to, as the blowing effect is strong enough, i.e. –0.65, the flow separation only occurred in the case ofm=0.0.Notation C Constant defined in Eq. (4.2) - C _f Local skin friction coefficient, 2v(u/y) _y=0/U ² - f Dimensionless stream function defined in Eq. (5.3) - g Gravitational acceleration - h Local heat transfer coefficient - k Thermal conductivity - m Pressure gradient parameter, /(2–) - Nu _x Local Nusselt number,hx/k - Pr Prandtl number,v/ - q _w Wall heat flux - Re _x Local Reynolds number,U x/v - T Temperature - T _w Wall temperature - T Temperature of ambient fluid - u Velocity component in thex-direction - U Potential flow velocity,Cx ^m - v Velocity component in they-direction - V _w Surface mass transfer - x Coordinate along the wedge surface - y Coordinate normal to the wedge surface - Thermal diffusivity - Angle factor of the wedge - Pseudosimilarity variable defined in Eq. (5.2) - Suction/blowing parameter defined in Eq. (5.1) - Total angle of the wedge - Dimensionless temperature defined in Eq. (5.4) - Kinematic viscosity - Stream function     

Mixed convection flow of micropolar fluid over an isothermal plate with variable spin gradient viscosity

Summary A steady two-dimensional mixed convection flow of viscous incompressible micropolar fluid past an isothermal horizotal heated plate with uniform free stream and variable spin-gradient viscosity is considered. With appropriate transformations the boundary layer equations are transformed into nonsimilar equations appropriate for three distinct regimes, namely, the forced convection regime, the free convection regime and the mixed convection regime. Solutions of the governing equations for these regimes are obtained by an implicit finite difference scheme developed for the present problem. Results are obtained for the pertinent parameters, such as the buoyancy parameter, in the range of 0 to 10 and the vortex viscosity parameters, =0.0, 1.0, 3.0, 5.0 and 10.0 for fluid with Prandtl number Pr=0.7 and are presented in terms of local shear-stress and the local rate of heat transfer. Effects of these parameters are also shown graphically on the velocity, temperature and the couple stress distributions. From the present analysis, it is observed that both the momentum boundary layer and the thermal boundary layer increase due to an increase in the vortex viscosity of the fluid.List of symbols f, F, dimensionless stream function for forced convection free convection and mixed convection, respectively - g acceleration due to gravity - Gr_x local Grashof number - j micro-inertia density - m ₂₃ distribution of couple stress - N microrotation component normal to (x, y)-plane - p pressure of the fluid - q dimensionless rate of heat transfer - Re_x local Reynolds number - T temperature of the fluid in the boundary layer - T temperature of the ambient fluid - T temperature at the surface - u, v thex andy-components of the velocity field - U free stream velocity - x, y axis in direction along and normal to the plate Greek thermal diffusivity - coefficient of volume expansion - vortex viscosity parameter - stream function - , , nondimensional similarity variables - buoyancy parameter (=Gr _x Re _x ^/5/2 ) - vortex viscosity - density of the fluid - v kinematic coefficient of viscosity - spin-gradient viscosity - stream function - dimensionless skin-friction - fluid viscosity     

Experimental study of free convection with porous blowing and suction on a vertical surface

The paper presents the results of an experimental study of the heat transfer and the temperature field in a free-convection boundary layer on a vertical surface with uniform porous blowing and suction and T_w=const. The method of measurement is described and the experimental data are compared with the theoretical results obtained by the authors in an earlier work. The experiments were carried out on a Zender-Mach interferometer. The theoretical and experimental results are found to be in good agreement. Critical values of the parameters are found, which determine the beginning of the transient and developed turbulent regions as a function of the rate of blowing or suction.     

Mixed convection of micropolar fluids along a vertical wavy surface

Summary This paper presents numerical results for the steady-state mixed convection in micropolar fluids along a vertical wavy surface. The problem has been formulated by a simple trnasposition theorem, and the spline alternating-direction implicit method has been applied to solve the governing momentum, angular momentum and energy equations. The influence of the micropolar parameters (R and ), the amplitude-wave length ratio and the Gr/Re² number on the skin-friction coefficient and Nusselt number have been studied. Results demonstrate that the skin friction coefficient and local Nusselt number consist of a mixture of two harmonics in micropolar fluids and in Newtonian fluids. As the vortex viscosity parameter (R) increases, the heat transfer rate decreases but the skin friction increases. In addition, when the spin gradient viscosity parameter () increases, the heat transfer rate and the skin friction decreases. However, the heat transfer rate of a micropolar fluid is smaller than a Newtonian fluid, but the skin friction of a micropolar fluid is larger than a Newtonian fluid under all circumstances.     

Natural convection from a discrete heater in enclosures filled with a micropolar fluid

In this study, we numerically investigate the steady laminar natural convective flow and heat transfer of micropolar fluids in enclosures with a centrally located discrete heater in one of its sidewalls by applying a finite difference method. The other sidewall is kept at isothermal conditions, while horizontal walls are assumed to be insulated. Computations are carried out to investigate effects of the dimensionless heater length, the material parameter of the micropolar fluid, the Rayleigh number and the Prandtl number both for weak and strong concentration cases. Local results are presented in the form of streamline and isotherm plots as well as the variation of the local Nusselt number through the discrete heater. It was shown that micropolar fluids presented lower heat transfer values than those of the Newtonian fluids. An increase at the material parameter, K is shown to decrease the heat transfer. The results for K = 0, which corresponds to the Newtonian fluid case is compared with those available in the existing literature and, an excellent agreement is obtained.     

Thermal convection of micropolar fluids past two-dimensional or axisymmetric bodies with suction/injection

Steady laminar forced convection of micropolar fluids past two-dimensional or axisymmetric bodies with porous walls and different thermal boundary conditions has been analyzed. New coordinate transformations are employed to reduce the streamwise-dependence in the coupled nonlinear boundary-layer equations. The analysis is applied to cylinders and spheres with fluid injection/suction at the surface. Of interest are the effects of material parameters, wall mass transfer, the Prandtl number and the distinct thermal boundary conditions on the local skin friction coefficient and heat transfer coefficient.     

Motion of a rigid sphere in a shear field in a micropolar fluid

The motion of a rigid sphere, suspended in a micropolar fluid which is undergoing a shearing motion, is discussed. The expressions for the pressure, velocity and spin in the fluid and those for the force and torque on the sphere are obtained. A compromise boundary condition, relating the spin of the particle with the vorticity vector at the boundary, is employed. The results are compared with the classical values and apart from other interesting observations, it is noted that the torque on the sphere depends upon the various parameters in a complicated manner. By extending the definitions of the effective viscosity for the viscous fluids, an expression for the viscosity of the suspension in the micropolar fluid is derived.