Home About us Contact
|
Home About us Contact | ||
|
|
||
Viscous Dissipation (viscous + dissipation)
Selected AbstractsEffects of Viscous Dissipation on Heat Transfer between an Array of Long Circular Cylinders and Power Law FluidsTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 6 2007R. P. Chhabra Abstract The free surface model has been combined with the equations of motion and of thermal energy to investigate the role of viscous dissipation on heat transfer between banks of long cylinders and power law (shear-thinning and shear-thickening) fluids. The equations of motion cast in the stream function/vorticity formulation have been solved numerically using a second-order accurate finite difference method to obtain extensive information on the behaviour of local and surface-averaged Nusselt numbers over a range of Reynolds numbers 1 , 500, for a wide range of power law indices (0.4 , n , 2.0), Brinkman numbers (0 , Br , 5) and Prandtl numbers (Pr = 1, 1000) at two representative solid volume fractions corresponding to the porosities of e = 0.4 and 0.9. Two different thermal boundary conditions are considered at the cylinder surface: constant temperature (CT) and constant heat flux (CHF). The results presented herein provide a fundamental knowledge about the influence of viscous dissipation on the heat transfer characteristics. The results reported herein further show that the effect of Brinkman number on heat transfer is strongly conditioned by the thermal boundary condition, Prandtl number and the power law index. On a combiné le modèle de surface libre aux équations de mouvement et de transfert de chaleur afin d'étudier le rôle de la dissipation visqueuse sur le transfert de chaleur entre des rangées de cylindres longs pour des fluides de loi de puissance (rhéofluidifiants et rhéoépaississants). Les équations de mouvement formulées en fonction de courant/vorticité ont été résolues numériquement à l'aide d'une méthode de différences finies du second ordre, afin d'obtenir des informations détaillées sur le comportement des nombres de Nusselt locaux et moyennés en surface pour une gamme de nombres de Reynolds compris entre 1 et 500, une large gamme d'indices de loi de puissance (0,4 , n , 2,0), de nombres de Brinkman (0 , Br , 5) et de nombres de Prandtl (Pr = 1,1000) à deux fractions de volume de solides correspondant à une porosité de e = 0,4 et 0,9. Deux conditions aux limites thermiques ont été considérées à la surface du cylindre: la température constante (CT) et le flux de chaleur constant (CHF). Les résultats présentés permettent de rendre compte de l'influence de la dissipation visqueuse sur les caractéristiques du transfert de chaleur et l'effet du nombre de Brinkman sur le transfert de chaleur qui est fortement influencé par la condition aux limites thermique, le nombre de Prandtl et l'indice de loi de puissance. [source] Energy,momentum consistent finite element discretization of dynamic finite viscoelasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010M. Groß Abstract This paper is concerned with energy,momentum consistent time discretizations of dynamic finite viscoelasticity. Energy consistency means that the total energy is conserved or dissipated by the fully discretized system in agreement with the laws of thermodynamics. The discretization is energy,momentum consistent if also momentum maps are conserved when group motions are superimposed to deformations. The performed approximation is based on a three-field formulation, in which the deformation field, the velocity field and a strain-like viscous internal variable field are treated as independent quantities. The new non-linear viscous evolution equation satisfies a non-negative viscous dissipation not only in the continuous case, but also in the fully discretized system. The initial boundary value problem is discretized by using finite elements in space and time. Thereby, the temporal approximation is performed prior to the spatial approximation in order to preserve the stress objectivity for finite rotation increments (incremental objectivity). Although the present approach makes possible to design schemes of arbitrary order, the focus is on finite elements relying on linear Lagrange polynomials for the sake of clearness. The discrete energy,momentum consistency is based on the collocation property and an enhanced second Piola,Kirchhoff stress tensor. The obtained coupled non-linear algebraic equations are consistently linearized. The corresponding iterative solution procedure is associated with newly proposed convergence criteria, which take the discrete energy consistency into account. The iterative solution procedure is therefore not complicated by different scalings in the independent variables, since the motion of the element is taken into account for solving the viscous evolution equation. Representative numerical simulations with various boundary conditions show the superior stability of the new time-integration algorithm in comparison with the ordinary midpoint rule. Both the quasi-rigid deformations during a free flight, and large deformations arising in a dynamic tensile test are considered. Copyright © 2009 John Wiley & Sons, Ltd. [source] Evaluating Energy Consumption and Efficiency of a Twin-Screw ExtruderJOURNAL OF FOOD SCIENCE, Issue 5 2002M. Liang ABSTRACT: Using the results from twin-screw extrusion of corn meal, both energy consumption and extruder efficiency were found to be significantly correlated with screw speed and specific feeding load (SFL). An increase in the SFL decreased the total specific mechanical energy, but increased the extruder efficiency. SFL influenced the extruder efficiency more than the screw speed. Increasing the screw speed from 300 to 450 rpm at a constant SFL level increased the extruder efficiency by 6 to 11%, whereas an increase of SFL from 0.0026 to 0.0038 kg rev 1 raised the extruder efficiency by 30%. Of the mechanical energy consumed per unit mass of extrudate, over 98% were used for shearing or viscous dissipation and less than 1.5% were for pumping during twin-screw extrusion of corn meal. [source] Energy Balance of Low Hydrated Starches Transition Under ShearJOURNAL OF FOOD SCIENCE, Issue 4 2002C. Barron ABSTRACT Moistened (25% to 30% total basis) starches were processed on a pre-shearing rheometer under controlled conditions of temperature, residence time, and shear rate. The specific mechanical energy (30 to 1000 J.g -1) was measured and starch transformations assessed. The conversion of compacted native starch into a suspension of granule fragments in a melt was modeled by a simplified energy balance of the shearing zone. A theoretical fragmentation mechanism was proposed with a critical fracture energy of 125 J.m -2. The computed mechanical energy and time necessary for achieving this transition varied in agreement with experimental results, for different operating conditions and starch botanical origins. Interparticle friction influenced granule fragmentation, whereas crystal melting was associated with viscous dissipation. [source] The role of viscous heating in Barrovian metamorphism of collisional orogens: thermomechanical models and application to the Lepontine Dome in the Central AlpsJOURNAL OF METAMORPHIC GEOLOGY, Issue 2 2005J.-P. BURG Abstract Thermal models for Barrovian metamorphism driven by doubling the thickness of the radiogenic crust typically meet difficulty in accounting for the observed peak metamorphic temperature conditions. This difficulty suggests that there is an additional component in the thermal budget of many collisional orogens. Theoretical and geological considerations suggest that viscous heating is a cumulative process that may explain the heat deficit in collision orogens. The results of 2D numerical modelling of continental collision involving subduction of the lithospheric mantle demonstrate that geologically plausible stresses and strain rates may result in orogen-scale viscous heat production of 0.1 to >1 ,W m,3, which is comparable to or even exceeds bulk radiogenic heat production within the crust. Thermally induced buoyancy is responsible for crustal upwelling in large domes with metamorphic temperatures up to 200 °C higher than regional background temperatures. Heat is mostly generated within the uppermost mantle, because of large stresses in the highly viscous rocks deforming there. This thermal energy may be transferred to the overlying crust either in the form of enhanced heat flow, or through magmatism that brings heat into the crust advectively. The amplitude of orogenic heating varies with time, with both the amplitude and time-span depending strongly on the coupling between heat production, viscosity and collision strain rate. It is argued that geologically relevant figures are applicable to metamorphic domes such as the Lepontine Dome in the Central Alps. We conclude that deformation-generated viscous dissipation is an important heat source during collisional orogeny and that high metamorphic temperatures as in Barrovian type metamorphism are inherent to deforming crustal regions. [source] Characterization of dynamical emulsification process in concentrated conditionsAICHE JOURNAL, Issue 8 2007Christophe Baravian Abstract Emulsification at constant shear rate in concentrated conditions (50% in volume fraction) is investigated experimentally by measuring simultaneously the droplet size and the global shear stress using a specially designed rheo-optical "Steady Light Transport" apparatus. The capillary number is varied by changing the continuous phase viscosity, corresponding to disperse to continuous phase viscosity ratios between 0.02 and 2. We show that when the capillary number is large enough (>0.35), emulsification occurs. At constant shear rate, this time-dependant process can be separated into four steps: (1) flow start-up, (2) premix formation, (3) a progressive reduction in droplet size, associated with an increase in shear stress, (4) changes in droplet size and shear stress stop at a well-defined emulsification time. Step (3), called dynamical emulsification, is fully controlled by the critical capillary number and the mechanism of drop size reduction stops when viscous dissipation dominates the droplet elongation and break-up mechanism. This approach accurately describes both the variation in shear stress with droplet size during Stage (3) and the final state of the emulsion in terms of droplet size and viscosity. © 2007 American Institute of Chemical Engineers AIChE J, 2007 [source] Coalescence of deformable granules in wet granulation processesAICHE JOURNAL, Issue 3 2000L. X. Liu In this work, the coalescence of deformable granules in wet granulation processes is modelled. The model accounts for both the mechanical properties of the granules and the effect of the liquid layer at the granule surface. It is an extension to the model of Ennis et al. (1991) to include the possibility of granule plastic deformation during collisions. The model is written in dimensionless groups such as viscous and deformation Stokes numbers and the ratio of granule dynamic yield strength to granule Young's modulus (Yd/E*). These variables are bulk parameters of the powder-binder mixture and also functions of the process intensity. The model gives the conditions for two types of coalescence,type I and type II. Type I coalescence occurs when granules coalesce by viscous dissipation in the surface liquid layer before their surfaces touch. Type II coalescence occurs when granules are slowed to a halt during rebound, after their surfaces have made contact. The model explains some of the trends observed in the literature, are preliminary validation of the coalescence criterion with drum granulation data is encouraging. An extension is also made to the case of surface dry granules, where liquid is squeezed to the surface during granule deformation. [source] An inverse estimation of initial temperature profile in a polymer processPOLYMER ENGINEERING & SCIENCE, Issue 1 2008Ali A. Ranjbar Since one of the most important parameter in polymer processing such as injection stretch blow molding is temperature distribution in the thickness direction, an inverse method has been applied to estimate this profile. This process comprises of four steps. In the first step the preform is injection molded, and in the second and third step it is stretched by a rod to its final length and then inflated and in the last step it is discharged from the mold. In such kind of polymer flows viscous dissipation plays a remarkable role in the evolution of temperature profile. Some theoretical temperature profile has been applied to confirm the validation of the inverse algorithm. Different solution techniques are applied in this article to the inverse problem under consideration, namely: the conjugate gradient and Levenberg,Marquardt method. After the preform is injection molded, which is the first step, it is removed from the mold, which corresponds to time t = 0. At this moment an infrared camera is used to record the surface temperature of the preform with a certain time step. With regard to variation of thermal properties with temperature, the inverse problem becomes nonlinear. These experimental data provided by the infrared camera are then used to estimate the temperature profile at the end of injection process before stretching and inflation took place. POLYM. ENG. SCI., 48:133,140, 2008. © 2007 Society of Plastics Engineers [source] Influence of melt-blending conditions on structural, rheological, and interfacial properties of polyamide-12 layered silicate nanocompositesPOLYMER ENGINEERING & SCIENCE, Issue 8 2006Pascal Médéric The influence of the melt-blending conditions on the structural, rheological, and interfacial properties of modified montmorillonite/Polyamide-12 nanocomposites has been studied performing transmission electron microscopy observation combined with X-Ray diffraction and rheological experiments. In the dilute regime, for short mixing times, the apparent aspect ratio of primary clay entities, determined from intrinsic viscosity measurements, is shown to increase with rotational speed. At high blade rotational speeds, the viscometric results suggest an almost achieved exfoliation, as confirmed by transmission electron microscopy micrographs. For longer mixing times, a significant drop of viscous dissipation is observed, which is very marked at high blade rotational speeds and attributed to a modification of the particle/matrix interface. In the concentrated regime, the rheological behavior of nanocomposites is attributed to the formation of a network of mesoscopic domains, composed of correlated clay entities. Upon increasing strain during mixing, the clay aggregates within these domains break into intercalated stacks and finally exfoliated layers, as shown by transmission electron microscopy micrographs and wide-angle X-ray diffraction patterns. The melt state elastic and viscous properties of the nanocomposites are mainly governed by the networked domains, and not by the nature and properties of the structure within the domains. POLYM. ENG. SCI. 46:986,994, 2006. © 2006 Society of Plastics Engineers. [source] Effects of Viscous Dissipation on Heat Transfer between an Array of Long Circular Cylinders and Power Law FluidsTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 6 2007R. P. Chhabra Abstract The free surface model has been combined with the equations of motion and of thermal energy to investigate the role of viscous dissipation on heat transfer between banks of long cylinders and power law (shear-thinning and shear-thickening) fluids. The equations of motion cast in the stream function/vorticity formulation have been solved numerically using a second-order accurate finite difference method to obtain extensive information on the behaviour of local and surface-averaged Nusselt numbers over a range of Reynolds numbers 1 , 500, for a wide range of power law indices (0.4 , n , 2.0), Brinkman numbers (0 , Br , 5) and Prandtl numbers (Pr = 1, 1000) at two representative solid volume fractions corresponding to the porosities of e = 0.4 and 0.9. Two different thermal boundary conditions are considered at the cylinder surface: constant temperature (CT) and constant heat flux (CHF). The results presented herein provide a fundamental knowledge about the influence of viscous dissipation on the heat transfer characteristics. The results reported herein further show that the effect of Brinkman number on heat transfer is strongly conditioned by the thermal boundary condition, Prandtl number and the power law index. On a combiné le modèle de surface libre aux équations de mouvement et de transfert de chaleur afin d'étudier le rôle de la dissipation visqueuse sur le transfert de chaleur entre des rangées de cylindres longs pour des fluides de loi de puissance (rhéofluidifiants et rhéoépaississants). Les équations de mouvement formulées en fonction de courant/vorticité ont été résolues numériquement à l'aide d'une méthode de différences finies du second ordre, afin d'obtenir des informations détaillées sur le comportement des nombres de Nusselt locaux et moyennés en surface pour une gamme de nombres de Reynolds compris entre 1 et 500, une large gamme d'indices de loi de puissance (0,4 , n , 2,0), de nombres de Brinkman (0 , Br , 5) et de nombres de Prandtl (Pr = 1,1000) à deux fractions de volume de solides correspondant à une porosité de e = 0,4 et 0,9. Deux conditions aux limites thermiques ont été considérées à la surface du cylindre: la température constante (CT) et le flux de chaleur constant (CHF). Les résultats présentés permettent de rendre compte de l'influence de la dissipation visqueuse sur les caractéristiques du transfert de chaleur et l'effet du nombre de Brinkman sur le transfert de chaleur qui est fortement influencé par la condition aux limites thermique, le nombre de Prandtl et l'indice de loi de puissance. [source] Turbulence energetics in stably stratified geophysical flows: Strong and weak mixing regimesTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 633 2008S. S. Zilitinkevich Abstract Traditionally, turbulence energetics is characterised by turbulent kinetic energy (TKE) and modelled using solely the TKE budget equation. In stable stratification, TKE is generated by the velocity shear and expended through viscous dissipation and work against buoyancy forces. The effect of stratification is characterised by the ratio of the buoyancy gradient to squared shear, called the Richardson number, Ri. It is widely believed that at Ri exceeding a critical value, Ric, local shear cannot maintain turbulence, and the flow becomes laminar. We revise this concept by extending the energy analysis to turbulent potential and total energies (TPE, and TTE = TKE + TPE), consider their budget equations, and conclude that TTE is a conservative parameter maintained by shear in any stratification. Hence there is no ,energetics Ric', in contrast to the hydrodynamic-instability threshold, Ric,instability, whose typical values vary from 0.25 to 1. We demonstrate that this interval, 0.25 < Ri < 1, separates two different turbulent regimes: strong mixing and weak mixing rather than the turbulent and the laminar regimes, as the classical concept states. This explains persistent occurrence of turbulence in the free atmosphere and deep ocean at Ri , 1, clarifies the principal difference between turbulent boundary layers and free flows, and provides the basis for improving operational turbulence closure models. Copyright © 2008 Royal Meteorological Society [source] Hydromagnetic flow and heat transfer of a conducting Casson fluid in a rectangular channelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2006Hazem Ali Attia Abstract The transient hydromagnetic flow of an electrically conducting viscous incompressible non-Newtonian Casson fluid bounded by two parallel non-conducting plates is studied with heat transfer considering the Hall effect. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a pressure gradient in the axial direction. The lower plate is stationary and the upper plate is suddenly set into motion and simultaneously suddenly isothermally heated to a temperature other than the lower plate temperature. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of the Hall term and the parameter describing the non-Newtonian behaviour on both the velocity and temperature distributions are studied. Copyright © 2005 John Wiley & Sons, Ltd. [source] | ||||||||||||||||