Effect of bubble morphology and behavior on power consumption in non-Newtonian fluids’aeration process

Due to a prolonged operation time and low mass transfer efficiency, the primary challenge in the aeration process of non-Newtonian fluids is the high energy consumption, which is closely related to the form and rate of impeller, ventilation, rheological properties and bubble morphology in the reactor. In this perspective, through optimal computational fluid dynamics models and experiments, the relationship between power consumption, volumetric mass transfer rate(kLa) and initial bubble size(d0) was constructed to establish an efficient operation mode for the aeration process of non-Newtonian fluids. It was found that reducing the d0could significantly increase the oxygen mass transfer rate, resulting in an obvious decrease in the ventilation volume and impeller speed. When d0was regulated within 2-5 mm,an optimal kLa could be achieved, and 21% of power consumption could be saved, compared to the case of bubbles with a diameter of 10 mm.

Influence of Anisotropic Permeability and Soret Effect on the Convective Heat and Mass Transfer through a Porous Cavity Saturated by a Non-Newtonian Fluid

In this work, an analytical study is carried out on double-diffusive natural convection through a horizontal anisotropic porous layer saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq approximations. The horizontal walls of the system are subject to vertical uniform fluxes of heat and mass, whereas the vertical walls are assumed to be adiabatic and impermeable. The Soret effect is taken into consideration. Based on parallel flow approximation theory, the problem is solved in the limit of a thin layer and documented the effects of the physical parameters describing this investigation.

Numerical Analysis of the Mixed Flow of a Non-Newtonian Fluid over a Stretching Sheet with Thermal Radiation

A mathematical model is elaborated for the laminar flow of an Eyring-Powell fluid over a stretching sheet.The considered non-Newtonian fluid has Prandtl number larger than one.The effects of variable fluid properties and heat generation/absorption are also discussed.The balance equations for fluid flow are reduced to a set of ordinary differential equations through a similarity transformation and solved numerically using a Chebyshev spectral scheme.The effect of various parameters on the rate of heat transfer in the thermal boundary regime is investigated,i.e.,thermal conductivity,the heat generation/absorption ratio and the mixed convection parameter.Good agreement appears to exist between theoretical predictions and the existing published results.

UNIFORM ATTRACTOR FOR NONAUTONOMOUS INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH A NEW CLASS OF EXTERNAL FORCES

This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces.

RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH MULTIPLICATIVE NOISE

This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.

ON THE EXISTENCE OF LOCAL CLASSICAL SOLUTION FOR A CLASS OF ONE-DIMENSIONAL COMPRESSIBLE NON-NEWTONIAN FLUIDS

In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero.

Influence of chemical reaction on heat and mass transfer of non-Newtonian fluid with yield stress by free convection from vertical surface in porous medium considering Soret effect

The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of the yield stress and the Soret effect. The governing boundary layer equations and boundary conditions are cast into a dimen- sionless form by similarity transformations, and the resulting system of equations is solved by a finite difference method. The results are preSented and discussed for concentration profiles, as well as the Nusselt number and the Sherwood number for various values of the parameters, which govern the problem. The results obtained show that the flow field is influenced appreciably by the presence of the chemical reaction parameter γ the order of.the chemical reaction parameter m, the Soret number St, the buoyancy ratio N, the Lewis number Le, and the dimensionless rheological parameter Ω.

EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW

This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.

Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction

A Jeffery-Hamel （J-H） flow model of the non-Newtonian fluid type inside a convergent wedge （inclined walls） with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary conditions based on similarity relationships. Unlike the usual power law model, this paper develops nonlinear viscosity based only on a tangential coordinate function due to the radial geometry shape. Two kinds of solutions are developed, i.e., analytical and semi-analytical （numerical） solutions with suitable assumptions. As a result of the parametric examination, it has been found that the Newtonian normalized velocity gradually decreases with the tangential direction progress. Also, an increase in the friction coefficient leads to a decrease in the normalized Newtonian velocity profile values. However, an increase in the Reynolds number causes an increase in the normalized velocity function values. Additionally, for the small values of wedge semi-angle, the present solutions are in good agreement with the previous results in the literature.

Analytical solutions to the Navier-Stokes equations for non-Newtonian fluid

The pressureless Navier-Stokes equations for non-Newtonian fluid are studied. The analytical solutions with arbitrary time blowup, in radial symmetry, are constructed in this paper. With the previous results for the analytical blowup solutions of the N-dimensional （N ≥ 2） Navier-Stokes equations, we extend the similar structure to construct an analytical family of solutions for the pressureless Navier-Stokes equations with a normal viscosity term （μ（ρ）｜ u｜^α u）.

Hydrothermal analysis of non-Newtonian fluid flow(blood)through the circular tube under prescrib e d non-uniform wall heat flux

The present article aims to investigate the Graetz-Nusselt problem for blood as a non-Newtonian fluid obeying the power-law constitutive equation and flowing inside the axisymmetric tube subjected to nonuniform surface heat flux.After the flow field is determined by solving the continuity and the momentum equations,the energy equation is handled by employing the separation of variables method.The resulting Eigen functions and Eigen values are numerically calculated using MATLAB built-in solver BVP4C.The analysis is first conducted for the situation of constant heat flux and subsequently generalized to apply to the case of sinusoidal variation of wall heat flux along the tube length,using Duhamel’s Theorem.Furthermore,an approximate analytic solution is determined,employing an integral approach to solve the boundary layer equations.With respect to the comparison,the results of approximate solution display acceptable congruence with those of exact solution with an average error of 7.4%.Interestingly,with decreasing the power-law index,the discrepancy between the two presented methods significantly reduces.Eventually,the influences of the controlling parameters such as surface heat flux and power-law index on the non-Newtonian fluid flow’s thermal characteristics and structure are elaborately discussed.It is found that switching from constant wall heat flux to non-uniform wall heat flux that sinusoidally varies along the tube length significantly improves the simulation’s accuracy due to the better characterization of the heat transport phenomenon in non-Newtonian fluid flow through the tube.In the presence of sinusoidally varying wall heat flux with an amplitude of 200 W/m 2 and when the power-law index is 0.25,the maximum arterial wall temperature is found to be about 311.56 K.

H^2-regularity random attractors of stochastic non-Newtonian fluids with multiplicative noise

In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.

Effect of thermal conductivity on heat transfer for a power-law non-Newtonian fluid over a continuous stretched surface with various injection parameters

The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governing equations in the present study are solved numerically using the Runge-Kutta method. Through a comparison, results for a special case of the problem show excellent agreement with those in a previous work. Two cases are considered, one corresponding to a cooled surface temperature and the other to a uniform surface temperature. Numerical results show that the thermal conductivity variation parameter, the injection parameter, and the power-law index have significant influences on the temperature profiles and the Nusselt number.

THE NUMERICAL SIMULATION OF TURBULENT FLOWS OF NEWTONIAN AND A SORT OF NON-NEWTONIAN FLUID IN 180-DEGREE SQUARE SECTIONED BEND

Using k- model of turbulence and measured wall functions, turbulent flows of Newtonian (pure water) andasort of non-Newtonian fluid (dilute, drag-reduction solution of polymer) in a 180-degree curved bend were simulated numerically. The calculated results agreed well with the measured velocity profiles. On the basis of calculation and measurement, appropriateness of turbulence model to complicated flow in which the large-scale vortex exists was analyzed and discussed.

The size-dependent elastohydrodynamic lubrication contact of a coated half-plane with non-Newtonian fluid

Based on the couple-stress theory,the elastohydrodynamic lubrication(EHL)contact is analyzed with a consideration of the size effect.The lubricant between the contact surface of a homogeneous coated half-plane and a rigid punch is supposed to be the non-Newtonian fluid.The density and viscosity of the lubricant are dependent on fluid pressure.Distributions of film thickness,in-plane stress,and fluid pressure are calculated by solving the nonlinear fluid-solid coupled equations with an iterative method.The effects of the punch radius,size parameter,coating thickness,slide/roll ratio,entraining velocity,resultant normal load,and stiffness ratio on lubricant film thickness,in-plane stress,and fluid pressure are investigated.The results demonstrate that fluid pressure and film thickness are obviously dependent on the size parameter,stiffness ratio,and coating thickness.

PERTURBATION SOLUTION OF NON-NEWTONIAN FLUID AXIAL LAMINAR FLOW THROUGH ECCENTRIC ANNULI

Using the perturbation method, the axial laminar flow of Non-Newtonian fluid through an eccentric annulus is studied in the present paper. The relative eccentricity e is taken as a perturbation parameter, and the first order perturbation solutions of the problem, such as velocity field, limit velocity and pressure gradient, are all obtained.

Transportation of heat through Cattaneo-Christov heat flux model in non-Newtonian fluid subject to internal resistance of particles

Thermal conduction which happens in all phases(liquid,solid,and gas)is the transportation of internal energy through minuscule collisions of particles and movement of electrons within a working body.The colliding particles comprise electrons,molecules,and atoms,and transfer disorganized microscopic potential and kinetic energy,mutually known as the internal energy.In engineering sciences,heat transfer comprises the processes of convection,thermal radiation,and sometimes mass transportation.Typically,more than one of these procedures may happen in a given circumstance.We use the Cattaneo-Christov(CC)heat flux model instead of the Fourier law of heat conduction to discuss the behavior of heat transportation.A mathematical model is presented for the Cattaneo-Christov double diffusion(CCDD)in the flow of a non-Newtonian nanofluid(the Jeffrey fluid)towards a stretched surface.The magnetohydrodynamic(MHD)fluid is considered.The behaviors of heat and mass transportation rates are discussed with the CCDD.These models are based on Fourier’s and Fick’s laws.The convective transportation in nanofluids is discussed,subject to thermophoresis and Brownian diffusions.The nonlinear governing flow expression is first altered into ordinary differential equations via appropriate transformations,and then numerical solutions are obtained through the built-in-shooting method.The impact of sundry flow parameters is discussed on the velocity,the skin friction coefficient,the temperature,and the concentration graphically.It is reported that the velocity of material particles decreases with higher values of the Deborah number and the ratio of the relaxation to retardation time parameter.The temperature distribution enhances when the Brownian motion and thermophoresis parameters increase.The concentration shows contrasting impact versus the Lewis number and the Brownian motion parameter.It is also noticed that the skin friction coefficient decreases when the ratio of the relaxation to retardation time parameter increases.

A three-dimensional immersed boundary method for non-Newtonian fluids

Fluid-structure-interaction （FSI） phenomenon is common in science and engineering. The fluidinvolved in an FSI problem may be non-Newtonian such as blood. A popular framework for FSIproblems is Peskin’s immersed boundary （IB） method. However, most of the IB formulations arebased on Newtonian fluids. In this letter, we report an extension of the IB framework to FSIinvolving Oldroyd-B and FENE-P fluids in three dimensions using the lattice Boltzmann approach.The new method is tested on two FSI model problems. Numerical experiments show that themethod is conditionally stable and convergent with the first order of accuracy.

VARIATIONAL PRINCIPLES IN HYDRODYNAMICS OF A NON-NEWTONIAN FLUID

In this paper, the principle of maximum power losses for the incompressible viscous fluid proposed by professor Chien Weizang in reference [1] is further extended to the hydrodynamic problem of the non-Newtonian fluid with constitutive law expressed as epsilon(y) = partial derivative tau/partial derivative sigma'(y). The constraint conditions of variation are eliminated by the method of identified Lagrangian multiplier and a generalized variational principle is established.

GEVREY CLASS REGULARITY FOR THE GLOBAL ATTRACTOR OF A TWO-DIMENSIONAL NON-NEWTONIAN FLUID

This article investigates Gevrey class regularity for the global attractor of an incompressible non-Newtonian fluid in a two-dimensional domain with a periodic boundary condition.This Gevrey class regularity reveals that the solutions lying in the global attractor are analytic in time with values in a Gevrey class of analytic functions in space.