Rheological properties of dilute polymer solutions: An extended thermodynamic approach

It is shown that extended irreversible thermodynamics can be used to account for the shear rate and frequency dependences of several material functions like shear viscosity, first and second normal stress coefficients, dynamic viscosity and storage modulus. Comparison with experimental data on steady shearing and small oscillatory shearing flows is performed. A good agreement between the model and experiment is reached in a wide scale of variation of the shear rate and the frequency of oscillations. The relation between the present model which includes quadratic terms in the pressure tensor and the Giesekus model is also examined.     

Stokes’ first problem for some non-Newtonian fluids: Results and mistakes

The well-known problem of unidirectional plane flow of a fluid in a half-space due to the impulsive motion of the plate it rests upon is discussed in the context of the second-grade and the Oldroyd-B non-Newtonian fluids. The governing equations are derived from the conservation laws of mass and momentum and three correct known representations of their exact solutions given. Common mistakes made in the literature are identified. Simple numerical schemes that corroborate the analytical solutions are constructed.     

An analysis for forced convection heat transfer from external surfaces to non-Newtonian fluids

A theoretical analysis has been proposed for the forced convection heat transfer from external surfaces immersed in non-Newtonian fluids of the power-law model. The integral treatment previously introduced for Newtonian fluids has been successfully extended to the non-Newtonian fluids over a flat plate and a wedge of an arbitrary included angle. The integral momentum and energy equations are transformed into a pair of characteristic equations, which can readily be solved for the velocity shape factor and the boundary layer thickness ratio, once the exponents in the expressions for the power-law model, free stream velocity and wall temperature variation are specified. It has been also found that an asymptotic expression derived under the assumption of large Prandtl number, is valid practically for all power-law fluids, and hence, can be used for a speedy, and yet accurate estimation of the local heat transfer to non-Newtonian fluids.     

Three-dimensional adaptive finite element computations and applications to non-Newtonian fluids

An adaptive strategy for the finite element solution of three-dimensional viscous flow problems is defined and implemented. The solution strategy is based on an advancing front mesh generator making use of binary data structures for fast geometrical data handling. The error is estimated a posteriori with a residual-type bound. The error estimate is shown to exhibit proper convergence for tetrahedral elements. Its combination with the mesh generator and an interpolation scheme for unstructured meshes is shown to generate adaptive meshes and to reduce the solution cost for a given error level, as illustrated by the isothermal flow of a shear-thinning fluid.     

Studies on heat transfer to Newtonian and non-Newtonian fluids in agitated vessel

Heat transfer studies to Newtonian and non-Newtonian fluids are carried out in a stirred vessel fitted with anchor/turbine impeller and a coil for heating/cooling with an objective of determining experimentally the heat transfer coefficient of few industrially important systems namely castor oil and its methyl esters, soap solution, CMC and chalk slurries. The effect of impeller geometry, speed and aeration is investigated. Generalized Reynolds and Prandtl numbers are calculated using an apparent viscosity for non-Newtonian fluids. The data is correlated using a Sieder–Tate type equation. A trend of increase in heat transfer coefficient with RPM in presence and absence of solids has been observed. Relatively high values of Nusselt numbers are obtained for non-Newtonian fluids when aeration is coupled with agitation. The contribution of natural convection to heat transfer has been accounted for by incorporating the Grashof number. The correlations developed based on these studies are applied for design of commercial scale soponification reactor. Power per unit volume resulted in reliable design of a reactor.     

Heat transfer to non-Newtonian fluids in laminar flow through rectangular ducts

Heat transfer to non-newtonian fluids flowing laminarly through rectangular ducts is examined. The conservation equations of mass, momentum, and energy are solved numerically with the aid of a finite volume technique. The viscoelastic behavior of the fluid is represented by the Criminale-Ericksen-Filbey (CEF) constitutive equation. Secondary flows occur due to the elastic behavior of the fluid, and, consequently, heat transfer is strongly enhanced. It is observed that shear thinning yields negligible heat transfer enhancement effect, when compared with the secondary flow effect. Maximum heat transfer is shown to occur for some combinations of parameters. Thus, there are optimal combinations of aspect ratio and Reynolds numbers, which depend on the fluid's mechanical behavior. This result can be usefully explored in thermal designs of certain industrial processes.     

Breakup of Newtonian and non-Newtonian fluids in air jets

The breakup of droplets of non-Newtonian fluids has been investigated by high speed photography and impaction following preliminary results of Newtonian fluids, which confirmed the suitability of the measurement techniques. Single droplets with diameters from 2.4 to 3.3 mm, were arranged to fall under gravity into a jet of air with velocities up to 36o m/s. The droplets of Newtonian fluids, water and Diesel oil, were atomised in the expected manner within three main regimes characterised by the Weber number of the droplet and air jet conditions, while similar droplets of non-Newtonian fluids were found not to atomise but to develop under shear and stretching into ligaments of fluid separated from a local region of their surface; these ligaments were elongated until breakup occurred, though not into small droplets as with the Newtonian fluids. Some of the non-Newtonian fluids (TEP with 7.5% and lo% K125, with and without water) were found not to break up at the maximum speed of the tests and they will be re-examined at higher jet velocities. Increase in the concentration of K125 in TEP resulted in higher critical speed for a given droplet diameter.The authors would like to thank Prof. J. H. Whitelaw of Imperial College for many discussions and useful suggestions during the course of this work, and Dr. G. Cambray of CBDE for his valuable administrative support     

An analytical solution to non-axisymmetric heat transfer with viscous dissipation for non-Newtonian fluids in laminar forced flow

Forced convection heat transfer in a non-Newtonian fluid flow inside a pipe whose external surface is subjected to non-axisymmetric heat loads is investigated analytically. Fully developed laminar velocity distributions obtained by a power-law fluid rheology model are used, and viscous dissipation is taken into account. The effect of axial heat conduction is considered negligible. The physical properties are assumed to be constant. We consider that the smooth change in the velocity distribution inside the pipe is piecewise constant. The theoretical analysis of the heat transfer is performed by using an integral transform technique – Vodicka’s method. An important feature of this approach is that it permits an arbitrary distribution of the surrounding medium temperature and an arbitrary velocity distribution of the fluid. This technique is verified by a comparison with the existing results. The effects of the Brinkman number and rheological properties on the distribution of the local Nusselt number are shown.     

Non-Newtonian fluids v frictional resistance of discs and cones rotating in power-law non-Newtonian fluids

Summary Relations have been derived for the frictional resistance of finite discs and cones rotating in Ostwald-de Waele (power-law) type non-Newtonian fluids. The obtained equations can be formulated as dimensionless relations between the dimensionless moment coefficient and the generalized Reynolds number; the flow-behaviour index n enters the equations as a parameter. The relations derived for cones contain the apex angle 2₀ as an additional parameter in the form of A=sin ₀. The validity of the theoretically derived relations has been verified by measurements of the torque of discs and cones for a number of pseudoplastic power-law fluids.Nomenclature A sin ₀ parameter - b exponent in regression equation (16) - C coefficient in regression equation (16) - c _Mi dimensionless moment coefficient, for bodies wetted on one side (i=1) and for completely wetted bodies (i=2), equations (8) and (9b) - d diameter of turntable - F, G velocity functions of exact solution, equation (4) - K consistency coefficient of non-Newtonian fluids - M _Ki torque of rotating bodies, i=1 for bodies wetted on one side, i=2 for completely wetted bodies - n flow-behaviour index of non-Newtonian fluids - N=K/ kinematic consistency coefficient - P tangential force - r(y) perpendicular distance of point on cone surface from axis - R radius of disc or of base of cone - modified Reynolds number defined by equation (14) - Re _ow generalized Reynolds number defined by equation (10) - S, S area - u, v components of velocity vector - x, y, z coordinates according to fig. 1 - ₀ half the apex angle of cone - coefficient of frictional resistance defined by equation (11) - thickness of boundary layer - independent variable in exact solution, defined by equation (5) - density of fluid - _zx, _zy tangential stresses - angular velocity of rotation Indices T theoretical value - E experimental value - 0 refers to surface of rotating body     

Cavitation-induced particle–wall interaction in Newtonian and non-Newtonian fluids

A novel hydrodynamic effect, namely, slow contactless motion of a heavy spherical particle along an inclined wall, accompanied by the formation of a finite particle–wall clearance under the action of a cavitation-induced lift force, is investigated. Similarity parameters controlling the particle motion, determined using the dimensionality theory, are validated experimentally. These parameters are related to the atmospheric pressure, the surface tension on the liquid–air interface, the density of the air dissolved in the fluid, the particle weight in the fluid, and the viscoelastic properties of the fluid.This paper was presented at the AERC 2005.     

An experimental approach to low-cycle fatigue damage based on thermodynamic entropy

This paper presents an experimental approach to fatigue damage in metals based on thermodynamic theory of irreversible process. Fatigue damage is an irreversible progression of cyclic plastic strain energy that reaches its critical value at the onset of fracture. In this work, irreversible cyclic plastic energy in terms of entropy generation is utilized to experimentally determine the degradation of different specimens subjected to low cyclic bending, tension-compression, and torsional fatigue. Experimental results show that the cyclic energy dissipation in the form of thermodynamic entropy can be effectively utilized to determine the fatigue damage evolution. An experimental relation between entropy generation and damage variable is developed.     

An approach to solving the stress problem of elasticity

It is shown that three equilibrium equations and three stress compatibility equations are sufficient to solve the stress problem of elasticity __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 23–28, July 2006.     

Simulation of particle settling in rotating and non-rotating flows of non-Newtonian fluids

Finite element solutions are presented for the flow of Newtonian and non-Newtonian fluids around a sphere falling along the centreline of a cylindrical tube. Both rotating and stationary tube scenarios are considered. Calculations are reported for three different inelastic constitutive models that manifest shear-thinning, extension-thickening and their combination. The influence of inertia and these various forms of viscous response are examined for their influence upon the drag on the settling particle and the structure of the flow. Simulations are performed by employing a semi-implicit time marching Taylor–Galerkin/pressure-correction finite element algorithm, a fractional-staged scheme of second-order-accuracy. © 1998 John Wiley & Sons, Ltd.     

An asymptotic approach to the torsion problem in thin rectangular domains

A rather straightforward derivation of the Γ-limit of the torsion problem on a thin rectangle as the thickness goes to zero is obtained. The limit stresses are evaluated and the distributional nature of one of the stress components is clarified.     

An approach to the problem of closure in non-linear stochastic mechanics

An approach combining the method of moment equations and the statistical linearization technique is proposed for analysis of the response of non-linear mechanical systems to random excitation. The adaptive statistical linearization procedure is developed for obtaining a more accurate mean square of responses. For these, a Duffing oscillator and an oscillator with cubic non-linear damping subject to white noise excitation are considered. It is shown that the adaptive statistical linearization proposed yields good accurate results for both weak and strong non-linear stochastic systems.Presented at the First European Solid Mechanics Conference, September 9–13, 1991. Munich, Germany     

Entropy generation in non-Newtonian fluids due to heat and mass transfer in the entrance region of ducts

A new solution for the Graetz problem (hydrodynamically developed forced convection in isothermal ducts) extended to power-law fluids and mass transfer with phase change at the walls is presented. The temperature and concentration spatial distributions in the corresponding entrance regions are obtained for two geometries (parallel-plates duct and circular pipe) in terms of appropriate dimensionless parameters. They are used to illustrate the effects of the fluid nature on the velocity, temperature and concentration distributions, on the axial evolution of the sensible and latent Nusselt numbers as well as on the local entropy generation rate due to velocity, temperature and concentration gradients.     

Heat transfer to non-Newtonian fluids in laminar flow through concentric annuli with or without suction

Rheologica Acta - In this paper we have investigated the heat transfer aspects of the flow of a power law fluid in an annulus with porous walls. The case of no suction (solid walls annulus) is also...     

An approach to three-dimensional elasticity problem of cylindrical orthotropic bodies

The state equation for a static or dynamic thermal elastic problem of cylindrical orthotropic bodies is derived using the three-dimensional theory of elasticity. The governing equation for displacement components is obtained by series expansion, and for simplicity the case of an axisymmetric problem of transverse isotropic bodies is given. For illustration, an axisymmetric problem of a combined-cylinder made of two transverse isotropic materials is also presented. Some interesting and significant results are obtained.Supported by-National Natural Science Foundation and Post-Doctor's Foundation of China