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This paper aims to assess the effectiveness of Hall currents and power-law slip condition on the hydromagnetic convective flow of an electrically conducting power-law fluid over an exponentially stretching sheet under the effect of a strong variable magnetic field and thermal radiation. Flow formation is developed using the rheological expression of a power-law fluid.

The nonlinear partial differential equations describing the flow are transformed into the nonlinear ordinary differential equations by employing the local similarity transformations and then solved numerically by an effective numerical approach, namely, fourth-order Runge–Kutta integration scheme, along with the shooting iteration technique. The numerical solution is computed for different parameters by using the computational software MATLAB bvp4c. The bvp4c function uses the finite difference code as the default. This method is a fourth-order collocation method. The impacts of thermophysical parameters on velocity and temperature distributions, skin friction coefficients and Nusselt number in the boundary layer regime are exhibited through graphs and tables and deliberated with proper physical justification.

Our investigation conveys that Hall current has an enhancing behavior on velocity profiles and reduces skin friction coefficients. An increase in the power-law index is observed to deplete velocity and temperature evolution. The temperature for the pseudo-plastic (shear-thinning) fluid is relatively higher than the corresponding temperature of the dilatant (shear-thickening) fluid. The streamlines are more distorted and have low intensity near the surface of the sheet for the dilatant fluid than the pseudo-plastic fluid.

The study is pertinent to the expulsion of polymer sheet and photographic films, hydrometallurgical industry, electrically conducting polymer dynamics, magnetic material processing, solutions and melts of polymer processing, purification of molten metals from nonmetallic. The results obtained in this work can be relevant in fluid mechanics and heat transfer applications.

The present problem has, to the authors' knowledge, not communicated thus far in the scientific literature. A comparative study with the published works is conducted to verify the accuracy of the present study. The results obtained in this analysis are significant in providing the standards for validating the accuracies of some numerical or empirical methods.

The paper focuses on the solution of a numerical model to explore the sliding and non‐Newtonian fluid behaviour in soft elastohydrodynamic nip contacts. The solution required the coupling of the fluid and elastomer regimes, with the non‐Newtonian fluid properties being described using a power law relationship. The analysis showed that the fluid characteristics as defined by the power law relationship led to large differences in the film thickness and flow rate with a movement of the peak pressure within the nip contact. The viscosity coefficient, power law index and sliding ratio were shown to affect the nip performance in a non‐linear manner in terms of flow rate and film thickness. This was found to be controlled principally by the level of viscosity defined by the power law equation. The use of a speed differential to control nip pumping capacity was also explored and this was found to be most sensitive at lower entrainment speeds.

This paper aims to investigate the effect of plugging of holes on the static performance characteristics of a constant flow valve compensated hole‐entry hybrid journal bearing system operating with Newtonian and non‐Newtonian lubricants. The analysis considers the generalized Reynolds equation governing the flow of lubricant having variable viscosity in the clearance space and equation of flow of lubricant through constant flow valve restrictor. The non‐Newtonian lubricant is assumed to follow the power law. The performance characteristics are computed for the two values of power law index (n=1.0 and 0.566). The computed results indicate that the blockage of holes during operation will not be the likely causes for the imminent failure of a well‐designed non‐recessed hole‐entry hybrid journal bearing.

Finite element method has been used to solve generalized Reynolds equation governing the flow of lubricant having variable viscosity in the clearance space and equation of flow of lubricant through constant flow valve restrictor.

The computed results indicate that the blockage of holes during operation will not be the likely causes for the imminent failure of a well‐designed non‐recessed hole‐entry hybrid journal bearing. The bearing configuration with plugged holes provides sufficient fluid film thickness and low power requirement as less lubricant is required to be pumped in the bearing.

To the best of the author's knowledge, no study which considers the influence of plugging of holes on the static performance characteristics of a constant flow valve compensated hole‐entry hybrid journal bearing system operating with Newtonian and non‐Newtonian lubricant is yet available in the literature.

Analytical and numerical studies are conducted for two‐dimensional steady‐state Marangoni convection of a non‐Newtonian power law fluid confined in a rectangular horizontal shallow cavity subjected to a horizontal temperature gradient between the two short vertical rigid sides, while the upper free surface and the lower rigid one are insulated. The effect of the non‐Newtonian behavior on the hydrodynamic stability, the fluid flow, the temperature field, and the heat transfer is studied. The parallel flow is obtained in some particular situations for which a good agreement is observed between the analytical results based on the parallel flow assumption and those corresponding to the numerical simulations.

The entropy and thermal behavior analyses of non-Newtonian nanofluid double-diffusive natural convection inside complex domains may captivate a bunch of scholars’ attention because of the potential utilizations that they possess in modern industries, for example, heat exchangers, solar energy collectors and cooling of electronic apparatuses. This study aims to investigate the second law and thermal behavior of non-Newtonian double-diffusive natural convection (DDNC) of Al₂O₃-H₂O nanofluid within a C-shaped cavity emplacing two hot baffles and impacted by a magnetic field.

For the governing equations of the complicated and practical system with all considered parameters to be solved via a formidable numerical approach, the finite element method acts as an approach to achieving the desired solution. This method allows us to gain a detailed solution to the studied geometry.

This investigation has been executed for the considered parameters of range, such as power-law index, baffle length, Lewis number, buoyancy ratio, Hartmann number and Rayleigh number. The main results reveal that isothermal and concentration lines are significantly more distorted, indicating intensified concentration and temperature distributions because of the growth of baffle length (L). Nu_ave decreases by 8.4% and 0.8% while it enhances by 49.86% and 33.87%, respectively, because of growth in the L from 0.1 to 0.2 and 0.2 to 0.3.

Such a comprehensive study on the second law and thermal behavior of DDNC of Al₂O₃-H₂O nanofluid within a C-shaped cavity emplacing two hot baffles and impacted by magnetic field has not yet been carried out.

The screw extruder is applied in cement-three-dimensional (3D) printing. The cement paste flow in 3D printing is the typical Herschel–Bulkley fluid. To understand the flow in the channel, the improved lattice Boltzmann method (LBM) is proposed.

For Herschel–Bulkley flow, an improved LBM is presented to avoid the poor stability and accuracy. The non-Newtonian effect is regard as a special forcing term. The Poiseuille flow is taken to discuss the detailed process of the method. With the method, the analytical solution and numerical solution are obtained and compared. Then, the effect of the initial yield stress on the numerical solution is both explored by the shear-thickening fluid and the shear-thinning fluid. Moreover, the variations of the relative errors under different lattice nodes and different power-law indexes are analyzed. Finally, the method is applied into the simulation of the flow in the extruder of cement-3D printing.

The results show that the improved method is effective for Herschel–Bulkley fluids, which can simulate the flow in the extruder stably and accurately.

The simulation can contribute to understand the cement paste flow in the screw extruder, which helps to optimize the structure of the extruder in the following periods.

The improve method provide a new way to analyze the flow in the extruder of cement-3D printing. Also, in the past research, LBM for Herschel–Bulkley fluid is ignored, whereas the study can provide the reference for the numerical simulation.

The purpose of this paper is to study two-dimensional nonlinear radiative-convective, steady-state boundary layer flow of non-Newtonian power-law nanofluids along a flat vertical plate in a saturated porous medium taking into account thermal and mass convective boundary conditions numerically.

The governing equations are reduced to a set of coupled nonlinear ordinary differential equations with relevant boundary conditions. The transformed equations are then solved using the Runge-Kutta-Fehlberg fourth-fifth order numerical method with Maple 17 and Adomian decomposition method (ADM) in Mathematica.

The transformed equations are controlled by the parameter: power-law exponent, n; temperature ratio, Tr; Rosseland radiation-conduction, R; conduction-convection, Nc; and diffusion-convection, Nd. Temperature and nanoparticle concentration is enhanced with convection-diffusion parameter as are temperatures. Velocities are depressed with greater power-law rheological index whereas temperatures are elevated. Increasing thermal radiation flux accelerate the flow but to strongly heat the boundary layer. Very good correlation of the Maple solutions with previous stationary free stream and ADM solutions for a moving free stream, are obtained.

The study is relevant to high temperature nano-polymer manufacturing systems.

Lie symmetry group is used for the first time to transform the governing equations into a set of coupled nonlinear ordinary differential equations with relevant boundary conditions. The study is relevant to high temperature nano-polymer manufacturing systems.

The paper's aim is to investigate the natural convection flow of an Ostwald‐de Waele type power law non‐Newtonian fluid past an isothermal vertical slotted surface.

The Keller‐Box method is used to solve the governing boundary layer equations for the natural convection flow of an Ostwald‐de Waele type power law non‐Newtonian fluid past an isothermal vertical slotted surface.

As the slip parameter increases, the friction factor increases whereas the heat transfer rate decreases. Owing to increase in the value of the Prandtl number, Pr, there is decrease in the value of the skin‐friction coefficient, and augmentation of heat transfer rate. As the viscosity index n increases, both the friction factor and the heat transfer rate increase.

The analysis is valid for steady, two‐dimensional laminar flow of an Ostwald‐de Waele type power law non‐Newtonian fluid past an isothermal vertical slotted surface. An extension to three‐dimensional flow case is left for future work.

The method is useful to analyze perforated plates and wire netting such as perforated wings in order to reduce the drag by suction of the boundary layer, filtration or air‐conditioning.

The results of this study may be of interest to engineers interested in heat transfer augmentation and drag reduction in heat exchangers.

The present analysis investigates the non‐Darcy mixed convection of a non‐Newtonian fluid from a vertical isothermal plate embedded in a homogeneous porous medium, in the presence of surface injection or suction. After a suitable coordinate transformation to reduce the complexity of the governing boundary‐layer equations, the resulting nonlinear, coupled differential equations were solved with an implicit finite difference scheme. The value of mixed convection parameter χ lies between 0 and 1. In addition, the power‐law model is used for non‐Newtonian fluids with exponent n<1 for pseudoplastic fluids; n=1 for Newtonian fluids; and n>1 for dilatant fluids. The effects of the mixed‐convection parameter χ, the power‐law viscosity index n, the suction/injection parameter ξ, and the non‐Darcy parameter Re* on the velocity and temperature profiles, and the local Nusselt number are discussed.

Although many studies have been conducted on the nanofluid flow in microtubes, this paper, for the first time, aims to investigate the effects of nanoparticle diameter and concentration on the velocity and temperature fields of turbulent non-Newtonian Carboxymethylcellulose (CMC)/copper oxide (CuO) nanofluid in a three-dimensional microtube. Modeling has been done using low- and high-Reynolds turbulent models. CMC/CuO was modeled using power law non-Newtonian model. The authors obtained interesting results, which can be helpful for engineers and researchers that work on cooling of electronic devices such as LED, VLSI circuits and MEMS, as well as similar devices.

Present numerical simulation was performed with finite volume method. For obtaining higher accuracy in the numerical solving procedure, second-order upwind discretization and SIMPLEC algorithm were used. For all Reynolds numbers and volume fractions, a maximum residual of 10⁻⁶ is considered for saving computer memory usage and the time for the numerical solving procedure.

In constant Reynolds number and by decreasing the diameter of nanoparticles, the convection heat transfer coefficient increases. In Reynolds numbers of 2,500, 4,500 and 6,000, using nanoparticles with the diameter of 25 nm compared with 50 nm causes 0.34 per cent enhancement of convection heat transfer coefficient and Nusselt number. Also, in Reynolds number of 2,500, by increasing the concentration of nanoparticles with the diameter of 25 nm from 0.5 to 1 per cent, the average Nusselt number increases by almost 0.1 per cent. Similarly, In Reynolds numbers of 4,500 and 6,000, the average Nusselt number increases by 1.8 per cent.

The numerical simulation was carried out for three nanoparticle diameters of 25, 50 and 100 nm with three Reynolds numbers of 2,500, 4,500 and 6,000. Constant heat flux is on the channel, and the inlet fluid becomes heated and exists from it.

The authors obtained interesting results, which can be helpful for engineers and researchers that work on cooling of electronic devices such as LED, VLSI circuits and MEMS, as well as similar devices.

This manuscript is an original work, has not been published and is not under consideration for publication elsewhere. About the competing interests, the authors declare that they have no competing interests.