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 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 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.     

Heat transfer accompanying forced convection in a poorly permeable medium

Heat transfer accompanying liquid motion in a medium of low porosity is investigated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 2, pp. 305–310, August, 1977.     

Laminar boundary layer at a permeable surface

A universal equation for the boundary layer with continuous suction is proposed and solved (to the first approximation) in Crocco variables.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.22, No. 5, pp. 859–865, May, 1972.     

Axisymmetric thermal boundary layer of a micropolar fluid on a cylinder

The laminar micropolar thermal boundary layer in axial flow along a long, thin circular cylinder is investigated using the theory of micropolar fluids formulated by Eringen. The governing energy equation has been solved numerically by the power series approach. Missing values of the thermal functions are tabulated for a wide range of the material parameters, the transverse curvature parameter, and Prandtl number of the fluid.     

The axisymmetric micropolar boundary layer on a long thin cylinder

The laminar micropolar boundary layer in axial flow along a long, thin cylinder is investigated using the theory of micropolar fluids due to Eringen. The governing equations are solved numerically by expanding the velocity and angular velocity functions in the form of power series. Wall values of the momentum and angular momentum functions are tabulated for a wide range of values of the material parameters and the transverse curvature parameter.     

A three-dimensional laminar boundary layer on a permeable plate

We examine the laminar boundary layer on a permeable half-plane for the case in which the streamline of the outside flow is a parabola, and in which the velocity of suction or expulsion is proportional to (x + const)^1/2. We have found the velocity profiles in the boundary layer, as well as the frictional stress distribution on the half-plane.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.16, No. 3, pp. 389–397, March, 1969.     

Unsteady forced and natural convection around a sphere immersed in a porous medium

Unsteady forced and natural convection around a sphere immersed in a fluid-saturated porous medium is investigated. The sphere is suddenly heated and, subsequently, maintains a constant temperature over the surface. For the forced convection problem, the method of matched asymptotic expansions is used to obtain an asymptotic solution of the energy equation in terms of the Peclet number. For the natural convection problem, asymptotic solutions in terms of the Rayleigh number are obtained by means of a regular perturbation method.     

Longitudinal surface curvature effects on boundary layer of a micropolar fluid

Summary The effect of longitudinal surface curvature on steady two-dimensional incompressible laminar boundary layer of a micropolar fluid has been considered. Van Dyke's first oder perturbation analysis is applied to the full equations of motion derived in curvilinear coordinate system which facilitates to carry out boundary layer approximation for flow past a curved surface. This results into two systems of partial differential equations which are called the zeroth order and the first order boundary layer equations. The zeroth order equations are the usual boundary layer equations for a micropolar fluid. The first order equations take into account the longitudinal surface curvature effect explicitly. Similar solution of the governing equations exists if (i) the inviscid flow velocity on the surface varies linearly along the surface and (ii) the longitudinal surface curvature is constant. Numerical results are presented illustrating the dependence of the important flow quantities of both zeroth order and first order boundary layers on the micropolar fluid parameters. The results have been compared with the corresponding results for a Newtonian fluid. It has been found that the skin friction decreases and the wall couple stress increases for convex side of the surface and vice versa for the concave side.

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Einfluß der longitudinalen Oberflächenkrümmung auf die Grenzschicht einer mikropolaren Flüssigkeit

Zusammenfassung Der Einfluß einer longitudinalen Oberflächenkrümmung auf die stationäre, zweidimensionale, inkompressible, laminare Grenzschicht einer mikropolaren Flüssigkeit wird untersucht. Van Dyke's Strömungsanalyse erster Ordnung wird angewendet auf die Bewegungsgleichungen in krummlinigen Koordinaten, die einfach die Grenzschichtnäherung für die Strömung hinter einer gekrümmten Oberfläche aufzeigen. Dies führt zu zwei Systemen partieller Differentialgleichungen, die die Grenzschichtgleichungen nullter und erster Ordnung genannt werden. Die Gleichungen nullter Ordnung sind die üblichen Grenzschichtgleichungen für eine mikropolare Flüssigkeit. Die Gleichungen erster Ordnung berücksichtigen den Einfluß der longitudinalen Oberflächenkrümmung explizit. Ähnliche Lösungen der Grundgleichungen existieren wenn: (i) sich die reibungsfreie Strömungsgeschwindigkeit an der Oberfläche linear entlang der Oberfläche ändert und (ii) die longitudinale Oberflächenkrümmung konstant ist. Numerische Ergebnisse werden angegeben, um die Abhängigkeit der wichtigsten Strömungsgrößen der Grenzschicht nullter und erster Ordnung von den Parametern der mikropolaren Flüssigkeit aufzuzeigen. Die Ergebnisse werden verglichen mit den entsprechenden Ergebnissen für eine Newtonsche Flüssigkeit. Es wurde festgestellt, daß für eine konvexe Fläche die Wandreibung abnimmt und die gekoppelten Spannungen an der Wand zunehmen; das Umgekehrte gilt für eine konkave Fläche.

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With 2 Figures     

Effects of fluid layer at micropolar orthotropic boundary surface

Effects of a fluid layer at a micropolar orthotropic elastic solid interface to a moving point load have been studied. After using the Fourier transform an eigen value approach has been employed to solve the problem. The displacement, microrotation and stress components for a micropolar orthotropic elastic solid so obtained in the physical domain are computed numerically by applying the numerical inversion technique. Micropolarity and anisotropy effects along with that of the depth of the fluid layer on various expressions have been depicted graphically for a particular model. Some special cases of interest have been presented     

Heat transfer in micropolar boundary layer flow over a flat plate

Boundary layer solutions are presented to study the steady state heat transfer from a semi-infinite flat plate to a micropolar fluid. The boundary conditions of isothermal wall, constant surface heat flux and insulated wall with viscous dissipation effects have been treated in this paper. Numerical results for the temperature distribution and the missing wall values of the thermal functions have been given. The range of Prandtl numbers investigated was from 10 to 1000 while the dimensionless grouping of the material properties was allowed to vary over a wide range.     

Heat transfer in micropolar boundary layer flow near a stagnation point

Using the micropolar theory, a set of boundary layer equations are obtained for the two dimensional flow of an incompressible micropolar fluid near a stagnation point. The boundary conditions of isothermal and insulated wall are taken with VISCOUS DISSIPATION effects. Numerical results for the temperature distribution has been shown graphically for different values of the material parameters and Prandtl number.     

Turbulent boundary layer on a permeable surface with intensive blowing

Results of an experimental investigation of the structure and integrated characteristics of a turbulent boundary layer on a permeable plate in a broad range of blowing intensities ¯j=0.005–0.04 are presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 5, pp. 773–779, May, 1976.