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Performance features of a thermoelectric system mounted in a chaotic channel with non-Newtonian power law fluid are numerically explored with finite element method. The analysis is performed for different values of Re number of the hot and cold fluid streams ( 250 ⩽ Re ⩽ 1000 ), power law indices ( 0.75 ⩽ n ⩽ 1.25 ) and solid volume fraction of alumina ( 0 ⩽ ϕ ⩽ 4 % ) in water. It is observed that the fluid type with different power law indices significantly affected the electric potential variations and power generation of the thermoelectric system. Impacts of Re number on the power generation enhancement amount depends upon the power law index. The power rises by about 123.78 % , 94.13 % and 52.30 % at the highest Re for different power law index combinations of (0.75,0.75), (0.75,12.5) and (1.25,1.25), respectively. Thermoelectric power reduces by about 39.71 % for shear thinning fluids in both channels while it rises by about 43.48 % for shear thickening fluids in chaotic channels. The potential of using nanofluids is more when both channels contain shear thinning fluids. Nanofluids rise the power of thermoelectric system by about 31 % , 29 % and 28 % for the case when the hot side fluid is shear thinning, Newtonian and shear thickening fluid types while the cold side chaotic channel is shear thinning. When constant and varying interface temperature configurations are compared, there is at most 3 % variations in the generated power while the trends in the curves for varying parameters are similar. The computational cost of constant interface temperature and computations only in the thermoelectric domains are much cheaper as compared to high fidelity coupled computational fluid dynamics simulations. The temperature field in the whole computational domain is approximated by using POD based approach with nine modes. A polynomial type regression model is used for POD-modal coefficients while fast and accurate results for interface temperatures are obtained.

A stabilized form of finite element formulation known as the Galerkin least-squares (GLS) method is implemented here for solving the two-dimensional incompressible non-Newtonian fluid model of blood flow in a diseased artery. The modelling for this type of flow is based on the conservation of mass and momentum equations, coupled with the generalised Newtonian liquid (GNL) constitutive equation characterized by the generalised power law (GPL) model. The flow of blood in this present study are assumed as steady, laminar and fully developed. The finite element algorithms considered herein are first solved for the Newtonian fluid in a straight artery with a bell shaped stenosis for validation purposes. As the efficiency and validity of the proposed algorithms are obtained through comparison with the findings from existing literature and COMSOL Multiphysics 5.2 software. Then, the algorithms are being implemented to the generalised power law fluid model of blood flow in a bifurcated artery with overlapping stenosis located at the parent's arterial lumen. The numerical results illustrate the arising of distinct sizes of vortex shedding downstream of the stenotic region for each generalised power law index.

In the present work, a numerical analysis of non-Newtonian impinging jets on a flat plate subjected to a constant heat flux is carried out under turbulent flow conditions. By employing the power-law constitutive model to describe the jet’s non-Newtonian behavior, simulations have been performed for two (2D) and three-dimensional (3D) jet flow conditions. For turbulence simulation, SST- $$k\omega$$ turbulence model has been used coupled with continuity and energy equations. Dimensional results have been obtained by varying the inflow conditions 0.5–1.4 m/s and at a constant heat flux of 5000 W/m2. To instill the influences of shear thinning, Newtonian, and shear-thickening fluids, the range of power-law indices (n) is varied from 0.6 to 1.6. The results of the simulations infer that the pseudoplastics fluids are more efficient than Newtonian and dilatant fluids. Increasing power law shows efficacy of the fluids to cool the surface decreases as is observed by the average values of the Nusselt number on the target. It is found that there is a small difference in the final average temperature of the plate after cooling with different fluids, but that owes it to the small heat flux used in the present analysis. It is observed that the higher the velocity of the jet, the better is the cooling. Finally, the energy-saving capabilities of the jets are characterized by altering the rheological characteristics of the jets.

The flow of a non-Newtonian, power-law fluid, directed normally to a rotating sphere is considered in the present paper. The problem is investigated by means of a three-dimensional numerical simulation with the SIMPLE algorithm. The investigation covers the power-law index from 0.2 up to 2, rotation rate from 0.1 up to 3 and Reynolds number from 0.1 up to 100. The following general rules are valid. The lift coefficient increases with increasing the rotation rate. At high Re numbers the drag coefficient increases with the power-law index. At high Re numbers the torque coefficient increases with the power-law index and with the rotation rate, whereas the torque coefficient reduces as the Reynolds number increases. In addition, there are some special cases which are analyzed in the text.

This work is about studying the natural convection of two-dimensional steady state non-Newtonian power law fluid numerically. The inner cylinder was put eccentrically into the outer one. The cylinders are held at constant temperatures with the inner one heated isothermally at temperature Th and the outer one cooled isothermally at temperature Tc (Th>Tc). The simulations have been taken for the parameters 103?Ra?105, 10?Pr?103, 0.6?n?1.4, 0???0.9 and an inclination angle ? from 0? up to 90?. The average Nusselt numbers for the previous parameters are obtained and discussed numerically. The results revealed that the average Nusselt number has the highest values when n=0.6, Ra=105 at ?=0 which is a signal for the large transfer herein and has the lowest values for n=1.4, Ra=103 at ?=90? which is a signal that the transfer is by conduction more than convection. Furthermore, the increasing of eccentricity causes an increase in the Nusselt number for all the cases. Finally, the best case where we can get the best heat transfer is at ? = 0, ?=0.9 among them all. The results have compared with some precedent works and showed good agreement.

Two phase flow of drilling fluids and cuttings in The eccentric annulus between The drill hole and drill pipe is studied. The effect of drilling fluids rheological parameters upon flow structure using The power law rheological model is investigated. axial velocity distribution of both drilling fluids and cutting are examined in The presence of drill pipe rotation. cuttings volume fraction distributions as well as flow contours are considered. numerical simulation of The two phase turbulent flow is carried out using The realizable k-e model using The computational fluid dynamics software fluent 6.3.26. The eccentric annulus has inner and outer diameters of 5 cm and 10 cm and 50% eccentricity. The results show That The velocity distributions of both drilling fluids and cuttings, as well as, drilled cuttings volumetric fraction distribution are strongly affected by The rheology of The drilling fluid. It has been verified that power law fluid consistency Kp and flow index (n) are significant parameters in determining The local flow structure in The different regions of The annulus. increasing fluids viscosity reduces The difference between The velocity distributions of drilling fluid and that of cuttings. The effect is more pronounced for The flow with large size cuttings.

In this article, the flow of non-Newtonian fluid (which is represented by the power-law model) in two-dimensional (2D) driven enclosures is studied. The enclosure consists of regular, rectangular shaped undulations on the bottom wall. Multiple-Relaxation time (MRT) collision model for the lattice Boltzmann equation method (LBM) is employed. First, numerical validation is performed by comparing the MRT-LBM results of power-law fluid flow inside the wall-driven square enclosure (no undulation) and flow inside diagonally flipped L-shaped enclosure with the literature. The strain rate profiles for square enclosure without undulations are compared using various equations available for strain rate calculation in the LBM literature. Further, the effect of different values of the non-hydrodynamic relaxation parameters on the flow is examined. Then, for the undulated enclosures, flow features and eddy dynamics are analyzed and discussed for the variations in the power-law index, n , to represent shear-thinning and shear thickening fluids. The effects of various parameters such as Reynolds numbers, wall undulation heights and wavelength of undulations on the power-law fluid flow are analyzed. Also, the variation of viscosity with spatial location for steady-state flow and total kinetic energy within the computational domain are presented for various values of power-law index.

The MHD free convection flow of non-Newtonian power-law fluids over a horizontal plate subjected to a constant heat flux is studied. The results are presented for various values of the three influential parameters, i. e. the generalized Hart?mann number, the generalized Prandtl number, and the non-Newtonian power-law viscosity index. Increasing the Hartmann number increases the thermal boundary-layer thickness and the surface temperature and consequently decreases the wall skin friction and Nusselt number. A lower generalized Prandtl number results in a larger skin friction coefficient and higher wall temperature as well as thicker thermal boundary-layer. The viscosity index is predicted to influence the flow conditions depending on the value of generalized Hartmann number. At high generalized Prandtl number numbers, by decreasing non-Newtonian power-law index, the wall skin friction, temperature scale, and thermal boundary-layer thickness are increased and the Nusselt number is decreased, while the opposite trend is observed for low generalized Prandtl number. A general correlation for the Nusselt number is derived using the numerical results

In this paper, we study the stationary incompressible power law fluid flow in a thin porous medium. The media under consideration is a bounded perforated 3D domain confined between two parallel plates, where the distance between the plates is very small. The perforation consists in an array solid cylinders, which connect the plates in perpendicular direction, distributed periodically with diameters of small size compared to the period. For a specific choice of the thickness of the domain, we found that the homogenization of the power law Stokes system results a lower-dimensional nonlinear Brinkman type law.

In this study, a numerical investigation on mixed convection inside a trapezoidal cavity with a pair of rotating cylinders has been conducted. Three different power-law fluid indexes (n = 1.4, 1.0, and 0.6) have been considered to model different sets of non-Newtonian fluids. Four separate cases are considered based on the rotational orientation of the cylinders within the cavity. In the first two cases, the cylinders rotate in the same direction, i.e., both counterclockwise (CCW), and both clockwise (CW), whereas, in the other two cases, cylinders rotate in opposite directions (CW–CCW and CCW–CW). Simulations have been carried out over a broad range of Reynolds number (from 0.5 to 500) and angular speeds (a dimensionless value from 0 to 10). The average Nusselt number values at the isothermal hot inclined cavity surface are determined to evaluate heat transfer performance in various circumstances. Streamlines and isotherm contours are also plotted for a better understanding of the effects of different cases for various parameters on thermal and fluid flow fields. It is found that the Nusselt number varies nonlinearly with different angular speeds of the cylinders. The combined effect of the mixing induced by cylinder rotation and viscosity characteristics of the fluid dictates the heat transfer in the system. Predictions from the numerical investigation provide insights into the sets of key parametric configurations that have a dominant influence on the thermal performance of the lid-driven cavity with double rotating cylinders.

The onset of convection in a porous layer saturated by a power-law fluid is here investigated. The walls are considered to be isothermal, isobaric and permeable in such a way that a vertical throughflow is described. The threshold for a buoyancy-driven cellular flow is investigated by means of a linear stability analysis. This study consists in introducing disturbances with small amplitude. The disturbances are plane waves, i.e. a normal modes stability analysis of the basic stationary solution is performed. The resulting problem is an ordinary differential equation eigenvalue problem which is solved numerically by coupling the Runge–Kutta method with the shooting method. Results are presented in the form of marginal stability curves and their critical points representing the values of the control parameters such that the growth rate of the disturbances is zero. It is found that, among roll disturbances, the most unstable modes are stationary and uniform with infinite wavelength. For this reason, an asymptotic analysis for vanishing wave numbers is carried out. The results of this asymptotic analysis are obtained analytically displaying a very good agreement with the numerical solution. It is found that vertical throughflow plays a destabilising role for pseudoplastic fluids and a stabilising role for dilatant fluids.

GPTMS ((3-Glycidoxypropyl) trimethoxysilane)-SiO2 nanofluids have the ability to alter the wettability of a rock surface and high colloidal stability, therefore, they can be used as injection fluids to enhance oil recovery in high-salinity and high-temperature reservoirs. The purpose of this study is to prepare GPTMS-SiO2 nanofluids that are stable under extreme reservoir conditions and investigate their rheological characteristics. Nanofluids with nanoparticle concentrations of 0.1 to 3 wt% were prepared and dispersed in 10 wt% API (American Petroleum Institute) brine, which served as the base fluid. The apparent viscosity of the base fluid and GPTMS-SiO2 nanofluids was measured in the shear rate range 3.7 to 93.1 s−1 between the temperatures of 5 and 85 °C. It was observed to be a function of temperature, but remained constant with the increase in shear rate. On the other hand, the nanofluids exhibited pseudoplastic behavior (shear thinning). The apparent viscosity of the nanofluids tended to increase with decreasing temperature and increasing particle concentration. The consistency index and power law index of the power law fluid model are used for the analysis of the flow behavior of the nanofluids. The consistency indices of GPTMS-SiO2 nanofluids were observed to be well matched with the exponential function, and the power law indices showed high correlations with the specific particle concentration and temperature conditions. The results revealed that the rheological characteristics of GPTMS-SiO2 nanofluids are functions of particle concentration and temperature at specific conditions.

The steady laminar flow of an incompressible power-law fluid in a plane T-shaped channel is studied at given pressure differences between the inflow and outflow sections. A non-Newtonian fluid, whose rheological behavior is governed by the Ostwald—de Waele law is called the power-law fluid. The mathematical formulation of the problem includes the equations of motion and continuity. The no-slip condition is imposed on solid walls. The problem solution is obtained using a finite-difference method invoking the SIMPLE procedure. A parametric investigation of the kinematic and dynamic flow parameters is carried out for different values of the relevant parameters of the problem. The flow regime map is constructed for different pressure differences between the inflow and outflow boundaries and different nonlinearity exponents of the rheological model.

In this paper, the two-dimensional forced convection heat transfer of non-Newtonian power-law fluid flow between two parallel plates filled with partially porous media is studied numerically using the thermal lattice Boltzmann method (TLBM). Shear-thinning (n=0.8), Newtonian (n=1.0), and shear-thickening (n=1.2) fluid are used to investigate the non-Newtonian behavior of power-law fluids. The porous media is prepared by the arrangement of circular obstacles. The effect of Reynolds numbers between 100

This paper emphasizes the radiative heat transfer of non-Newtonian fluid on free convection around a slender paraboloid in a non-Darcy porous medium. The Ostwald-de Waele power-law representation is employed to express the non-Newto?nian behavior of fluid. Similarity analysis is applied to transform the set of non-dimensional PDE into set of ODE and then the resulting system of equations are solved by 4th order Runge-Kutta scheme with Shooting technique. The control of pertinent parameters on velocity, temperature and non-dimensional heat transfer rates are analyzed through graphical representation and explored in detail. It is evident that as the radius of the slender body increases the heat transfer coefficient decreases but the role of radiation on heat transfer rate getting reduced for all feasible values of the power-law index parameter.

This paper investigates the electroosmotic micromixing of non-Newtonian fluid in a microchannel with wall-mounted obstacles and surface potential heterogeneity on the obstacle surface. In the numerical simulation, the full model consisting of the Navier–Stokes equations and the Poisson–Nernst–Plank equations are solved for the electroosmotic fluid field, ion transport, and electric field, and the power law model is used to characterize the rheological behavior of the aqueous solution. The mixing performance is investigated under different parameters, such as electric double layer thickness, flow behavior index, obstacle surface zeta potential, obstacle dimension. Due to the zeta potential heterogeneity at the obstacle surface, vortical flow is formed near the obstacle surface, which can significantly improve the mixing efficiency. The results show that, the mixing efficiency can be improved by increasing the obstacle surface zeta potential, the flow behavior index, the obstacle height, the EDL thickness.

Piezoelectric three-dimensional inkjet printing has been used to manufacture heterogeneous objects due to its high level of flexibility. The materials used are non-Newtonian inks with complex rheological properties, and their behavior in the context of inkjet printing has not been fully understood: for example, the fact that the shear-thinning viscosity affects the droplet generation. Therefore, a control strategy coping with shear-thinning behaviors is needed to ensure printing consistency. In this paper, a novel model-based approach is presented to describe the shear-thinning ink dynamics inside the piezoelectric inkjet printhead, which provides the basis to design the excitation parameters in a systematic way. The dynamic equation is simplified into a quasi-one-dimensional equation through the combination of the boundary layer theory and the constitutive equation of the power-law fluid, of which the viscosity is shear-thinning. Based on this, a nonlinear time-varying equivalent circuit model is presented to simulate the power-law fluid flow rate inside the tube. The feasibility and effectiveness of this model can be evaluated by comparing the results of computational fluid dynamics and the experimental results.

This paper reports an analytical and numerical study of double-diffusive mixed convection in a non-Newtonian power-law fluid contained in a double lid driven horizontal rectangular enclosure submitted to uniform heat and mass fluxes along its short vertical sides, while the horizontal ones are insulated and impermeable. The first part from this study is devoted to the numerical solution of the governing equations, and the effect of the governing parameters, namely, flow behavior index for a power law fluid at the reference temperature and Lewis numbers, is examined. In the second part, an analytical solution, based on the parallel flow approximation in the case of a shallow cavity A ≫ 1, is proposed and a good agreement is found between the two types of solutions.

The effect of non-Newtonian biomagnetic power-law fluid in a channel undergoing external localised magnetic fields is investigated. The governing equations are derived by considering both effects of Ferrohydrodynamics (FHD) and Magnetohydrodynamics (MHD). These governing equations are difficult to solve due to the inclusion of source term from magnetic equation and the nonlinearity of the power-law model. Numerical scheme of Constrained Interpolation Profile (CIP) is developed to solve the governing equations numerically. Extensive results carried out show that this method is efficient on studying the biomagnetic and non-Newtonian power-law flow. New results show that the inclusion of power-law model affects the vortex formation, skin friction and heat transfer parameter significantly. Regardless of the power-law index, the vortex formation length increases when Magnetic number increases. The effect of this vortex however decreases with the inclusion of power-law where in the shear thinning case, the arising vortex is more pronounced than in the shear thickening case. Furthermore, increasing of power-law index from shear thinning to shear thickening, decreases the wall shear stress and heat transfer parameters. However for high Magnetic number, the wall shear stress and heat transfer parameters increase especially near the location of the magnetic source. The results can be used as a guide on assessing the potential effects of radiofrequency fields (RF) from electromagnetic fields (EMF) exposure on blood vessel.

To help in the efficient design of fluid flow in electroosmotic pumps, electroosmotic flow of non-Newtonian fluid through porous polymer membrane at high zeta potentials is studied by mainly evaluating the total flow rate at different physical parameters. Non-Newtonian fluid is represented by the power-law model and the porous polymer membrane is considered as arrays of straight cylindrical pores. The electroosmotic flow of non-Newtonian fluid through a single pore is studied by solving the complete Poisson&ndash, Boltzmann equation and the modified Cauchy momentum equation. Then assuming the pore size distribution on porous polymer membrane obeys Gaussian distribution, the performance of electroosmotic pump operating non-Newtonian fluid is evaluated by computing the total flow rate of electroosmotic flow through porous polymer membrane as a function of flow behavior index, geometric parameters of porous membrane, electrolyte concentration, applied voltage, and zeta potential. It is found that enhancing zeta potential and bulk concentration rather than the applied voltage can also significantly improve the total flow rate in porous polymer membrane, especially in the case of shear thinning fluid.

This paper demonstrates a numerical study of heat transfer in a square porous cavity filled with non-Newtonian power-law fluid. A Graphics Processing Unit (GPU) has been used to accelerate the numerical simulation, which uses the Multiple-Relaxation-Time (MRT) Lattice Boltzmann Method. A modified power-law model has been employed to characterize the flow of non-Newtonian fluids. The simulations have been conducted for the power-law index $n$ ranging from $(0.6 \leq n \leq 1.0)$, the Darcy number $Da$ ranging from $(10^{-3} \leq Da \leq 10^{-1})$ and the Rayleigh number $Ra$ ranging from $(10^3 \leq Ra \leq 10^5)$. Results show that the average Nusselt number ($\overline{Nu}$) decreases with an increase in the value of $n$ while $\overline{Nu}$ increases with an increase in the value of $Da$. Moreover, an increment in the value of $Ra$ leads to an increase in the average Nusselt number., Comment: Accepted Version, International Conference on Mechanical Engineering 2019 (ICME2019) 18-20 December, Dhaka, Bangladesh

The rheological characteristics of the oil film on the rod-seal interface in the sealing zone have a major influence on the behavior of reciprocating seals. Because of the addition of polymers, the viscosity and temperature properties of hydraulic oil have improved and the fluid presents non-Newtonian characteristics. To investigate the influence of these characteristics on seal behavior, a soft elastohydrodynamic lubrication (EHL) numerical model is introduced to simulate a step seal under a mixed lubrication condition. A modified Reynolds equation is derived for calculating the fluid film pressure distribution more accurately. The equation is based on the power law fluid model and Jakobsson-Floberg-Olsson (JFO) cavitation theory. Results are presented to gain insight into the effect of non-Newtonian fluid characteristics on seal behavior, and the simulated results are compared to those of a Newtonian fluid to reveal the seal mechanism. The influence of operating parameters and the seal surface root mean square (RMS) roughness on sealing performance under different power law indexes is also investigated and discussed.

A mathematical model is proposed to study the influence of elasticity on the peristaltic flow of a generalized Newtonian fluid in a tube. A power-law model is considered in the present study to understand the effect of elasticity on the peristaltic flow of blood through arteries. Application of blood flow through arteries is studied by expressing a relationship between pressure gradient and volume flow rate in an elastic tube. The results show the significant effect of elasticity on flow quantities. It is observed that the flux increases as the fluid behaviour index increases and that the flux is more for a Newtonian fluid when compared to non-Newtonian cases. The trapping phenomenon is presented graphically for various physical parameters. The results obtained in the present study are compared with an earlier investigation of Vajravelu et al. (Peristaltic transport of a Herschel–Bulkley fluid in an elastic tube. Heat Transf-Asian Res. 2014;44:585–598).

The present research performed a numerical simulation of laminar forced convection nanofluid-based non-Newtonian flow in a channel connecting a tank with heating regions. To achieve a rapid diffusion of heat, a cylindrical agitator is inserted into the tank. Power-law modelling is employed to describe the effect of non-Newtonian behaviour. The velocity and temperature fields and heat transfer coefficient ratio are studied systematically, taking into account the impact of various parameters, such as the generalised Reynolds number Re, generalised Prandtl number Pr, angular velocity of a cylinder ω, nanoparticle volume fraction ϕ, mixer size and location. Our research reveals that, to improve the heat transfer in practice, several applicable strategies are available, including the addition of more nanoparticles into the base fluid, which proved to be the most efficient method to enhance the heat transfer of a nanofluid.