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.     

Free convection boundary layer flow of a micropolar fluid past slender bodies

The transverse curvature effects on axisymmetric free convection boundary layer flow of a micropolar fluid past vertical cylinders are investigated using the theory of micropolar fluids formulated by Eringen. 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, transverse curvature parameter and Prandtl number 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 as compared with Newtonian fluids.     

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.     

Mixed convection boundary layer flow on a vertical surface in a saturated porous medium

Summary The flow of a uniform stream past an impermeable vertical surface embedded in a saturated porous medium and which is supplying heat to the porous medium at a constant rate is considered. The cases when the flow and the buoyancy forces are in the same direction and when they are in opposite direction are discussed. In the former case, the flow develops from mainly forced convection near the leading edge to mainly free convection far downstream. Series solutions are derived in both cases and a numerical solution of the equations is used to describe the flow in the intermediate region. In the latter case, the numerical solution indicates that the flow separates downstream of the leading edge and the nature of the solution near this separation point is discussed.     

Natural convection flow of a non-Newtonian fluid between two concentric vertical cylinders

Summary The natural convection of a homogeneous incompressible fluid of grade three between two infinite concentric vertical cylinders is studied. We consider the effect of the non-Newtonian nature of the fluid on the skin friction and heat transfer. Some numerical experimentation is presented to show the effect on the velocity and temperature profiles as the dimensionless parameters are varied.     

Unsteady incompressible boundary layer flow of a micropolar fluid at a stagnation point

The flow, heat and mass transfer on the unsteady laminar incompressible boundary layer in micropolar fluid at the stagnation point of a 2-dimensional and an axisymmetric body have been studied when the free stream velocity and the wall temperature vary arbitrarily with time. The partial defferential equations governing the flow have been solved numerically using a quasilinear finite-difference scheme. The skin friction, microrotation gradient and heat transfer parameters are found to be strongly dependent on the coupling parameter, mass transfer and time, whereas the effect of the microrotation parameter on the skin friction and heat transfer is rather weak, but microrotation gradient is strongly affected by it. The Prandtl number and the variation of the wall temperature with time affect the heat-transfer very significantly but the skin friction and micrortation gradient are unaffected by them.     

Free convection boundary layer flow of a thermomicropolar fluid with stretch

The free convective boundary layer of a micropolar fluid with stretch has been studied numerically. The governing equations and boundary conditions are stated and solved in the case of a flow past a vertical flat plate. Steady state and transient developments of the flow field are given along with a detailed study of the effect of microstructure on heat transfer.     

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.     

The asymptotic boundary layer on a circular cylinder in axisymmetric micropolar fluid flow

An asymptotic boundary layer analysis is presented using the theory of micropolar fluids due to Eringen. The laminar boundary layer induced on the outside of a long, slender cylinder due to the flow of an incompressible micropolar fluid parallel to the axis of the cylinder is investigated. For reasons of both analytical and practical interests the boundary layer characteristics far down stream from the leading edge are analyzed on the basis of their asymptotic nature. Asymptotic series solutions for the velocity and micro-rotation fields are obtained. An expression for the new micropolar boundary layer thickness is derived. Central to the present investigation is the result that while calculating the skin friction one should take into account the total surface stress effects, not only due to the usual shear stresses but also due to the couple stresses. As a result, it is shown that the micropolar theory does predict a reduction in skin friction as is observed in experiments thus confirming Eringen's well known conjecture.     

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.     

Thermal boundary layer flow of a micropolar fluid past a wedge with constant wall temperature

Summary The steady laminar flow of micropolar fluids past a wedge has been examined with constant surface temperature. The similarity variables found by Falkner and Skan are employed to reduce the streamwise-dependence in the coupled nonlinear boundary layer equation. Numerical solutions are presented for the heat transfer characteristics with Pr=1 using the fourth-order Runge-Kutta method, and their dependence on the material parameters is discussed. The distributions of dimensionless temperature and Nusselt number across the boundary layer are compared with the corresponding flow problems for a Newtonian fluid over wedges. Numerical results show that for a constant wedge angle with a given Prandtl number Pr=1, the effect of increasing values ofK results in an increasing thermal boundary thickness for a micropolar fluid, as compared with a Newtonian fluid. For the case of the constant material parameterK, however, the heat transfer rate for a micropolar fluid is lower than that of a Newtonian fluid.Nomenclature h Dimensionless microrotation - j Micro-inertia density - K Dimensionless parameter of vortex viscosity - m Falkner-Skan power-law parameter - Re Reynolds number - T Temperature - u, v Fluid velocities in thex andy directions, respectively - U Free stream velocity - x Streamwise coordinate along the body surface - y Coordinate normal to the body surface Greek symbols Thermal diffusivity - Wedge angle parameter - Spin gradient viscosity - Pseudo-similarity variable - Vortex viscosity - Absolute viscosity of the fluid - v Kinematic viscosity - Dimensionless temperature - Density of the micropolar fluid - Angular velocity of micropolar fluid - Stream function     

Numerical solution of free convection micropolar fluid flow between two parallel porous vertical plates

The fully developed free convection micropolar fluid flow between two vertical porous parallel plates is studied in the presence of temperature dependent heat sources including the effect of frictional heating. The basic equations are solved using quasi-linearization finite difference technique with an error of order 0.5 × 10₋₆. The velocity, microrotation and temperature are displayed in graphs whereas the skin friction, couple stress and Nusselt numbers at the plates are shown in tables. It is noted that the couple stress on either plates increases numerically with increase in micropolar parameter. Also the Nusselt number follows the same pattern for a negative suction velocity.     

Mixed convection of micropolar fluid about a sphere with blowing and suction

An analysis is performed to study the skin friction characteristics of laminar mixed forced and free convection flow of micropolar fluid about a permeable sphere with various prescribed thermal conditions on the surface. The problem was formulated by applying a suitable variables transformation and solutions were obtained by an efficient difference method. Numerical results were carried out for a wide range of mass transfer parameter as the Prandtl number at 0.7 or 7 with several values of material parameters and buoyancy force parameter of the micropolar fluid. The variations of the local friction factor and local Nusselt number are plotted and discussed. A comparison between the present solution and finite-difference solution from T.S. Chen, etc. is also shown.     

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.