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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 use a fractional constitutive model with a nonlocal velocity gradient for replacing the nonlinear constitutive model to characterize its complex rheological behavior, where non-linear characteristics exist, for example, the inherent viscous behavior of the crude oil. The feasibility and flexibility of the fractional model are tested via a case study of non-Newtonian fluid. The finite element method is non-Newtonian used to numerically solve both momentum equation and energy equation to describe the fluid flow and convection heat transfer process.

This paper provides a comprehensive theoretical and numerical study of flow and heat transfer of non-Newtonian fluids in a pipe based on the fractional constitutive model. Contrary to fractional order a, the rheological property of non-Newtonian fluid changes from shear-thinning to shear-thickening with the increase of power-law index n, therefore the flow and heat transfer are hindered to some extent.

This paper discusses two dimensionless parameters on flow regime and thermal patterns, including Reynolds number (Re) and Nusselt number (Nu) in evaluating the flow rate and heat transfer rate. Analysis results show that the viscosity of the non-Newtonian fluid decreases with the rheological index (order α) increasing. While large fractional (order α) corresponds to the enhancement of heat transfer capacity.

First, it is observed that the increase of the Re results in an increase of the local Nusselt number (Nul). It means the heat transfer enhancement ratio increases with Re. Meanwhile, the increasement of the Nul indicating the enhancement in the heat transfer coefficient, produces a higher speed flow of crude oil.

This study presents a new numerical investigation on characteristics of steady-state pipe flow and forced convection heat transfer by using a fractional constitutive model. The influences of various non-dimensional characteristic parameters of fluid on the velocity and temperature fields are analyzed in detail.

The purpose of this paper is to present a theoretical study of non-Newtonian effects in conical squeeze-film plates that is based on the Rabinowitsch fluid model.

A non-linear, modified Reynolds equation accounting for the non-Newtonian properties following the cubic stress law equation is derived. Through a small perturbation method, first-order closed-form solutions are obtained.

It is found that the non-Newtonian properties of dilatant fluids increase the load capacity and lengthen the response time as compared to the case using a Newtonian lubricant; however, the non-Newtonian behaviors of pseudoplastic lubricants result in reverse influences.

Numerical tables for squeeze-film loads of conical plates are also provided for engineering applications.

This study aims to evaluate the melting process of the phase-change RT-35 material in a shell and tube heat exchanger saturated with a porous medium. Titanium porous media with isotropic and inhomogeneous structures are studied. The considered tubes in the shell and tube exchanger are made of copper with specific thicknesses. The phase-change material has a non-Newtonian behavior and follows the endorsed Carreau–Yasuda Model.

The enthalpy–porosity method is used for modeling of the melting process. The governing equations were transferred to their dimensionless forms. Finally, the equations are solved by applying the Galerkin finite element method.

The findings for different values of the relative permeability (K*) and permeability deviation angle (λ) are represented in the forms of charts, streamlines and constant temperature contours. The considerable effects of the relative permeability (K*) and deviation angle (λ) on the flow line patterns of the melting phase-change material are some of the significant achievements of this works.

This study was conducted using data from relevant research articles provided by reputable academic sources. The data included in this manuscript have not been published previously and are not under consideration by any other journal.

The purpose of this paper is to discuss a combined similarity-numerical approach that is used to study the unsteady two-dimensional flow of a non-Newtonian nanofluid over a contracting cylinder using Buongiorno’s model and the Casson fluid model that is used to characterize the non-Newtonian fluid behavior.

Similarity transformations are employed to transform the unsteady Navier-Stokes partial differential equations into a system of ordinary differential equations. The transformed equations are then solved numerically by means of the very robust symbolic computer algebra software MATLAB employing the routine bvpc45.

The effect of increasing values of the Casson parameter is to suppress the velocity field (in absolute sense), the temperature and concentration decrease as Casson parameter increase. The heat and mass transfer rates decrease with the increase of unsteadiness parameters and Brownian motion parameter. In addition, they increase as the Casson parameter and the thermophoresis parameter increase.

The problem is relatively original and represents a very important contribution to the field of non-Newtonian nanofluids.

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.

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 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.

The modified Reynolds equation for non-Newtonian lubricant is derived using the viscous adsorption theory for thin-film elastohydrodynamic lubrication (TFEHL) of circular contacts. The proposed model can reasonably calculate the phenomenon in the thin-film lubrication (TFL) unexplained by the conventional EHL model. The differences between classical EHL and TFEHL with the non-Newtonian lubricants are discussed.

The power-law lubricating film between the elastic surfaces is modeled in the form of three layers: two adsorption layers on each surface and one middle layer. The modified Reynolds equation with power-law fluid is derived for TFEHL of circular contacts using the viscous adsorption theory. The finite difference method and the Gauss–Seidel iteration method are used to solve the modified Reynolds equation, elasticity deformation, lubricant rheology equations and load balance equations simultaneously.

The simulation results reveal that the present model can reasonably calculate the pressure distribution, the film thickness, the velocity distribution and the average viscosity in TFL with non-Newtonian lubricants. The thickness and viscosity of the adsorption layer and the flow index significantly influence the lubrication characteristics of the contact conjunction.

The present model can reasonably predict the average viscosity, the turning point and the derivation (log film thickness vs log speed) phenomena in the TFEHL under constant load conditions.

The purpose of this paper is to investigate the effect of different viscosity models (Cross and Al-Ma’aiteh) and different printing speeds on the numerical results (e.g. pressure over stencil) of a numerical model regarding stencil printing.

A finite volume model was established for describing the printing process. Two types of viscosity models for non-Newtonian fluid properties were compared. The Cross model was fitted to the measurement results in the initial state of a lead-free solder paste, and the parameters of a Al-Ma’aiteh material model were fitted in the stabilised state of the same paste. Four different printing speeds were also investigated from 20 to 200 mm/s.

Noteworthy differences were found in the pressure between utilising the Cross model and the Al-Ma’aiteh viscosity model. The difference in pressure reached 33-34% for both printing speeds of 20 and 70 mm/s and reached 31% and 27% for the printing speed of 120 and 200 mm/s. The variation in the difference was explained by the increase in the rates of shear by increasing printing speeds.

Parameters of viscosity model should be determined for the stabilised state of the solder paste. Neglecting the thixotropic paste nature in the modelling of printing can cause a calculation error of even approximately 30%. By using the Al-Ma’aiteh viscosity model over the stabilised state of solder pastes can provide more accurate results in the modelling of printing, which is necessary for the effective optimisation of this process, and for eliminating soldering failures in highly integrated electronic devices.