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This study aims at investigating two-dimensional laminar flow of power-law fluids around three unconfined side-by-side cylinders.

The numerical study is performed by solving the governing (continuity and momentum) equations using a finite volume-based code ANSYS Fluent. The numerical results have been presented for different combinations of the governing dimensionless parameters (dimensionless spacing, 1.2 = L = 4; Reynolds number, 0.1 = Re = 100; power-law index, 0.2 = n = 1.8). The dependence of the kinematic and macroscopic characteristics of the flow such as streamline patterns, distribution of the surface pressure coefficient, total drag coefficient with its components (pressure and friction) and total lift coefficient on these dimensionless parameters has been discussed in detail.

It is found that the separation of the flow and the apparition of the wake region accelerate as the dimensionless spacing decreases, the number of the cylinder increases and/or the fluid behavior moves from shear-thinning to Newtonian then to shear-thickening behavior. In addition, the distribution of the pressure coefficient on the surface of the cylinders presents a complex dependence on the fluid behavior index and Reynolds number when the dimensionless spacing between two adjacent cylinders is varied. At low Reynolds numbers, the drag coefficient of shear-thinning fluids is stronger than that of Newtonian fluids; this tendency decreases progressively with increasing of Re until a critical value; beyond the critical Re, the opposite trend is observed. The lift coefficient of the middle cylinder is null, whereas, the exterior cylinders experience opposite lift coefficients, which show a complex dependence on the dimensionless spacing, the Reynolds number and the power-law index.

The flow over bluff bodies is a practical engineering problem. In the literature, it can be seen that the previous studies on non-Newtonian fluids are limited to the flow over one or two cylinders (effect of an odd number of cylinders on each other). Besides that, the available results concerning the flow of Newtonian fluids over three cylinders are limited to the high Reynolds numbers region only. However, this work treats the flow of non-Newtonian power-law fluids past three circular cylinders in side-by-side arrangements under a wide range of Re. The outcome of the present study demonstrates that the augmentation of the geometry complexity to three cylinders (effect of pair surrounding cylinders on the surrounded ones in what concerns Von Karman Street phenomenon) causes a drastic change in the flow patterns and in the macroscopic characteristics. The present results may be used to predict the flow behavior around multiple side-by-side cylinders.

The purpose of this paper is to analyze the mangnetohydrodynamic boundary layer flow of a viscous, incompressible and electrically conducting non-Newtonian nanofluid obeying power-law model over a non-linear stretching sheet under the influence of thermal radiation with heat source/sink.

The transverse magnetic field is applied normal to the sheet. The model used for the nanofluid incorporates the effects of Brownian motion with thermophoresis in the presence of thermal radiation. On this regard, thermophoresis effect on convective heat transfer on nanofluids are investigated simultaneously. The governing partial differential equations are reduced to ordinary differential equations by suitable similarity transformations which are solved numerically by variational finite element method.

The computations carried out for some values of the power-law index, magnetic parameter, radiation parameter, Brownian motion and thermophoresis. The effect of these parameters on the velocity, temperature and nanoparticle volume fraction distribution are presented graphically. The skin friction coefficient, Nusselt number and Sherwood number for various values of the flow parameters of the problem are also presented.

To the best of the authors’ knowledge, no investigations has been reported regarding the study of non-Newtonian nanofluids which obeying power-law model over a nonlinear stretching sheet. The principal aim of this paper is to study the boundary layer MHD flow of a non-Newtonian power-law model over a non-linear stretching sheet on a quotient viscous incompressible electrically conducting with a nanofluid.

Heat transfer characteristics of a non‐Newtonian fluid on a power‐law stretched surface with suction or injection were investigated. Similarity solutions of the laminar boundary layer equations describing heat transfer flow in a quiescent fluid were obtained and solved numerically. Temperature profiles as well as the Nusselt number Nu, were obtained for two thermal boundary conditions; namely, uniform surface temperature (b=0) and cooled surface temperature (b=–1), for different governing parameters such as Prandtl number Pr, injection parameter d and power‐law index n. It was found that decreasing injection parameter d and power‐law index n and increasing Prandtl number Pr enhanced the heat transfer coefficient.

The flow development and heat transfer in a differentially heated cavity containing a non‐Newtonian fluid is studied using CFD techniques. Investigations are made for a fluid obeying a power‐law type behaviour, for a nominal Rayleigh number of 10⁵. Both dilatant and pseudoplastic regimes are considered and the Nusselt number is obtained for a range of power‐law index values. The results, given in a graphical and tabular form, suggest that deviations from Newtonian stress‐strain behaviour can lead to large changes in overall heat transfer. These changes are due to the behaviour of the wall boundary layers. In the dilatant, or shear‐thickening regime, the isothermal wall layers are thick and slow‐moving; as a consequence, buoyancy induced flow affects the whole of the cavity volume. In contrast, the pseudoplastic (or shear‐thinning) regime leads to thin, fast‐moving wall layers whose effect does not propagate to the core of the cavity which remains stagnant. This behaviour, which is directly attributable to the local value of the fluid viscosity, causes the average Nusselt number to decrease with the power‐law index, n. Pseudoplastic fluids are therefore better at conducting heat than Newtonian fluids, and conversely dilatant fluids are worse. The information contained in this paper is of general interest to workers in heat transfer, but is more specifically relevant to researchers in non‐Newtonian fluids. Example applications include biotechnology, where close temperature control of bio‐cultures in enclosed vessels is required, the food processing industry, the metals casting industry and areas where heat transfer in fine suspensions is required.

The thermal-diffusion (Soret) and the diffusion-thermo (Dufour) effects play a crucial role in double diffusive mixed convection in a lid-driven cavity; but they have not been studied properly by researchers. The purpose of this paper is to investigate effects of Soret and Dufour parameters on double diffusive laminar mixed convection of shear-thinning and Newtonian fluids in a two-sided lid-driven cavity.

Finite Difference Lattice Boltzmann method (FDLBM) has been applied to solve the complex problem. This study has been conducted for the certain pertinent parameters of Richardson number (Ri=0.00062-1), power-law index (n=0.2-1), Soret parameter (Sr=−5-5) as Dufour number effects have been investigated from Dr=−5 to 5 at Buoyancy ratio of N=1 and Lewis number of Le=5.

Results indicate that the augmentation of Richardson number causes heat and mass transfer to decrease. The fall of the power-law index declines heat and mass transfer at Ri=0.00062 and 0.01 in various Dufour and Soret parameters. At Ri=1, the heat and mass transfer rise with the increment of power-law index for Dr=0 and Sr=0. The least effect of power-law index on heat and mass transfer among the studied Richardson numbers was observed at Ri=1. The positive Dufour numbers augment the heat transfer gradually as the positive Soret numbers enhance the mass transfer. The Dr=−5 and Sr=−5 provokes the negative average Nusselt and Sherwood numbers, respectively, to be generated. The least magnitude of the average Nusselt and Sherwood numbers were obtained at Dr=−1 and Sr=−1, respectively.

Soret and Dufour effects in double diffusive mixed convection has not been studied in a lid-driven cavity. In addition. this study has been conducted also for shear-thinning fluids.

This paper aims to use a fractional constitutive model with a nonlocal velocity gradient for replacing the nonlinear constitutive model to characterize its complex rheological behavior, where non-linear characteristics exist, for example, the inherent viscous behavior of the crude oil. The feasibility and flexibility of the fractional model are tested via a case study of non-Newtonian fluid. The finite element method is non-Newtonian used to numerically solve both momentum equation and energy equation to describe the fluid flow and convection heat transfer process.

This paper provides a comprehensive theoretical and numerical study of flow and heat transfer of non-Newtonian fluids in a pipe based on the fractional constitutive model. Contrary to fractional order a, the rheological property of non-Newtonian fluid changes from shear-thinning to shear-thickening with the increase of power-law index n, therefore the flow and heat transfer are hindered to some extent.

This paper discusses two dimensionless parameters on flow regime and thermal patterns, including Reynolds number (Re) and Nusselt number (Nu) in evaluating the flow rate and heat transfer rate. Analysis results show that the viscosity of the non-Newtonian fluid decreases with the rheological index (order α) increasing. While large fractional (order α) corresponds to the enhancement of heat transfer capacity.

First, it is observed that the increase of the Re results in an increase of the local Nusselt number (Nul). It means the heat transfer enhancement ratio increases with Re. Meanwhile, the increasement of the Nul indicating the enhancement in the heat transfer coefficient, produces a higher speed flow of crude oil.

This study presents a new numerical investigation on characteristics of steady-state pipe flow and forced convection heat transfer by using a fractional constitutive model. The influences of various non-dimensional characteristic parameters of fluid on the velocity and temperature fields are analyzed in detail.

The present work aims to predict accurately the bearing design data for non‐recessed hybrid journal bearings, considering the effect of non‐Newtonian behavior of lubricant for different symmetric and non‐symmetric bearing geometric configurations.

The simultaneous solution of generalized Reynold's equation governing the laminar flow of incompressible lubricant and the equation of flow of lubricant through the capillary restrictor, considering variable viscosity of lubricant following the “Power law”, has been carried out using FEM. For a given set of bearing geometric, operating parameters and for given external vertical load, the values of various performance characteristics have been obtained for a range of values of power law index, after establishing the journal center equilibrium position, the analysis for which has been elaborately explained.

The results obtained have been presented graphically for various bearing performance characteristics. It has been observed that with decrease in power law index “n”(0<n≤1), the value of h¯_min and load carrying capacity decreases, while bearing flow rate increases for all configuration. The load‐carrying capacity of asymmetric configurations is better and stable over entire range of restrictor design parameter. Bearing configuration with land width ratio = 0.25 and aspect ratio = 1.0, having two rows of holes and six holes in each row, will be better suited for high‐load support, as it has maximum value of minimum fluid film thickness, moderate value of bearing flow and value of attitude angle is almost constant.

The performance characteristics of journal bearing have been presented for a wide range of values of power law index and for different values of restrictor design parameter for capillary restrictor, after establishing the journal center equilibrium position. The comparison of the different symmetric and non‐symmetric journal‐bearing configurations to find the best geometric configuration at different operating conditions, considering the effect of non‐Newtonian behavior of lubricant, represents the originality of the work.

The purpose of this paper is to study the boundary layer flow and heat transfer of a power-law non-Newtonian nanofluid over a non-linearly stretching sheet.

The governing equations describing the problem are transformed into a nonlinear ordinary differential equations by suitable similarity transformations. The resulting equations for this investigation are solved numerically by using the variational finite element method.

It was found that the local Nusselt number increases by increasing the Prandtl number, stretching sheet parameter and decreases by increasing the power-law index, thermophoresis parameter and Lewis number. Increases in the stretching sheet parameter, Prandtl number and thermophoresis parameter decrease the local Sherwood number values. The effects of Brownian motion and Lewis number lead to increases in the local Sherwood number values.

The work is relatively original as very little work has been reported on non-Newtonian nanofluids.

To investigate the forced convection heat transfer to hydrodynamically and thermally fully developed laminar steady flow of power‐law non‐Newtonian fluid in a partially porous square duct.

The modified Brinkmann‐Forchheimer extended Darcy model for power‐law fluids is used in the porous layer. The solutions for the velocity and temperature fields are obtained numerically using the finite volume method. Computations are performed over a range of Darcy number, power‐law indices, porous insert thickness and thermal conductivity ratio.

The average Nusselt number and the Fanning factor, so obtained are found to be in good agreement with the literature. It is highlighted that a heat transfer improvement is obtained when the channel is entirely porous and this enhancement is maximized at low permeability. While depending on the working conditions, heat transfer enhancement can also be obtained by filling partially the duct with the porous insert, even if the conductivity ratio is equal to 1. The results indicate also that the conductivity ratio has a strong impact on the heat transfer enhancement at high permeability, while this impact is significant beyond a critical thickness of the porous layer at low permeability. It is found that both shear‐thinning (n<1) and shear‐thickening (n>1) fluids allow obtaining the highest Nusselt number according to the properties of the porous insert. The presence of the porous insert causes a significant increase in pressure drop. This added pressure drop is found to be more important with shear thickening fluids (n>1).

The results of this paper are valid for square ducts and H1 thermal boundary condition, corresponding to an axially uniform heat flux and peripherally uniform temperature. The inertial effects are neglected in the porous region.

The obtained results can be used in the design of heat exchangers and in the cooling of electronic equipments.

This work investigates some interesting ways to enhance heat transfer in three‐dimensional square ducts by using porous substrates and non‐Newtonian fluids. It is believed that the case studied in this paper has not previously been investigated.

The aim of this work is to study numerically and analytically flow and heat transfer characteristics and multiplicity of steady states for natural convection in a horizontal rectangular cavity, filled with non‐Newtonian power‐law fluids and heated from all sides.

The governing equations are discretised by using the well known second‐order central finite difference method and integrated by combining the ADI and PSOR techniques. The analytical approach is based on the parallel flow assumption.

Natural and anti‐natural flows existence is proved when the Rayleigh number exceeds a critical value and the side lateral heating intensity values is chosen inside a specific range. The analytical results are found to agree well with those obtained numerically. The fluid flow and the heat transfer are found to be rather sensitive to the non‐Newtonian power‐law behaviour.

The obtained results are limited to non‐Newtonian power‐law fluids and cannot be extended to fluids having other behaviours.

The problem is implied in some industrial thermal processes.

Existence of multiple steady state‐solutions in the range of the side lateral heating intensity values ensuring, that is reduced by the shear‐thickening behaviour and extended by the shear‐thinning one for a given value of Rayleigh number.