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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.

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.

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 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.

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.

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.

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.

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.

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 purpose of this paper is to study the mixing performance of the electrokinetically-driven power-law fluids in a zigzag microchannel.

The Poisson-Boltzmann equation, the Laplace equation, the modified Cauchy momentum equation, and the convection-diffusion equation are solved to describe the flow characteristics and mixing performance of power-law fluids in the zigzag microchannel. A body-fitted grid system and a generalized coordinate transformation method are used to model the grid system and transform the governing equations, respectively. The transformed governing equations are solved numerically using the finite-volume method.

The mixing efficiency of dilatant fluids is higher than that of pseudoplastic fluids. In addition, the mixing efficiency can be improved by increasing the width of the zigzag blocks or extending the total length of the zigzag block region.

The results presented in this study provide a useful insight into potential strategies for enhancing the mixing performance of the power-law fluids in a zigzag microchannel. The results of this study also provide a useful source of reference for the development of efficient and accurate microfluidic systems.