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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 investigate numerically the effect of rheology on the leveling of thin fluid films on horizontal solid substrates.

A mathematical model based on the lubrication approximation which defines non-Newtonian rheology using a Power-law model is presented. The rheology is described by two parameters: the consistency factor and the flow behavior index. The resulting highly non-linear coupled set of equations is discretized using Finite-Difference and the resulting algebraic system is solved via an efficient Multigrid algorithm.

Importantly, the non-dimensionalization process leads to a pair of Partial Differential Equations which depends on one parameter only, the flow behavior index. The authors show that the consistency factor only affects the time scale of the leveling process, hence stretching or contracting the time line. Results for the leveling of sinusoidal perturbations of the fluid film highlights important differences between the leveling of shear-thinning and shear-thickening fluids. In a normalized time frame, the onset of leveling occurs earlier for the shear-thinning fluid than for the shear-thickening one. However, the dimensionless leveling rate is higher for the shear-thickening fluid than the shear-thinning one. This results in a “threshold thickness” which delimits two regimes: the shear-thinning fluid levels to a thickness above this threshold faster than the shear-thickening fluid but the opposite is true for a film thickness below this threshold. An important aspect of this study is the verification of the numerical implementation using the Method of Manufactured Solutions (MMS), a first in the context of thin film studies. The paper also highlights differences between the leveling of two-dimensional and three-dimensional thickness perturbations.

The study of the leveling of disturbances at the free surface of a liquid film using a Power-law rheological model does not appear to have been covered in the literature. Also, the paper uses the MMS to test the validity of the implementation. This appears to be the first time it has been used in the context of the lubrication approximation. Finally, unlike most prior studies, the work does away with the planar assumption.

By solving a long-wave evolution model numerically for power-law fluids, the authors aim to investigate the hydrodynamic and thermal characteristics of thermocapillary flow in an evaporating thin liquid film of pseudoplastic fluid.

The flow reversal attributed to the thermocapillary action is manifestly discernible through the streamline plots.

The thermocapillary strength is closely related to the viscosity of the fluid, besides its surface tension. The thermocapillary flow prevails in both Newtonian and pseudoplastic fluids at a large Marangoni number and the thermocapillary effect is more significant in the former. The overestimate in the Newtonian fluid is larger than that in the pseudoplastic fluid, owing to the shear-thinning characteristics of the latter.

This study provides insights into the essential attributes of the underlying flow characteristics in affecting the thermal behavior of thermocapillary convection in an evaporating thin liquid film of the shear-thinning fluids.

This paper aims to summarize the latest developments both in terms of theoretical understanding and experimental techniques related to inkjet fluids. The purpose is to provide practitioners a self-contained review of how the performance of inkjet and inkjet-based three-dimensional (3D) printing is fundamentally influenced by the properties of inkjet fluids.

This paper is written for practitioners who may not be familiar with the underlying physics of inkjet printing. The paper thus begins with a brief review of basic concepts in inkjet fluid characterization and the relevant dimensionless groups. Then, how drop impact and contact angle affect the footprint and resolution of inkjet printing is reviewed, especially onto powder and fabrics that are relevant to 3D printing and flexible electronics applications. A future outlook is given at the end of this review paper.

The jettability of Newtonian fluids is well-studied and has been generalized using a dimensionless Ohnesorge number. However, the inclusion of various functional materials may modify the ink fluid properties, leading to non-Newtonian behavior, such as shear thinning and elasticity. This paper discusses the current understanding of common inkjet fluids, such as particle suspensions, shear-thinning fluids and viscoelastic fluids.

A number of excellent review papers on the applications of inkjet and inkjet-based 3D printing already exist. This paper focuses on highlighting the current scientific understanding and possible future directions.

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 purpose of this article is to analyze the heat and mass transfer with entropy generation during magnetohydrodynamics (MHD) flow of non-Newtonian Sisko nanofluid over a linearly stretching cylinder under the influence of velocity slip, chemical reaction and thermal radiation. The Brownian motion, thermophoresis and activation energy are assimilated in this nanofluid model. Convective boundary conditions on heat and mass transfer are considered. The physical model may have diverse applications in several areas of technology underlying thermohydrodynamics including supercritical fluid extraction, refrigeration, ink-jet printing and so on.

The dimensional governing equations are nondimensionalized by using appropriate similarity variables. The resulting boundary value problem is converted into initial value problem using the method of superposition and numerically computed by employing well-known fourth-order Runge–Kutta–Fehlberg approach along with shooting technique (RKF4SM). The quantitative impacts of emerging physical parameters on the velocity, temperature, concentration, skin friction coefficient, Nusselt number, Sherwood number, entropy generation rate and Bejan number are presented graphically and in tabular form, and the salient features are comprehensively discussed.

From graphical outcomes, it is concluded that the slip parameters greatly influence the flow characteristics. Fluid temperature is elevated with rising radiation parameter and thermal Biot number. Nanoparticle concentration is reported in decreasing form with activation energy parameter. Entropy is found to be an increasing function of magnetic field, Brownian motion and material parameters. The entropy is less generated for shear-thinning fluid compared to shear-thickening as well as Newtonian fluids in the system.

Till now no study has been documented to explore the impact of binary chemical reaction with Arrhenius activation energy on entropy generation in an MHD boundary layer flow of non-Newtonian Sisko nanofluid over a linear stretching cylinder with velocity slip and convective boundary conditions.

Cavitation in piston-ring lubrication is studied as part of the performance of piston-ring assemblies. Cavitation degrades performance in engineering applications and its effect is that it alters the oil film pressure, generated at the converging-diverging wedge of the interface. Studies tried to shed light to the phenomenon of cavitation and compare it with cavities that have been identified in bearings. The paper aims to discuss this issue.

Lubricant formulations were used for parametric study of oil film thickness (OFT) and friction providing the OFT throughout the stroke and LIF for OFT point measurements. Lubricant formulation affects cavitation appearance and behaviour when fully developed.

Cavitation affects the ring load carrying capacity. Different forms of cavitation were identified and their shape and size (length and width) is dictated from reciprocating speed and viscosity of the lubricant. A clear picture is given from both techniques and friction results give quantifiable data in terms of the effect in wear and cavitation, depending on the lubricant properties.

Engine results are limited due to manufacturing difficulties of visualisation windows and oil starvation. Therefore, full stroke length sized windows were not an option and motoring tests were implemented due to materials limitations (adhesive and quartz windows). Lubricant manufacturer has to give data regarding the chemistry of the lubricants.

The contribution of cavitation in piston-ring lubrication OFT, friction measurements and lubricant parameters that try to shed light to the different forms of cavitation. A link between viscosity, cavitation, shear thinning properties, OFT and friction is given.

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.

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.

To achieve material-invariant formulation for heat transfer of Carreau nanofluid, the effect of Cattaneo–Christov heat flux is studied on a natural convective flow of Carreau nanofluid past a vertical plate with the periodic variations of surface temperature and the concentration of species. Buongiorno model is considered for nanofluid transport, which includes the relative slip mechanisms, Brownian motion and thermophoresis.

The governing equations are non-dimensionalized using suitable transformations, further reduced to non-similar form using stream function formulation and solved by local non-similarity method with homotopy analysis method. The numerical computations are validated and verified by comparing with earlier published results and are found to be in good agreement.

The effects of varying the physical parameters such as Prandtl number, Schmidt number, Weissenberg number, thermophoresis parameter, Brownian motion parameter and buoyancy ratio parameter on velocity, temperature and species concentration are discussed and presented through graphs. The results explored that the velocity of shear thinning fluid is raised by increasing the Weissenberg number, while contrary response is seen for the shear thickening fluid. It is also found that heat transfer in Cattaneo–Christov heat conduction model is less than that in Fourier’s heat conduction model. Furthermore, the temperature and thermal boundary layer thickness expand with the increase in thermophoresis and Brownian motion parameter, whereas nanoparticle volume fraction increases with increase in thermophoresis parameter, but reverse trend is observed with increase in Brownian motion parameter.

The present investigation is relatively original as very little research has been reported on Carreau nanofluids under the effect of Cattaneo–Christov heat flux model.