Flow Of non-Newtonian Power-law Fluid Research Articles

Diffusion of a chemically reactive species of a power-law fluid past a stretching surface

A numerical solution for the steady magnetohydrodynamic (MHD) non-Newtonian power-law fluid flow over a continuously moving surface with species concentration and chemical reaction has been obtained. The viscous flow is driven solely by the linearly stretching sheet, and the reactive species emitted from this sheet undergoes an isothermal and homogeneous one-stage reaction as it diffuses into the surrounding fluid. Using a similarity transformation, the governing non-linear partial differential equations are transformed into coupled nonlinear ordinary differential equations. The governing equations of the mathematical model show that the flow and mass transfer characteristics depend on six parameters, namely, the power-law index, the magnetic parameter, the local Grashof number with respect to species diffusion, the modified Schmidt number, the reaction rate parameter, and the wall concentration parameter. Numerical solutions for these coupled equations are obtained by the Keller–Box method, and the solutions obtained are presented through graphs and tables. The numerical results obtained reveal that the magnetic field significantly increases the magnitude of the skin friction, but slightly reduces the mass transfer rate. However, the surface mass transfer strongly depends on the modified Schmidt number and the reaction rate parameter; it increases with increasing values of these parameters. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially shear-thinning phenomena. Shear thinning reduces the wall shear stress.

Simulation of non-Newtonian (Power-law) fluid flow past a row of square cylinders

The power-law fluid flow past a row of uniform placed square cylinders is investigated using the Lattice Boltzmann method (LBM). The flow is assumed to be two-dimensional and incompressible. The relaxation time τ is assumed to be shear-dependent and determined by using a variable parameter related to the local shear rate. The effects of both shear-thinning/ shear-thickening property and the cylinder spacing on the confluence of the jets are mainly concerned. The bifurcation diagrams of the flow are obtained, which include confluences of double and quadruple jets. The results show that both the first and second pitchfork bifurcations are advanced due to the effect of the shear-thinning property, and postponed due to the shear-thickening property.

Analysis of Marangoni convection of non-Newtonian power law fluids with linear temperature distribution

The problem of steady, laminar, thermal Marangoni convection flow of non-Newtonian power law fluid along a horizontal surface with variable surface temperature is studied. The partial differential equations are transformed into ordinary differential equations by using a suitable similarity transformation and analytical approximate solutions are obtained by an efficient transformation, asymptotic expansion and Pad? approximants technique. The effects of power law index and Marangoni number on velocity and temperature profiles are examined and discussed.

Unsteady natural convective power-law fluid flow past a vertical plate embedded in a non-Darcian porous medium in the presence of a homogeneous chemical reaction

A numerical solution is presented for unsteady coupled heat and mass transfer by natural convection from a non-Newtonian power-law fluid flow past a vertical plate embedded in a non-Darcian porous medium in the presence of viscous dissipation and chemical reaction effects. The governing equations are formulated and a numerical solution is obtained by using an explicit finite-difference scheme. The solutions at each time step have been found to reach the steady state solution properly. The numerical results are presented in tabular and graphical form to show the effects of material parameters of the problem on the solution.

Laminar flow and convective heat transfer of non-Newtonian fluids in doubly connected ducts

A hybrid numerical–analytical solution based on the Generalized Integral Transform Technique (GITT) is obtained for laminar heat and fluid flow of power-law non-Newtonian fluids inside doubly connected ducts. The mathematical formulation is constructed in the cylindrical coordinates system in such a way that the solid surfaces are described in terms of internal and external radii as functions of the angular coordinate, thus avoiding discontinuities in the boundary conditions. An annular doubly connected duct of arbitrary geometric configuration is considered for the analysis of the fully developed velocity field, as well as for the temperature field under thermally developing flow with boundary conditions of prescribed wall temperature. For illustration purposes, the case of eccentric annular ducts is more closely analyzed in order to demonstrate the ability of the GITT approach in dealing with such class of problems. Numerical results for the velocity field, the product of the Fanning friction factor-Reynolds number, temperature field and Nusselt numbers were produced for different values of the governing parameters, i.e., eccentricity, radii ratio and power-law indices. Such results were examined against previously reported ones, providing critical comparisons in order to illustrate the adequacy of the employed integral transform approach.

MHD power-law fluid flow and heat transfer over a non-isothermal stretching sheet

This article presents a numerical solution for the magnetohydrodynamic (MHD) non-Newtonian power-law fluid flow over a semi-infinite non-isothermal stretching sheet with internal heat generation/absorption. The flow is caused by linear stretching of a sheet from an impermeable wall. Thermal conductivity is assumed to vary linearly with temperature. The governing partial differential equations of momentum and energy are converted into ordinary differential equations by using a classical similarity transformation along with appropriate boundary conditions. The intricate coupled non-linear boundary value problem has been solved by Keller box method. It is important to note that the momentum and thermal boundary layer thickness decrease with increase in the power-law index in presence/absence of variable thermal conductivity.

Flow of power-law fluids in self-affine fracture channels

The two-dimensional pressure driven flow of non-Newtonian power-law fluids in self-affine fracture channels at finite Reynolds number is calculated. The channels have constant mean aperture and two values zeta=0.5 and 0.8 of the Hurst exponent are considered. The calculation is based on the lattice-Boltzmann method, using a different technique to obtain a power-law variation in viscosity, and the behavior of shear-thinning, Newtonian, and shear-thickening liquids is compared. Local aspects of the flow fields, such as maximum velocity and pressure fluctuations, are studied, and the non-Newtonian fluids are compared to the (previously studied) Newtonian case. We find a scaling relation between permeability and mean aperture in the low Reynolds number regime, generalizing an earlier result for Newtonian fluids. As the Reynolds number increases, we observe the same sequence of transitions to nonlinearity found in intergranular porous media. Furthermore, the permeability results may be collapsed into a master curve of friction factor vs Reynolds number, using a scaling similar to that employed for power-law fluids in porous media.

Non-Newtonian Power Law Fluid Flow and Heat Transfer in a Porous Medium Over a Nonisothermal Stretching Sheet

In this paper, we present a numerical solution for heat transfer in the flow of a non-Newtonian power law fluid immersed in a saturated porous medium over a nonisothermal stretching sheet in the presence of internal heat generation/absorption. Thermal conductivity is assumed to vary as a linear function of temperature. Similarity transformations are used to convert highly nonlinear partial differential equations into ordinary differential equations. The resulting coupled nonlinear ordinary differential equations are solved numerically by the efficient Keller box method for two different cases, namely, a surface with prescribed surface temperature and surface with prescribed wall heat flux. The important findings of our study are that the effect of the power law index is to decrease the horizontal velocity boundary layer thickness and thermal boundary layer thickness. The effect of the porous parameter is to reduce the horizontal boundary layer thickness and increase the thermal boundary layer thickness. © 2008 Begell House, Inc.

Free convection film flows and heat transfer

From the contents Introduction.- Part I: Free Convection.- Basic Conservation Equations for Free Convection.- Brief Review of Previous Analysis Methods for Laminar Free Convection.- Laminar Free Convection of Monatomic and Diatomic Gases, Air and Water Vapor.- Laminar Free Convection of Polyatomic Gas.- Laminar Free Convection of Liquid.- Deviation of Laminar Free Convection Heat Transfer Caused due to Boussinesq Approximation.- Experimental Measurement of Free Convection with Larger Temperature Difference.- Relationship on Free Convection Flow and Heat Transfer between Inclined and Vertical Plates.- Part II: Film Boiling and Condensation.- Saturated Film Boiling.- Subcooled Film Boiling.- Film Condensation Free Convection of Saturated Vapour.- Film Condensation Free Convection of Superheated Vapour.- Laminar Film Condensation of Superheated Steam.- Part III: Falling Film Flow of Non-Newtonian Fluids.- Hydrodynamics of Falling Film Flow of Non-Newtonian Power-law Fluids.- Analyses of pseudo-similarity and boundary layer thickness of the Falling Film Flow.- Heat transfer of the Falling Film Flow.

Variation of the Recirculation Length of Newtonian and Non-Newtonian Power-Law Fluids in Laminar Flow Through a Suddenly Expanded Axisymmetric Geometry

Abstract A numerical study has been carried out for the laminar flow of Newtonian and non-Newtonian power-law fluids through a suddenly expanded axisymmetric geometry. Mathematical correlations are proposed for the prediction of the length of the recirculating eddy in terms of Reynolds number, expansion ratio and rheological parameters. A wide range of expansion ratios (1.25⩽ER⩽8.0) has been covered for the Newtonian fluid and both the shear-thinning and shear-thickening flow characteristic fluids have been considered for the non-Newtonian fluids.

MASS TRANSFER WITH HETEROGENEOUS CHEMICAL REACTION OF THE FIRST ORDER IN FALKNER-SKAN FLOW OF A POWER-LAW FLUID

ABSTRACT Mass transfer with a heterogeneous chemical reaction of the first order in a Falkner-Skan flow of non-Newtonian power-law fluid is investigated. This problem is solved by the method of Laplace transform following the approach suggested by Apelblat (1980). The solution is obtained in a closed analytical form.

MHD Flow and heat transfer of non-Newtonian power-law fluid with diffusion and chemical reaction on a moving cylinder

The problem of flow and heat transfer of an electrically conducting non-Newtonian fluid over a continuously moving cylinder in the presence of a uniform magnetic field is analyzed for the case of power-law variation in the temperature and concentration at the cylinder surface. A diffusion equation with a chemical reaction source term is taken into account. The governing non-similar partial differential equation are solved numerically by employing shooting method. The effects of various parameters on the velocity, temperature and concentration profiles as well as the heat and mass transfer rate from the cylinder surface to the surrounding fluid are presented graphically and in tabulated form.

MHD combined convection flow of a non-Newtonian power-law fluid due to a rotating cone or disk

The problem of laminar mixed convection flow of non-Newtonian power-law fluids from a constantly rotating isothermal cone or disk in the presence of a uniform magnetic field is investigated in this paper. The effect of Joule heating is also considered. The governing partial-differential equations are transformed into ordinary differential equations using similarity transformations. The transformed equations, on the assumption of a small magnetic Reynolds number, are solved numerically by employing the shooting method. Graphical results for the velocity and temperature profiles as well as tabulated results for the skin friction and the Nusselt number for various parametric conditions are presented and discussed. PACS No.: 47.50.td

Weakly Nonlinear Stability Analysis of Condensate/Evaporating Power-Law Liquid Film Down an Inclined Plane

Weakly nonlinear stability analysis of thin power-law liquid film flowing down an inclined plane including the phase change effects at the interface has been investigated. A normal mode approach and the method of multiple scales are employed to carry out the linear stability solution and the nonlinear stability solution for the film flow system. The results show that both the supercritical stability and subcritical instability are possible for condensate, evaporating and isothermal power-law liquid film down an inclined plane. The stability characteristics of the power-law liquid film show that isothermal and evaporating films are unstable for any value of power-law index ‘n’ while there exists a critical value of power-law index ‘n’ for the case of condensate film above which condensate film flow system is always stable. Thus, the results of the present analysis show that the mass transfer effects play a significant role in modifying the stability characteristics of the non-Newtonian power-law fluid flow system. The condensate (evaporating) power-law fluid film is more stable (unstable) than the isothermal power-law fluid film flowing down an inclined plane.

Solutions for the internal boundary layer equations in simultaneously developing flow of power-law fluids within parallel plates channels

The generalized integral transform technique (GITT) is employed in the solution of the boundary layer equations in simultaneously developing laminar flow of power-law non-Newtonian fluids within a parallel plates channel. In the modeling of the related momentum and energy equations within the range of validity of the boundary layer equations, a streamfunction formulation is employed which offers a better computational performance than the primitive-variables formulation. Numerical results for the bulk temperature and Nusselt numbers are established at different axial positions along the channel and for various power-law indices, and critical comparisons with previously reported works in the literature are also performed.

Hybrid solution for the laminar flow of power-law fluids inside rectangular ducts

The so-called generalized integral transform technique (GITT) is employed in the hybrid numerical–analytical solution of two-dimensional fully-developed laminar flow of non-Newtonian power-law fluids inside rectangular ducts. The characteristic of the automatic and straightforward global error control procedure inherent to this approach, permits the determination of fully converged benchmark results to assess the performance of purely numerical techniques. Therefore, numerical results for the product Fanning friction factor-generalized Reynolds number are computed for different values of power-law index and aspect ratio, which are compared with previously reported results in the literature, providing critical comparisons among them as well as illustrating the powerfulness of the integral transform approach. The resulting velocity profiles computed by using this methodology are also compared with those calculated by approximated methods for power-law fluids, within the range of governing parameters studied.

Application of unsteady couette flow of non-Newtonian power-law fluids in concentric annular wellbore

Fluid flow phenomena that occur when the fluid is confined between two co-axial cylinders, one of which is stationary and the other is moving at a specified velocity, is known as couette flow. Such flow is representative of that which occurs in the borehole annulus where the wall of the wellbore is represented by the stationary cylinder, and the drill string or casing is represented by the moving cylinder. The fluid local velocity is dependent on the velocity of the moving cylinder or pipe. Different mathematical relations have been developed for surge and swab pressure calculations for flow of power-law fluids in the wellbore annulus. The application of couette flow equations and relationships to evaluate the surge or swab pressure has been limited. These equations are either too complex for field use or require much computation for field application. In this study, the motion equations are analytically solved for non-Newtonian power-law fluids. The solutions of the equations are presented in both dimensionless and graphical forms, which are applied to predict the surge or swab pressure encountered when running tubular goods in liquid-filled boreholes. The technique presented here is easy to use and requires minimal computational efforts for determining the surge or swab pressure for an unsteady motion of a moving inner pipe in a concentric annulus. The results of this study show that the magnitude of surge or swab pressure increases with increase in the pipe acceleration.

Further finite element analyses of fully developed laminar flow of power-law non-Newtonian fluid in rectangular ducts: Heat transfer predictions

Forced convection heat transfer to hydrodynamically and thermally fully developed laminar flow of power-law non-Newtonian fluid in rectangular ducts has been studied for the H1 and T thermal boundary conditions. The solutions for the velocity and temperature fields were obtained numerically using the finite element method with quartic triangular elements. From these solutions, very accurate Nusselt number values were determined. Computations were performed over a range of power-law indices and duct aspect ratios.

Unsteady Axial Laminar Couette Flow of Power-Law Fluids in a Concentric Annulus

The unsteady laminar couette flow of non-Newtonian power-law fluids in a concentric annulus is a flow phenomenon that can be applied to predict the surge or swab pressure encountered when running or pulling pipes in a liquid-filled borehole. It is similar to a moving cylinder, concentrically placed in a liquid-filled outer cylinder. This flow phenomenon has a wide variety of applications in the solution of problems in petroleum, chemical, mechanical, and ceramic industries. Several numerical models have been proposed by several authors for surge or swab pressure predictions. Though previous investigators had reported that the magnitude of the surge or swab pressure is determined by the annular geometry, the moving pipe velocity, and the drilling fluid properties, there has been no reported simple analytical presentation of the application of the unsteady couette flow phenomenon to predict either the surge or swab pressure which occurs when the casing pipes are in motion in a liquid-filled borehole. In this study, the motion equations are analytically solved for power-law fluids by the perturbation method. The solutions of the resulting pressure gradient equations are presented in both dimensionless and graphical forms and for different pipe/borehole diameter ratios and power-law index values. These allow for a more general application in annular fluid flow analysis and for predicting the surge or swab pressure during the unsteady motion of casing strings.

Finite-element analysis of fully developed laminar flow of power-law non-Newtonian fluid in a rectangular duct

The finite-element method has been applied to solve numerically equations governing fully developed laminar flow of power-law non-Newtonian fluid in a rectangular duct. The resulting finite-element solutions for the velocity profile have been further utilized to obtain the numerical values of the friction factor-Reynolds number product for duct aspect ratios ranging from 0.05 to 1.0 and for power-law indices ranging from 0.2 to 2.0, i.e., both shear-thinning and shear-thickening cases are considered.