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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 present numerical investigation examines the magnetohydrodynamic (MHD) double diffusion natural convection of power-law non-Newtonian nano-encapsulated phase change materials (NEPCMs) in a trapezoidal cavity.

The governing Navier-Stokes, energy and concentration equations based on the Cartesian curvilinear coordinates are solved using the collocated grid arrangement’s finite volume method. The in-house FORTRAN code is validated with the different benchmark problems. The NEPCM nanoparticles consist of a core-shell structure with Phase Change Material (PCM) at the core. The enclosure, shaped as a trapezoidal hollow, features a warmed (T_h) left wall and a cold (T_c) right wall. Various parameters are considered, including the power law index (0.6 ≤ n ≤ 1.4), Hartmann number (0 ≤ Ha ≤ 30), Rayleigh number (10⁴ ≤ Ra ≤ 10⁵) and fixed variables such as buoyancy ratio (Br = 0.8), Prandtl number (Pr = 6.2), Lewis number (Le = 5), fusion temperature (Θ_f = 0.5) and volume fraction (ϕ = 0.04).

The findings indicate a decrease in local Nusselt (Nu) and Sherwood (Sh) numbers with increasing Hartmann numbers (Ha). Additionally, for a shear-thinning fluid (n = 0.6) results in the maximum local Nu and Sh values. As the Rayleigh number (Ra) increases from 10⁴ to 10⁵, the structured vortex in the streamline pattern is disturbed. Furthermore, for different Ra values, an increase in n from 0.6 to 1.4 leads to a 67.43% to 76.88% decrease in average Nu and a 70% to 77% decrease in average Sh.

This research is for two-dimensioal laminar flow only.

PCMs represent a class of practical substances that behave as a function of temperature and have the innate ability to absorb, release and store heated energy in the form of hidden fusion enthalpy, or heat. They are valuable in these systems as they can store significant energy at a relatively constant temperature through their latent heat phase change.

As per the literature review and the authors’ understanding, an examination has never been conducted on MHD double diffusion natural convection of power-law non-Newtonian NEPCMs within a trapezoidal enclosure. The current work is innovative since it combines NEPCMs with the effect of magnetic field Double diffusion Natural Convection of power-law non-Newtonian NEPCMs in a Trapezoidal enclosure. This outcome can be used to improve thermal management in energy storage systems, increasing safety and effectiveness.

This paper aims to theoritically investigate the free convection flow and heat transfer of a non-Newtonian fluid with pseudoplastic behavior in a cylindrical vertical cavity partially filled with a layer of a porous medium.

The non-Newtonian behavior of the pseudoplastic liquid is described by using a power-law non-Newtonian model. There is a temperature difference between the internal and external cylinders. The porous layer is attached to the internal cylinder and has a thickness of D. Upper and lower walls of the cavity are well insulated. The governing equations are transformed into a non-dimensional form to generalize the solution. The finite element method is used to solve the governing equations numerically. The results are compared with the literature results in several cases and found in good agreement.

The influence of the thickness of the porous layer, Rayleigh number and non-Newtonian index on the heat transfer behavior of a non-Newtonian pseudoplastic fluid is addressed. The increase of pseudoplastic behavior and increase of the thickness of the porous layer enhances the heat transfer. By increase of the porous layer from 0.6 to 0.8, the average Nusselt number increased from 0.15 to 0.25. The increase of non-Newtonian effects (decrease of the non-Newtonian power-law index) enhances the heat transfer rate.

The free convection behavior of a pseudoplastic-non-Newtonian fluid in a cylindrical enclosure partially filled by a layer of a porous medium is addressed for the first time.

This paper aims to investigate melting heat transfer of a non-Newtonian phase change material (PCM) in a cylindrical enclosure-space between two tubes using a deformed mesh method.

Metal foam porous layers support the inner and outer walls of the enclosure. The porous layers and clear space of the enclosure are filled with PCM. The natural convection effects during the phase change are taken into account, and the governing equations for the molten region and solid region of the enclosure are introduced. The governing equations are transformed into non-dimensional form and then solved using finite element method. The results are compared with the literary works and found in good agreement. The non-Newtonian effects on the phase change heat transfer and melting front are studied.

The results show that the increase of non-Newtonian effects (the decrease of the power-law index) enhances the heat melting process in the cavity at the moderate times of phase change heat transfer. The temperature gradients in porous metal foam over the hot wall are small, and hence, the porous layer notably increases the melting rate. When the melting front reaches the cold porous layer, strong non-linear behaviors of the melting front can be observed.

The phase change heat transfer of non-Newtonian fluid in a cylindrical enclosure partially filled with metal foams is addressed for the first time.

In this article we report on progress in the development of software tools for fluid flow prediction in the polymer processing industry. This involves state‐of‐the‐art numerical techniques and the study of a number of non‐trivial model flow problems, in an effort to investigate realistic transient problems relevant to industrial processes. Here we study particularly the effects of variations in non‐Newtonian and heat transfer properties of the flowing materials in the flows, both throughout the transient development period and at steady‐state.

The purpose of this paper is to focus on MHD unsteady flow of Carreau fluid over a variable thickness melting surface in the presence of chemical reaction and non-uniform heat sink/source.

The flow governing partial differential equations are transformed into ordinary ones with the help of similarity transformations. The set of ODEs are solved by a shooting technique together with the R.K.–Fehlberg method. Further, the graphs are depicted to scrutinize the velocity, concentration and temperature fields of the Carreau fluid flow. The numerical values of friction factor, heat and mass transfer rates are tabulated.

The results are presented for both Newtonian and non-Newtonian fluid flow cases. The authors conclude that the nature of three typical fields and the physical quantities are alike in both cases. An increase in melting parameter slows down the velocity field and enhances the temperature and concentration fields. But an opposite outcome is noticed with thermal relaxation parameter. Also the elevating values of thermal relaxation parameter/ wall thickness parameter/Prandtl number inflate the mass and heat transfer rates.

This is a new research article in the field of heat and mass transfer in fluid flows. Cattaneo–Christov heat flux model is used. The surface of the flow is assumed to be melting.

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.

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 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.

On the basis of the power‐law fluid model, the rheological effects of an isothermal incompressible non‐Newtonian laminar lubricating film on the steady and dynamic characteristics of finite slider bearings are presented in the absence of fluid inertia and cavitation.

To account for the motion that the pad undergoes prescribed small‐amplitude oscillations in a direction perpendicular to itself, the non‐Newtonian dynamic Reynolds equation including the squeezing‐action effect is obtained. Both the steady pressure and the perturbed pressure are numerically solved and used to evaluate the steady‐state performance and dynamic characteristics.

According to the results, higher steady load‐carrying capacity, dynamic stiffness and damping coefficients are predicted for the finite bearing with small wedge parameter and high viscosity‐shear rate index. In addition, the effects of non‐Newtonian power‐law lubricants on the bearing characteristics are more pronounced when the bearing width becomes large.

The paper provides useful information on the dynamic characteristics of finite bearings lubricated by a non‐Newtonian power‐law fluid.