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The hydrodynamic development of non‐Newtonian fluid flow in the entrance region of a duct with porous walls is examined numerically by solving the modified Navier‐Stokes equations. Cases involving blowing, suction, and no mass transfer through the walls are considered. Velocity distributions, pressure drops, and skin friction coefficients are presents for each case. A definite concavity is found in the velocity profile near the duct entrance for all cases. Results for Newtonian fluids are compared with previous studies in which boundary‐layer theory was used. In the region away from the entrance it is found that the present results are in good agreement with previous works. In the region close to the entrance, or in the case of suction, boundary‐layer theory is shown to be inappropriate.

The article aims to provide an accurate and efficient numerical algorithm for viscous flows in power-law fluids under various thermal boundary and partial slip conditions.

We are conducting a numerical investigation using the Taylor–Galerkin/pressure correction finite element method, which builds upon the work of previous researchers. Here, attention is therefore given to the interplay of various thermal boundary and stick-slip conditions and their impact on non-isothermal inelastic fluid.

The results demonstrate the influence of the Prandtl, Brinkman and Reynolds numbers on the flow’s thermal and hydrodynamic behavior, concentrating on the impact of slip at the wall. Furthermore, we have presented the effects of these dimensionless parameters on the detailed local and average Nusselt numbers, illustrated the high accuracy we obtained for numerical convergence, and compared our results with those of previous papers, observing excellent agreement.

We have successfully tested the code under the presented industrial conditions. Future research directions on this topic aim for efficient and robust solvers for non-Newtonian thermal rheological models; this algorithm can be used for that purpose.

This algorithm has never been used for numerical analysis of such a problem previously.

The peristaltic motion for Carreau fluid by means of an infinite train of sinusoidal waves traveling along the walls of a circular cylindrical flexible tube is investigated. The fluid is subjected to a constant transverse magnetic field. A perturbation solution is obtained for the case in which Weissenberg number is small. The effects of Hartmann number, Weissenberg number, power‐law index and amplitude ratio on the pressure rise and the friction force are discussed. The trapping limit and the trapping occurrence region at the centerline decrease by increasing Hartmann number but they are independent approximately of Weissenberg number and power‐law index.

In the present computational study, the heat transfer and two-dimensional natural convection flow of non-Newtonian power-law fluid in a tilted rectangular enclosure is examined. The left wall of enclosure is subjected to spatially varying sinusoidal temperature distribution and right wall is cooled isothermally while the upper and lower walls are retained to be adiabatic. The flow is considered to be laminar, steady and incompressible under the influence of magnetic field. The governing mass, momentum and energy equations are transformed into dimensionless form in terms of stream function, vorticity and temperature.

Then resulted highly non-linear partial differential equations are solved computationally using Galerkin finite element method.

The exhaustive flow pattern and temperature fields are displayed through streamlines and isotherm contours for various parameters, namely, Prandtl number, Rayleigh number, Hartmann number by considering different power-law index and inclination angle. The effect of inclination angle on average Nusselt number is also shown graphically. This problem observes the potential vortex flow with elliptical core. The results show that the circular strength of the vortex formed reduces as the magnetic field strength grows. As the inclination angle increases the intensity of flow field decreases while the value of average Nusselt number increases.

This study has important applications in thermal management such as cooling techniques used in buildings, nuclear reactors, heat exchangers and power generators.

This study examines fluid flow within a rectangular porous medium bounded by walls capable of expansion or contraction. It focuses on a non-Newtonian fluid with Casson characteristics, incompressibility, and electrical conductivity, demonstrating temperature-dependent impacts on viscosity.

The flow is two-dimensional, unsteady, and laminar, influenced by a small electromagnetic force and electrical conductivity. The Hybrid Analytical and Numerical Method (HAN method) resolves the constitutive differential equations.

The fluid’s velocity is influenced by the Casson parameter, viscosity variation parameter, and resistive force, while the fluid’s temperature is affected by the radiation parameter, Prandtl number, and power-law index. Increasing the Casson parameter from 0.1 to 50 results in a 4.699% increase in maximum fluid velocity and a 0.123% increase in average velocity. Viscosity variation from 0 to 15 decreases average velocity by 1.42%. Wall expansion (a from −4 to 4) increases maximum velocity by 19.07% and average velocity by 1.09%. The average fluid temperature increases by 100.92% with wall expansion and decreases by 51.47% with a Prandtl number change from 0 to 7.

Understanding fluid dynamics in various environments is crucial for engineering and natural systems. This research emphasizes the critical role of wall movements in fluid dynamics and offers valuable insights for designing systems requiring fluid flow and heat transfer. The study presents new findings on heat transfer and fluid flow in a rectangular channel with two parallel, porous walls capable of expansion and contraction, which have not been previously reported.

The purpose of this paper is to investigate the effect of uniform lateral mass flux on non-Darcy natural convection of non-Newtonian fluid along a vertical cone embedded in a porous medium filled with a nanofluid.

The resulting governing equations are non-dimensionalized and transformed into a non-similar form and then solved numerically by Keller box finite-difference method.

A comparison with previously published works is performed and excellent agreement is obtained.

The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. It is assumed that the cone surface is preamble for possible nanofluid wall suction/injection, under the condition of uniform heat and nanoparticles volume fraction fluxes.

The effects of nanofluid parameters, Ergun number, surface mass flux and viscosity index are investigated on the velocity, temperature, and volume fraction profiles as well as the local Nusselt and Sherwood numbers.

The purpose of this paper is to deal with the qualitative analysis of hydrodynamic lubrication of asymmetric rollers with non-Newtonian incompressible power law lubricants including Newtonian.

The fluid flow governing equations such as equation of motion along with continuity and thermal equations are solved first analytically and investigated numerically by the Runge-Kutta Fehlberg method.

As a result of this work, it is found that there is a significant change in temperature, pressure, load and traction with Newtonian and non-Newtonian fluids.

The authors considered incompressible hydrodynamic lubrication of two rigid asymmetric rollers, one of them is assumed to be adiabatic. The convection term of the heat flow equation is taken in its average form.

It is a theoretical problem of two heavily loaded rigid cylindrical rollers with cavitations, where the consistency of the power law lubricant is assumed to vary with pressure and the mean film temperature. It has not appeared 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.

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power‐law type non‐Newtonian fluids along a vertical wedge with variable wall temperature distribution. The mixed convection regime is divided into two regions, namely, the forced convection dominated regime and the free convection dominated regime. The two solutions are matched. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.

The purpose of this paper is to analyze and discuss the coupled effects of surface roughness and flow rheology for a homogeneous mixture of Newtonian base oil and power law fluids on the performance of elastohydrodynamic lubrication (EHL) circular contact problems.

The average flow model is adapted for the interaction of the flow rheology of lubricant and surface roughness. The average Reynolds type equation (ARTE) and the related flow factors (which describes the coupled effects of surface roughness and flow rheology of a mixture), the viscosity‐pressure and density‐pressure relations equations, the elastic deformation equation, and the force balance equation are then solved simultaneously. The multilevel multi‐integration algorithm and Gauss‐Seidel iteration method are utilized to calculate the film thickness and pressure distributions of the EHL circular contact problems effectively.

The effects of volume fraction, flow index of power law fluid, and surface roughness parameters (Peklenik number, standard deviation of composite surface roughness) on the film thickness and pressure distributions are discussed. The results show that the effects of surface roughness should be considered especially in EHL contact problems.

The EHL of circular contacts lubricating with mixture of two lubricants is first analyzed. The coupling effects of surface roughness and flow rheology of mixture (a Newtonian fluid and a power‐law fluid) on the EHL performance are first discussed in this paper.