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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.

Most studies of power‐law fluids are carried out using stress‐based system of Navier‐Stokes equations; and least‐squares finite element models for vorticity‐based equations of power‐law fluids have not been explored yet. Also, there has been no study of the weak‐form Galerkin formulation using the reduced integration penalty method (RIP) for power‐law fluids. Based on these observations, the purpose of this paper is to fulfill the two‐fold objective of formulating the least‐squares finite element model for power‐law fluids, and the weak‐form RIP Galerkin model of power‐law fluids, and compare it with the least‐squares finite element model.

For least‐squares finite element model, the original governing partial differential equations are transformed into an equivalent first‐order system by introducing additional independent variables, and then formulating the least‐squares model based on the lower‐order system. For RIP Galerkin model, the penalty function method is used to reformulate the original problem as a variational problem subjected to a constraint that is satisfied in a least‐squares (i.e. approximate) sense. The advantage of the constrained problem is that the pressure variable does not appear in the formulation.

The non‐Newtonian fluids require higher‐order polynomial approximation functions and higher‐order Gaussian quadrature compared to Newtonian fluids. There is some tangible effect of linearization before and after minimization on the accuracy of the solution, which is more pronounced for lower power‐law indices compared to higher power‐law indices. The case of linearization before minimization converges at a faster rate compared to the case of linearization after minimization. There is slight locking that causes the matrices to be ill‐conditioned especially for lower values of power‐law indices. Also, the results obtained with RIP penalty model are equally good at higher values of penalty parameters.

Vorticity‐based least‐squares finite element models are developed for power‐law fluids and effects of linearizations are explored. Also, the weak‐form RIP Galerkin model is developed.

Several power law relations are found to occur in bibliographic studies of scientific journals, articles, and citations. These can be interpreted in a self‐consistent manner in terms of growth parameters of articles, journals, and citations. Similar models have been proposed earlier in physical, biological, and behavioural sciences.

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.

This paper aims to discuss the stagnation-point flow and heat transfer for power-law fluid pass through a stretching surface with heat generation effect. Unlike the previous considerations about the research on stagnation-point flow, the process of heat transfer and the convective heat transfer boundary condition use the modified Fourier’s law in which the heat flux is power-law-dependent on velocity gradient.

The similarly transformation is used to convert the governing partial differential equations into a series of ordinary differential equations which are solved analytically by using the differential transform method and the base function method.

The variations of the velocity and temperature fields for different specific related parameters are graphically discussed and analyzed. There is a special phenomenon that all the velocity profiles converge from the initial value of velocity to stagnation parameter values. And the larger power-law index enhancesthe momentum diffusion. A significant phenomenon can be observed that the larger power-law index causes a decline in the heat flux. This influence indicates that the higher viscosity restricts the heat transfer. Furthermore, both velocity gradient and temperature gradient play an indispensable role in the processes of heat transfer.

This paper researches the process of heat transfer of stagnation-point flow ofpower-law magneto-hydro-dynamical fluid over a stretching surface with modified convective heat transfer boundary condition.

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 purpose of this paper is to investigate the flow and heat transfer of power-law fluids over a non-linearly stretching sheet with non-Newtonian power-law stretching features.

The governing non-linear partial differential equations are reduced to a series of ordinary differential equations by suitable similarity transformations and the numerical solutions are obtained by the shooting method.

As the temperature power-law index or the power-law number of the fluids increases, the dimensionless stream function, dimensionless velocity and dimensionless temperature decrease, while the velocity boundary layer and temperature boundary layer become thinner for other fixed physical parameters. The thermal diffusivity varying as a function of the temperature gradient can be used to present the characteristics of flow and heat transfer of non-Newtonian power-law fluids.

Unlike classical works, the effect of power-law viscosity on the temperature field is considered by assuming that the temperature field is similar to the velocity field with modified Fourier’s law heat conduction for power-law fluid media.

The purpose of this paper is to investigate the steady flow of a non‐Newtonian power‐law type fluid over a permeable stretching surface. The surface is stretched with a prescribed skin velocity following a power‐law variation along its length.

Using appropriate similarity variables and boundary layer approximations, the continuity and momentum equations are reduced to an ordinary differential equation subject to appropriate transformed boundary conditions, with three dimensionless parameters: the power‐law index of the non‐Newtonian fluid, suction/injection parameter and the power law index of the skin velocity. These equations are solved numerically by using the fourth‐order Runge‐Kutta integration algorithm coupled with a conventional shooting procedure. Comparisons with closed form analytical solutions obtained for the case of Newtonian fluid by previous authors are also performed.

It was found that the dimensionless entrainment velocity decreases with the power exponent m, of the prescribed skin velocity, irrespective of the non‐Newtonian fluid nature, for both impermeable and permeable surfaces. Large rates of injection lead to very large values of the skin friction, the effect being more intense for small values of the dimensionless flow index n. At the same rate of the injection/suction, the skin friction S is increased when the surface is stretched linearly than uniformly.

This type of problem has potential to serve as a prototype for many manufacturing processes such as rolling sheet drawn from a die, cooling and/or drying of paper and textile, manufacturing of polymeric sheets, sheet glass and crystalline materials, etc.

A thorough analysis of the hydrodynamics of a stretching surface is performed in the present paper, by combining analytical and numerical means. The topics covered here (Ostwald‐de Waele power‐law fluid + prescribed skin velocity + permeability of the stretching surface) seem to be not reported till now in the literature.

The purpose of this paper is to analyze two-dimensional steady-state Rayleigh–Bénard convection within rectangular enclosures in different aspect ratios filled with yield stress fluids obeying the Herschel–Bulkley model.

In this study, a numerical method based on the finite element has been developed for analyzing two-dimensional natural convection of a Herschel–Bulkley fluid. The effects of Bingham number Bn and power law index n on heat and momentum transport have been investigated for a nominal Rayleigh number range (5 × 10³ < Ra < 10⁵), three different aspect ratios (ratio of enclosure length:height AR = 1, 2, 3) and a single representative value of nominal Prandtl number (Pr = 10).

Results show that the mean Nusselt number Nu¯ increases with increasing Rayleigh number due to strengthening of convective transport. However, with the same nominal value of Ra, the values of Nu¯ for shear thinning fluids n < 1 are greater than shear thickening fluids n > 1. The values of Nu¯ decrease with Bingham number and for large values of Bn, Nu¯ rapidly approaches unity, which indicates that heat transfer takes place principally by thermal conduction. The effects of aspect ratios have also been investigated and results show that Nu¯ increases with increasing AR due to stronger convection effects.

This paper presents a numerical study of Rayleigh–Bérnard flows involving Herschel–Bulkley fluids for a wide range of Rayleigh numbers, Bingham numbers and power law index based on finite element method. The effects of aspect ratio on flow and heat transfer of Herschel–Bulkley fluids are also studied.

The purpose of this paper is to numerically investigate two dimensional steady state convective heat transfer in a differentially heated square cavity with constant temperatures and an inner rotating cylinder. The gap between the cylinder and the enclosure walls is filled with power law non-Newtonian fluid.

Finite volume-based CFD software, Fluent (Ansys 15.0) is used to solve the governing equations. Attribution of the various flow parameters of fluid flow and heat transfer are investigated including Rayleigh number, Prandtl number, power law index, the cylinder radius and the angular rotational speed.

Outcomes are reported in terms of isotherms, streamlines and average Nusselt number (Nu) of the heated wall for various considered here.

A detailed investigates is needed in the context of 3D flow. This will be a part of the future work.

The effect of a rotating cylinder on heat transfer and fluid flow in a differentially heated rectangular enclosure filled with power law non-Newtonian fluid has practical importance in the process industry.

The results of this study may be of some interest to the researchers of the field of chemical or process engineers.