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This paper deals with the investigation of time dependent boundary layer flow of a modified power-law fluid of fourth grade on a stretched surface with an injection or suction boundary condition. The fluid model is a mixture of fourth grade and power-law fluids in which the fluid may display shear thickening, shear thinning or normal stress textures. By using the scaling and translation transformations which is a type of Lie Group transformation, time dependent boundary layer equations are reduced into two alternative ordinary differential equations systems (ODEs) with boundary conditions. During this reduction, special Lie Group transformations are used for translation, scaling and combined transformation. Numerical solutions have been carried out for the ordinary differential equations for various fluids and boundary condition parameters. As a result of numerical analysis, it is observed that the boundary layer thickness decreases as the power-law index value increases. It was also observed that for the fourth-grade fluid parameter, as the parameter increases, the boundary layer thickness decreases while the velocity in the y direction increases.

The influence of non-Newtonian fluid behavior on the flow statistics of turbulent bubble-laden downflow in a vertical channel is investigated. A Direct Numerical Simulation (DNS) study is conducted for power-law fluids with power-law indexes of 0.7 (shear-thinning), 1 (Newtonian) and 1.3 (shear-thickening) in the liquid phase at a gas volume fraction of 6%. The flow is driven downward by a constant volumetric flow rate corresponding to a friction Reynolds number of Reτ≈127.3. The Eötvös number is varied between Eo=0.3125 and Eo=3.75 in order to investigate the influence of quasi-spherical as well as wobbling bubbles and thus the interplay of the bubble deformability with the power-law behavior of the liquid bulk. The resulting first- and second-order fluid statistics, i.e., the gas fraction, mean velocity and velocity fluctuation profiles across the channel, show clear trends in reply to varying power-law indexes. In addition, it was observed that the bubble oscillations increase with decreasing power-law index. In the channel core, the bubbles significantly increase the dissipation rate, which, in contrast to its behavior at the wall, shows similar orders of magnitude for all power-law indexes.

Fluid dynamics and heat transfer behaviour are studied past side-by-side square cylinders at incidence in vertical flow arrangement numerically considering laminar, Newtonian, steady, incompressible and two-dimensional flow using Finite Volume Method based ANSYS Fluent solver. Using air (Pr = 0.7) as the working fluid, computations are performed at a representative value of Re = 100. The angle of incidence (alpha) is varied from 0 degrees to 45 degrees in the step of 5 degrees, whereas, the lateral distance between the cylinders is kept constant. To consider all possibilities, cylinders are rotated either clockwise or counter-clockwise, simultaneously or individually, which generates thirty-four different orientations. Buoyancy assisting phenomenon is created by changing the Richardson number (Ri) from 0 to 1 in step of 0.25. Due to the variation of the angle of incidence and its orientations, vortex generation is observed in the buoyancy assisting case at a critical value of Ri. To study heat transfer characteristics, time average and the local Nusselt number are analysed. For a fixed lateral distance between the cylinders, maximum heat transfer is found to occur at an incident angle of 45 degrees. Other important parameters, such as drag coefficient (C-D), lift coefficient (C-L), Strouhal number (St) are also studied. (C) 2018 Elsevier Ltd. All rights reserved.

The velocity and thermal slip impacts on the magnetohydrodynamics (MHD) nanofluid flow and heat transfer through a stretched thin sheet are discussed in the paper. The no slip condition is substituted for a new slip condition consisting of higher-order slip and constitutive equation. Similarity transformation and Lie point symmetry are adopted to convert the derived governed equations to ordinary differential equations. An approximate analytical solution is gained through the homotopy analysis method. The impacts of velocity slip, temperature jump, and other physical parameters on flow and heat transfer are illustrated. Results indicate that the first-order slip and nonlinear slip parameters reduce the velocity boundary layer thickness and Nusselt number, whereas the effect on shear stress is converse. The temperature jump parameter causes a rise in the temperature, but a decline in the Nusselt number. With the increase of the order, we can get that the error reaches 10 − 6 from residual error curve. In addition, the velocity contours and the change of skin friction coefficient are computed through Ansys Fluent.

This paper aims to discuss mixed electroosmotic/pressure driven flow of power-law fluids in a T-shaped microchannel subject to externally applied electric filed. The Possion-Boltzmann equation and Laplace equation are numerically solved and substituted into the modified Navier-Stokes equations. Considering the Possion-Boltzmann equation in the form without Debye-Huckel approximation, high order compact finite difference schemes are used for better simulation of velocity field and pressure field as a function of flow behavior index, zeta potential and dimensionless electrokinetic width. By setting the electric force at the inlet, detailed numerical results indicate that the shear thinning fluids are more sensitive to effects of zeta potential and dimensionless electrokinetic width compared with Newtonian and shear thickening fluids. If we set the electric force at the inlet and along the horizontal walls, the dimensionless electrokinetic width effects on the flow increase as the flow behavior index decreases, and the zeta potential effects result in the buildup of reverse flow in vertical channel, independent of the value of the flow behavior index.

This paper describes the induced pressure of power-law fluids electroosmotic flow (EOF) in micro-diffuser at different angles such as 30° and 60°. Ostwald-De Wael model is used to describe the power-law fluids, and high accuracy compact difference algorithm is used to solve complete Poisson-Boltzmann equations and modified two-dimension Cauchy momentum equations. Poisson equation of pressure is solved by the velocity and pressure method. Dimensionless induced pressure nephogram and mean axial velocity are shown in this study. While the diffuser angles is 30° or 60°, the impact of induced pressure is much more significant than that without pressure gradient. Dimensionless mean velocity profiles with induced pressure have a larger error than the situation without it. Shear thinning fluid is sensitive to the change of flow filed while shear thickening fluid is the opposite. For EOF in variable section, the influence of induced pressure should not be neglected. Especially for less viscous fluid such as shear thinning fluid, it has a larger error with induced pressure compared without it.

Microfluidic droplet technology has been developing rapidly. However, precise control of dynamical behaviour of droplets remains a major hurdle for new designs. This study is to understand droplet deformation and breakup under simple shear flow in confined environment as typically found in microfluidic applications. In addition to the Newtonian–Newtonian system, we consider also both a Newtonian droplet in a non-Newtonian matrix fluid and a non-Newtonian droplet in a Newtonian matrix. The lattice Boltzmann method is adopted to systematically investigate droplet deformation and breakup under a broad range of capillary numbers, viscosity ratios of the fluids, and confinement ratios considering shear-thinning and shear-thickening fluids. Confinement is found to enhance deformation, and the maximum deformation occurs at the viscosity ratio of unity. The droplet orients more towards the flow direction with increasing viscosity ratio or confinement ratio. In addition, it is noticed that the wall effect becomes more significant for confinement ratios larger than 0.4. Finally, for the whole range of Newtonian carrier fluids tested, the critical capillary number above which droplet breakup occurs is only slightly affected by the confinement ratio for a viscosity ratio of unity. Upon increasing the confinement ratio, the critical capillary number increases for the viscosity ratios less than unity, but decreases for the viscosity ratios more than unity.

The present paper presents fluid flow and mixed convective heat transfer characteristics past a semi-circular cylinder at incidence with a tandem square cylinder in cross flow. Using air ( Pr = 0.71 ) as an operating medium, numerical simulations are performed for the range of Reynolds numbers, 10 ≤ Re ≤ 45 and incidence angles, 0 0 ≤ α ≤ 180 0 . The effect of thermal buoyancy is brought about by varying the Richardson number in the range 0 ≤ R i ≤ 2 . The mathematical model is firstly validated with the experimental and numerical results from the literature and found to be in good agreement. The steady separated flow is observed to become unsteady periodic under the superimposed thermal buoyancy. Furthermore, apart from thermal buoyancy effect, angle of incidence is found to play a pivotal role in bringing hydrodynamic instabilities and thereby vortex shedding for such steady mixed convective flows. Functional dependence of drag ( C D ) , lift ( C L ) , and moment ( C M ) coefficients on the combined influence of α and R i , is explored and analysed in detail. Additionally, other global quantities, such as local and average Nusselt number distribution, Strouhal number ( S t ) are determined with respect to the various ranges of parameters considered in the present investigation.

The formation behavior of a single bubble in power-law fluids (carboxymethyl cellulose solution, CMC) and Newtonian fluids (glycerol solution) was experimentally investigated via a high-speed camera. The effects of liquid property, orifice diameter and gas flow rate on bubble volume and aspect ratio were observed. It was found that the formation time and detaching volume increased with the increase of fluid viscosity. The increase of bubble aspect ratio during the bubble formation process was complex, with main emphasis on the decrease in the initial stage and an increase in the final stage along with the shear thinning property variation. Nevertheless, the bubble detaching volume, instantaneous volume and formation time increased following the increase of orifice diameter and gas flow rate. On the contrary, the bubble aspect ratio decreased with the orifice diameter increase but increased with a higher gas flow rate. Keywords : Bubble formation; Power-law fluids; Rheological property; Bubble volume; Aspect ratio.

Steady two-dimensional natural convection in fluid filled cavities is numerically investigated for the case of non- Newtonian shear thickening power law liquids. The conservation equations of mass, momentum and energy under the assumption of a Newtonian Boussinesq fluid have been solved using the finite volume method for Newtonian and non-Newtonian fluids. The computations were performed for a Rayleigh number, based on cavity height, of 105 and a Prandtl number of 100. In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side-walls and the inclination angle is varied. The simulations have been carried out for aspect ratios of 1 and 4. Comparison between the Newtonian and the non-Newtonian cases is conducted based on the dependence of the average Nusselt number on angle of inclination. It is shown that despite significant variation in heat transfer rate both Newtonian and non-Newtonian fluids exhibit similar behavior with the transition from multi-cell flow structure to a single-cell regime.

Submitted by Jairo Amaro (jairo.amaro@sibi.ufrj.br) on 2019-07-04T16:29:53Z No. of bitstreams: 1 2010_COTTA_IJHMT_v53_p2434-2448-min.pdf: 419310 bytes, checksum: 738382a583a71b661b9b2d403961f838 (MD5) Made available in DSpace on 2019-07-04T16:29:53Z (GMT). No. of bitstreams: 1 2010_COTTA_IJHMT_v53_p2434-2448-min.pdf: 419310 bytes, checksum: 738382a583a71b661b9b2d403961f838 (MD5) Previous issue date: 2010-02-23 Indisponível. 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.

We perform a complete analysis of all the Lie point symmetries admitted by the equation describing the axisymmetric spreading under gravity of a thin power-law liquid drop on a horizontal plane. We then investigate the existence of group-invariant solutions for particular values of the power-law parameter β.

In the current study, a direct-forcing immersed boundary–non-Newtonian lattice Boltzmann method (IB–NLBM) is developed to investigate the sedimentation and interaction of particles in shear-thinning and shear-thickening fluids. In the proposed IB–NLBM, the non-linear mechanics of non-Newtonian particulate flows is detected by combination of the most desirable features of immersed boundary and lattice Boltzmann methods. The noticeable roles of non-Newtonian behavior on particle motion, settling velocity and generalized Reynolds number are investigated by simulating benchmark problem of one-particle sedimentation under the same generalized Archimedes number. The effects of extra force due to added accelerated mass are analyzed on the particle motion which have a significant impact on shear-thinning fluids. For the first time, the phenomena of interaction among the particles, such as Drafting, Kissing, and Tumbling in non-Newtonian fluids are investigated by simulation of two-particle sedimentation and twelve-particle sedimentation. The results show that increasing the shear-thickening behavior of fluid leads to a significant increase in the kissing time. Moreover, the transverse position of particles for shear-thinning fluids during the tumbling interval is different from Newtonian and the shear-thickening fluids. The present non-Newtonian particulate study can be applied in several industrial and scientific applications, like the non-Newtonian sedimentation behavior of particles in food industrial and biological fluids.

We present a numerical study of Dean instability for non-Newtonian fluids in a laminar 180deg curved-channel flow of rectangular cross section. A methodology based on the Papanastasiou model (Papanastasiou, T. C., 1987, J. Rheol., 31(5), pp. 385–404) was developed to take into account the Bingham-type rheological behavior. After validation of the numerical methodology, simulations were carried out (using FLUENT CFD code) for Newtonian and non-Newtonian fluids in curved channels of square or rectangular cross section and for a large aspect and curvature ratios. A criterion based on the axial velocity gradient was defined to detect the instability threshold. This criterion was used to optimize the grid geometry. The effects of curvature and aspect ratio on the Dean instability are studied for all fluids, Newtonian and non-Newtonian. In particular, we show that the critical value of the Dean number decreases with increasing curvature ratio. The variation of the critical Dean number with aspect ratio is less regular. The results are compared to those for Newtonian fluids to emphasize the effect of the power-law index and the Bingham number. The onset of Dean instability is delayed with increasing power-law index. The same delay is observed in Bingham fluids when the Bingham number is increased.

In this study, a slider bearing lubricated with a non-Newtonian fluid namely a Power-Law fluid is considered. First the equations of motion are derived. Perturbation methods are employed in search of approximate solutions. The simplest perturbation expansion, namely the pedestrian expansion, is used. The velocity distribution and the pressure distribution are calculated approximately. The solutions are expressed in dimensionless form for convenience. The variation of pressure and velocity with the non-Newtonian behaviour and bearing dimensions are plotted., Bu çalışmada non-Newtonyen bir akışkan olan Power-Law akışkanı ile yağlanmış kaymalı yatak problemi ele alınmıştır. Çalışmada önce akışkana ait hareket denklemleri çıkartılmıştır. Denklemlerin çözümü için perturbasyon tekniği kullanılmıştır. Çözümde en basit perturbasyon açılımı olan yaya açılımı kullanılmıştır. Perturbasyon açılımı ile önce hız dağılımı sonra da basınç dağılımı yaklaşık olarak bulunmuştur. Bulunan bu sonuçlar boyutsuzlaştırılarak uygun bir formda ifade edilmiştir. Non-Newtonyen karakterin artmasıyla ve yatak boyutlarının değişmesiyle hız ve basınç dağılımının nasıl bir değişim gösterdiği çizilmiştir.

In this study, we compare different diffuse and sharp interface schemes of direct-forcing immersed boundary — thermal lattice Boltzmann method (IB-TLBM) for non-Newtonian flow over a heated circular cylinder. Both effects of the discrete lattice and the body force on the momentum and energy equations are considered, by applying the split-forcing Lattice Boltzmann equations. A new technique based on predetermined parameters of direct forcing IB-TLBM is presented for computing the Nusselt number. The study covers both steady and unsteady regimes (20n

Due to the increasingly wide application of electroosmotic flow in micromachines, this paper investigates the electroosmotic flow of the power-law fluid under high zeta potential in a cylindrical microcapillary for different dimensionless parameters. The electric potential distribution inside a cylindrical microcapillary is presented by the complete Poisson-Boltzmann equation applicable to an arbitrary zeta potential. By solving the Cauchy momentum equation of power-law fluids, the velocity profile, the volumetric flow rate, the average velocity, the shear stress distribution and dynamic viscosity of electroosmotic flow of power-law fluids in a cylindrical microcapillary are studied for different low/high zeta potential, flow behavior index, dimensionless electrokinetic width. The velocity profile gradually changes from parabolic to plug-like shape as the flow behavior index decreases or as the dimensionless electrokinetic width increases. For shear thinning fluids, the viscosity is greater in the center of the microchannel than that near the channel wall, the reverse is true for the shear thickening fluids. Greater volumetric rate and average velocity can be achieved by enhancing the dimensionless electrokinetic width, flow behavior index and zeta potential. It is noted that zeta potential and flow behavior index are important parameters to adjust electroosmotic flow behavior in a cylindrical microcapillary.

The fully-developed mixed convection of power-law fluids is investigated for laminar flow in a parallel-plate vertical channel. The boundary condition of uniform and unequal temperatures prescribed at the channel walls is considered. The velocity field, the viscous stress field and the temperature field are obtained by solving analytically the momentum and energy balance equations as well as the stress-strain constitutive equation. An expression which allows the evaluation of the friction factors is presented. The condition for the occurrence of flow reversal is obtained.

International audience; This paper focuses on the non-incremental solution of transient coupled non-linear models, in particular the one related to the Rayleigh-Benard flow problem that models natural thermal convection. For this purpose we are applying the so-called Proper Generalized Decomposition that proceeds by performing space-time separated representations of the different unknown fields involved by the flow model. This non-incremental solution strategy allows significant computational time savings and opens-new perspectives for introducing some flow and/or fluid parameters as extra-coordinates.

In the lubrication limit, the time needed for the drainage of the liquid film between two particles or between particles and walls is of industrial importance, because it controls the dynamics and aggregation of nondilute suspensions. This problem is also of fundamental interest in the application of the dynamic surface force apparatus to nanorheology. Even if this problem has an exact solution in Newtonian fluid when the sphere moves steadily and slowly towards or away from a plane wall, this problem remains, to our knowledge, without any exact analytical solution in non-Newtonian fluids with negligible viscoelastic components. But Rodin, using the method of asymptotic expansions, gives an asymptotic solution to this problem in the lateral unbounded power-law fluid. Therefore, in this study, we give a numerical result using the dynamic mesh technique and an asymptotic analytical formula valid in the lubrication regime, for a fluidity index $$0.5 < n\, \leqslant \,1.8.$$ The comparison between the two results confirms their mutual validity.

Effect of channel-confinement and rotation on the flow and heat-transfer across a cylinder is studied for various blockage ratio (beta = 0-50%), nondimensional rotational velocity (alpha = 0-2), and Reynolds number (Re = 35-170). The cylinder is maintained at a constant wall temperature with air as the working fluid. Criss-cross motion of the shed-vortices is noticed for the channel-confined flow across a rotating cylinder at intermediate blockage ratio. The effect of channel-confinement (rotation) is an enhancement (reduction) in the drag force and heat transfer. A downward lift force is generated under the influence of counterclockwise rotation, which increases with increasing blockage ratio. Rotation and channel-confinement have a stabilizing effect and can be used for flow control.

International audience; The velocity, shape, and trajectory of the rising bubble in polyacrylamide (PAM) and carboxymethylcellulose (CMC) aqueous solutions were experimentally investigated using a set of homemade velocimeters and a video camera. The effects of gas the flowrate and solution concentration on the bubble terminal velocity were examined respectively. Results show that the terminal velocity of the bubble increases with the increase in the gas flowrate and the decrease in the solution concentration. The shape of the bubble is gradually flattened horizontally to an ellipsoid with the increase in the Reynolds number (Re), Eoumltvoumls number (Eo), and Morton number (Mo). With the increase in the Re and Eo, the rising bubble in PAM aqueous solutions begin to oscillate, but there is no oscillation phenomena for CMC aqueous solutions. By dimensional analysis, the drag coefficient of a single bubble in non-Newtonian fluids in a moderate Reynolds number was correlated as a function of Re, Eo, and Archimedes number (Ar) based on the equivalent bubble diameter. The predicted results by the present correlation agree well with the experimental data.

We investigate the enhancement of both mixing and heat transfer in a two-rod mixer for highly-viscous non-Newtonian fluids. The mixer is composed of two vertical, circular rods in a cylindrical tank. Chaotic flows are obtained by imposing the temporal modulations of the rotational velocities of the walls. We study the effects of different stirring protocols, which lead to non-chaotic and chaotic flows, on the efficiency of both mixing and heat transfer for three different rheological fluid behaviors: shear-thinning, Newtonian and shear-thickening. For this purpose, we use statistical indicators that characterize the mean value of the fluid temperature and its homogenization. We find that chaotic mixing is suitable for shear-thickening fluids for which we observe a clear enhancement of the thermal mixing (heat extraction and homogenization). This is due to the increase in the apparent fluid viscosity in the vicinity of the rotating walls. This aspect confirms the relevance of chaotic mixing for highly-viscous fluids., 24 pages

A second-law analysis of a gravity-driven film of non-Newtonian fluid along an inclined heated plate is investigated. The flow is assumed to be steady, laminar and fully-developed. The upper surface of the liquid film is considered to be free and adiabatic. The effect of heat generation by viscous dissipation is included. Velocity, temperature and entropy generation profiles are presented. The effects of the flow behaviour index, the Brinkman number and the group parameter on velocity, temperature and entropy generation number are discussed. The results show that velocity profile depends largely on the flow behaviour index. They are flat near the free surface for pseudoplastic fluids and linear for dilatant fluids. Temperature profiles are higher for higher flow behaviour index and Brinkman number. The entropy generation number increases with Brinkman number and the group parameter because of the heat generated by the viscous dissipation effect. For pseudoplastic fluids, the irreversibility is dominated by heat transfer, whereas, for dilatant fluids, irreversibility due to fluid friction is more dominant.

In the present work laminar flows of Newtonian and power-law fluids through cross-corrugated chevron-type plate heat exchangers (PHEs) are numerically studied in terms of the geometry of the channels. The plates area enlargement factor was a typical one (1.17), the corrugation angle, β, varied between 30° and 60° and the flow index behaviour, n, between 0.25 and 1. Single friction curves fReg = K for both Newtonian and non-Newtonian fluids are proposed for each β by developing an adequate definition of the generalised Reynolds number, Reg. The coefficient K compares well with experimental data, for all (seven) values of β, and depends on the tortuosity coefficient, τ. It was found that, for each β, τ decreases with the decrease of n. Food fluids are frequently processed in PHEs and usually behave as non-Newtonian fluids. This study can be useful in engineering applications as well as in the characterization of transport phenomena in PHEs.

The paper deals with measurements of non-Newtonian fluids on a viscometer with coaxial cylinders. The procedure for determining the rheological model parameters is recommended for power-law fluids and Bingham plastics.

In this study, CFD calculations were made in order to analyze the hydrodynamic behaviour of a power-law fluid in the channels of plate heat exchangers with corrugation angles of 30º and 60º during a non-isothermal flow. For the observed laminar flow, the numerical results show that a typical velocity profile in the 3D channel of the plate heat exchanger with corrugation angle 30º assumes an approximate parabolic shape and that for a corrugation angle of 60º the profile have a irregular core. Simulations considering and discarding the influence of temperature on the non-Newtonian fluid viscosity were performed for the two geometries and the impact of these variations on the relations between fanning friction factors and Reynolds number was analyzed as well as on the ratio between wall and bulk shear rate.

We solve the stationary Navier–Stokes equations for non-Newtonian incompressible fluids with shear dependent viscosity in domains with unbounded outlets, in the case of shear thickening viscosity, i.e. the viscosity is given by the shear rate raised to the power p − 2 where p > 2 . The flux assumes arbitrary given values and the Dirichlet integral of the velocity field grows at most linearly in the outlets of the domain. Under some smallness conditions on the “energy dispersion” we also show that the solution of this problem is unique. Our results are an extension of those obtained by O.A. Ladyzhenskaya and V.A. Solonnikov [O.A. Ladyzhenskaya, V.A. Solonnikov, Determination of the solutions of boundary value problems for steady-state Stokes and Navier–Stokes equations in domains having an unbounded Dirichlet integral, J. Soviet Math. 21 (1983) 728–761] for Newtonian fluids ( p = 2 ).

In this paper, a finite difference scheme is developed to solve the unsteady problem of combined heat and mass transfer from an isothermal curved surface to a porous medium saturated by a non-Newtonian fluid. The curved surface is kept at constant temperature and the power-law model is used to model the non-Newtonian fluid. The explicit finite difference method is used to solve simultaneously the equations of momentum, energy and concentration. The consistency of the explicit scheme is examined and the stability conditions are determined for each equation. Boundary layer and Boussinesq approximations have been incorporated. Numerical calculations are carried out for the various parameters entering into the problem. Velocity, temperature and concentration profiles are shown graphically. It is found that as time approaches infinity, the values of wall shear, heat transfer coefficient and concentration gradient at the wall, which are entered in tables, approach the steady state values.

Least squares is a robust and simple method in function approximation. Collocated Discrete Least Squares (CDLS) is a meshless method based on least squares technique. In this paper CDLS is used with a non-incremental projection method for the solution of incompressible generalized Newtonian fluid flow equations in the simulation of laminar flow of power-law fluids. The scheme is used to solve two benchmark problems named lid-driven cavity flow and flow past a circular cylinder for the power-law fluids.

It is aimed to study forced convection heat transfer for non-Newtonian power-law fluids in a parallel-plate channel with transverse rectangular cavities numerically. A finite volume based computation was performed using power-law discretization scheme and SIMPLE algorithm. The flow is assumed to be two-dimensional, incompressible, laminar and steady. Complex flow patterns such as deflection and re-circulation caused by the variation of cross-section area along the stream wise direction have been studied. Also, temperature distribution influenced by these perturbations has been discussed. In particular, the effects of Reynolds number ( 50 ≤ Re ≤ 350 ) , power law index ( 0.5 ≤ n ≤ 2 ) and aspect ratio of channel cavities (A.R=0.25, 0.5) on heat transfer characteristics have been explored for channels of single and double cavity configuration. In all examined cases, varying levels of heat transfer enhancement were observed. The constant wall temperature condition has been applied.

This manuscript presents the effect of Reynolds number (Re) and proximity of the bodies on the hydrodynamics of flow of shear-thinning, Newtonian and shear-thickening fluids over a pair of cylinders kept in side-by-side arrangement. Results obtained from the numerical simulations carried out with a combination of different parameters in the range of 0.2 ≤ power law index (n) ≤ 1.8, 0.1 ≤ Re ≤ 100 and 1.2 ≤ G (gap between the cylinders/diameter) ≤ 4 have been discussed in details. Analysis of the results gives a clear insight into the complex influence of Re on streamline patterns, surface pressure profiles, drag and lift coefficients for various fluids when the gap between two cylinder is changed.

The work presented in this paper is focused on deductive group-theoretic transformations to develop the similarity solution of steady, laminar, incompressible quasi three dimensional boundary layer flow governing power law fluid. The application of one-parameter group reduces the number of independent variables to one and consequently the system of governing, highly non-linear partial differential equations reduces to a self similar, non-linear ordinary differential equation with appropriate auxiliary conditions. The numerical solution for a power law fluid considered for small cross flow is obtained systematically using MSABC in dimensionless form.