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In this paper, viscous cosmological dynamics are studied in the presence of dark matter Bose-Einstein condensation by curved-FRW background. For this purpose, we use the BEC regime rather than normal dark matter (cold dark matter or barotropic dark matter) with the dark matter equation of state as [p.sub.dm] [varies] [[rho].sup.2.sub.dm], which arises from the gravitational form. Therefore, we obtain the corresponding continuity equations with the existence of the universe components by considering an interacting model with modified Chaplygin gas. Afterward, we derive the energy density and the pressure of dark energy in terms of the redshift parameter. And then, by introducing a parametrization function and fitting it with 51 supernova data with the likelihood analysis, we find the cosmological parameters versus redshift parameter. In what follows, we plot the corresponding dynamic graphs proportional to redshift, and then we represent that the universe is currently undergoing an accelerated expansion phase. Finally, we explore the stability and the instability of the present model with the sound speed parameter. Key words: dark energy, dark matter, Bose-Einstein condensation, modified Chaplygin gas, bulk viscosity. Sur un fond cosmologique FRW courbe, nous etudions ici la dynamique cosmologique visqueuse, en presence de matiere noire resultant d'un condensat de Bose-Einstein. A cette fin, nous utilisons le regime CBE plutot que la matiere noire normale (la matiere noire froide ou barotrope), avec une equation d'etat de la matiere noire [p.sub.dm] [varies] [[rho].sup.2.sub.dm], qui est de forme gravitationnelle. En consequence, nous obtenons les equations de continuite correspondantes avec l'existence de composants d'univers en considerant un modele interactif avec gaz de Chaplygin modifie. Ensuite, nous derivons la densite d'energie et la pression de l'energie sombre en termes du parametre de decalage vers le rouge (spectral). C'est suivi de l'introduction d'une fonction de parametrage et par ajustage numerique avec les donnees de 51 supernovae et une analyse de vraisemblance, nous trouvons les parametres cosmologiques versus le parametre du decalage spectral. Dans ce qui suit, nous tracons les graphiques dynamiques correspondants proportionnels au decalage spectral, qui presentent l'univers couramment soumis a une phase d'expansion acceleree. Finalement, nous explorons la stabilite et l'instabilite du present modele a l'aide du parametre de la vitesse du son. [Traduit par la Redaction] Mots-cles : energie sombre, matiere noire, condensation de Bose-Einstein, gaz de Chaplygin modifie, viscosite volumique., 1. Introduction As we know, the contents of the universe are dark matter, dark energy, and visible matter, in which visible matter consists of the galaxies, stars, planets, and every [...]

This study investigates entropy generation for the unsteady flow of a second- grade fluid over a uniformly heated vertical cylinder. The fluid viscosity is assumed to vary with temperature. The mathematical model of this problem is given by highly time-reliant nonlinear coupled equations and resolved by an efficient unconditionally stable implicit scheme. The time histories of average values of momentum and heat-transport coefficients, entropy-generation and Bejan number, and steady-state flow variables are discussed for several values of non-dimensional parameters arising in the flow equations. The results indicate that entropy-generation parameter and Bejan number increase with rising values of group parameter and Grashof number. The results also show that entropy-generation number declines with increasing viscoelastic parameter. Key words: second-grade fluid, transient, entropy generation, vertical cylinder, heat transfer, finite difference method. Notre etude vise a examiner la generation d'entropie dans l'ecoulement instable d'un fluide de seconde classe sur un cylindre vertical chauffe uniformement. Nous supposons que la viscosite du fluide varie avec la temperature. Le modele mathematique de ce probleme est donne par des equations couplees non lineaires fortement dependantes du temps et solutionnees par une methode implicite tres stable et efficace. Pour plusieurs valeurs des parametres sans dimension qui controlent les equations d'ecoulement, nous analysons le developpement temporel des valeurs moyennes des variables d'impulsion et de transport de chaleur, l'entropie et le nombre de Bejan, ainsi que les variables d'ecoulement en etat stationnaire. Les resultats indiquent que la generation d'entropie et le nombre de Bejan augmentent avec les valeurs croissantes du parametre de groupe et du nombre de Grashof. Ces resultats indiquent aussi que la generation d'entropie decroit pour des valeurs plus elevees de la viscosite. [Traduit par la Redaction] Mots-cles : fluide de seconde classe, transitoire, generation d'entropie, transfert de chaleur., Introduction The laws of thermodynamics and Newton's second law of motion are the basic principles on which all of today's flow and heat-transfer systems developed. The first law of thermodynamics [...]

In this paper, we study the heat transfer and flow characteristics of a pressure-driven flow of nanofluids between two plates. For modelling the motion of nanoparticles, a concentration convection- diffusion equation is applied, where the effect of the Brownian motion and thermophoretic diffusion are included. We consider that the shear viscosity and the thermal conductivity of the nanofluids depend on the concentration of the nanoparticles. Furthermore, the viscosity is also a function of shear rate, which has been widely observed by many experiments. The flow is assumed to be fully developed and steady state. The effect of the dimensionless parameters related to shear thinning viscosity, thermal diffusivity, particle transport flux, etc., are studied numerically. Key words: heat transfer, nanofluids, dilute suspension, shear thinning viscosity, concentration, Nusselt number. Nous etudions le transfert de chaleur et les caracteristiques d'ecoulement de nano-fluides entre deux plaques sous l'effet de la pression. Afin de modeliser le mouvement des nanoparticules, nous utilisons une equations de convexion- diffusion de concentrations, en tenant compte de l'effet du mouvement Brownien et de la thermophorese. Nous considerons que la viscosite de cisaillement et la conductivite thermique des nano-fluides dependent de la concentration des nanoparticules. De plus, la viscosite est aussi une fonction du taux de cisaillement, ce qui a ete largement observe dans plusieurs experiences. Nous supposons l'ecoulement completement developpe et en etat stationnaire. Nous etudions numeriquement l'effet des parametres sans dimension relies a la rheofluidification, a la diffusivite thermique, au flux de transport des particules, etc. [Traduit par la Redaction] Mots-cles: transfert de chaleur, nano-fluide, suspension dilues, rheofluidification, nombre de Nusselt., 1. Introduction With the rapid development of nanotechnology, a sort of dilute solid-fluid suspension, called nanofluid, has drawn attention for their outstanding performance on enhancing heat transfer efficiency [1, 2]. [...]

The present paper is devoted to exploring the effect of bulk viscosity in the context of F(T, [T.sub.G]) gravity. We consider a time-dependent viscosity model with a particular expression of Hubble parameter. We evaluate viscous effective equation of state parameter for three well-known F(T, [T.sub.G]) models. The behavior of the accelerated expanding universe is explored graphically through the viscous equation of state parameter. This parameter indicates the phantom-dominated era as well as crosses the phantom divide line for all three models. We conclude that the universe shows a transition from quintessence to phantom region in the presence of bulk viscosity. Key words: F(T, [T.sub.G]) gravity, dark energy, bulk viscosity. Nous nous interessons ici a l'etude de l'effet de la viscosite volumique dans un contexte de gravite F(T, [T.sub.G]). Nous considerons un modele a viscosite dependante du temps avec une expression particuliere du parametre de Hubble. L'equation d'etat effective visqueuse pour le parametre d'etat est evaluee pour trois modeles F(T, [T.sub.G]) bien connus. Nous explorons graphiquement le comportement de l'univers en expansion acceleree via l'equation visqueuse du parametre d'etat. Ce parametre nous donne l'ere dominee par le fantome ainsi que la frontiere du fantome pour les trois modeles. Nous concluons que l'univers presente une transition de la quintessence vers la region du fantome en presence de viscosite volumique. [Traduit par la Redaction] Mots-cles: gravite F(T; [T.sub.G]), energie sombre, viscosite volumique., 1. Introduction The most remarkable achievement of cosmology is the accelerated expansion of the universe confirmed through various cosmological observations. It is observed that rapid expansion of the universe is [...]

Stiff fluid inflationary cosmological model with variable bulk viscosity in the frame work of locally rotationally symmetric (LRS) Bianchi type I space-time, is investigated. To get the deterministic solution, we have also assumed that a is proportional to 0 and [zeta][theta] = constant = [alpha] where a is shear, 0 the expansion, and [zeta] the coefficient of bulk viscosity. The ansatz [zeta][theta] = constant, was found to connect with the occurrence of Little Rip cosmology using Friedmann-Robertson-Walker metric given by Brevik et al. (Phys. Rev. D, 84,103508 (2011)). We find that the model has constant expansion but represents accelerating phase. The model in general represents an anisotropic universe but in special case, it leads to an isotropic one. The spatial volume increases exponentially with time representing the inflationary scenario. The presence of bulk viscosity tends to increase the inflationary phase. Also, the model leads to the de Sitter model in a special case. The presence of bulk viscosity prevents the matter density to vanish at late time. The energy conditions as given by Kolassis et al. (Classical Quantum Gravity, 5,1129 (1988)). Chatterjee and Banerjee (Gen. Relativ. Gravitation, 36, 303 (2004)) are also discussed. We find that the energy conditions are satisfied for stiff fluid inflationary universe with variable bulk viscosity. PACS Nos.: 04.20.-q, 04.20.20.Jb, 04.20.ev. Nous etudions un modele cosmologique de fluide ferme avec une viscosite volumique, dans le cadre d'un espacetemps de Bianchi de type I (LRS). Afin d'obtenir une solution deterministe, nous supposons que a est proportionnel a 0 et que [zeta][theta] = constante = [alpha], la ou a est le cisaillement, 0 l'expansion et [zeta] le coefficient de viscosite volumique. Nous avons trouve que l'ansatz [zeta][theta] = constante est connecte a la cosmologie de Petite Dechirure (Little Rip) utilisant une metrique FRW et proposee par Brevik et al. (Phys. Rev. D, 84, 103508 (2011)). Nous observons que le modele a une expansion constante, mais represente une phase d'acceleration. Nous trouvons que ce modele represente un univers anisotrope, qui devient isotrope dans certains cas speciaux. Le volume spatial augmente exponentiellement dans un scenario d'inflation. La presence de la viscosite volumique tend a accroitre la phase d'inflation et empeche la densite de matiere de devenir nulle dans un futur lointain. Dans un cas special, ce modele mene au modele de de-Sitter. Nous discutons egalement des conditions sur l'energie telles que donnees par Kolassis et al. (Classical Quantum Gravity, 5,1129 (1988)) et par Chatterjee et Banerjee (Gen. Relativ. Gravitation, 36, 303 (2004)). Nous trouvons que ces conditions sont remplies dans un univers de fluide ferme en inflation, avec une viscosite volumique variable. [Traduit par la Redaction], 1. Introduction Stiff fluid universes create more interest in the study because for such models speed of light equals speed of sound and the governing equations have the same characteristics [...]

The evolution of the viscosity of two commercial epoxy resin systems subjected to manufacturer's recommended cure cycles was studied in detail. The two systems were characterized through rotational viscosimetry and [...]

A method for the determination of pressure-affected viscosity from capillary rheometry and pressure- volume-temperature (PVT) data was tested on polyphenylsulfone melt. Shear viscosity data evaluated at selected temperatures (345-375°C) were interlinked to the PVT data at pressures ranging from 1 to 200 MPa. According to the recently proposed correlation approach, a pressure-dependent shear viscosity is derived from the relationship (verified on several commodity polymers) between temperature-dependent viscosity and a free volume parameter computed using the Simha-Somcynsky equation of state. Finally, the predicted pressure-viscosity coefficient was compared with the value obtained experimentally on a modified single piston rheometer. POLYM. ENG. SCI., 54:711-715, 2014. © 2013 Society of Plastics Engineers, INTRODUCTION Generally speaking, equations of state (eos) describing polymers can be divided into two groups-phenomenological and molecular. The volumetric data characterized by the eos from the first group, are represented [...]

The objective of this study was to determine the role of Omukunzi root (Boscia albitrunca) in the viscosity or consistency, sensory and bacteriological profile of Omashikwa, traditional fermented buttermilk from Namibia. Omashikwa is a popular traditional fermented buttermilk product made with Omukunzi root among the Owambo and Herero tribes living in the North and Central Namibia. It is processed by fermenting raw milk in the presence of Omukunzi root in a calabash and agitated to obtain butter granules. Butter granules are then removed, washed, salted and made into butter or processed into ghee (butter oil). The remaining fermented milk is Omashikwa or traditional fermented buttermilk. The results of this study indicated that the root of Omukunzi tree had low pH (4.9), exhibited bacterial inhibition properties and had high content of soluble carbohydrates (19.4%). Omashikwa made with Omukunzi root (TO) was more viscous, 2.9 Pa.s compared to 2.5 Pa.s of laboratory Omashikwa made without the root (LO). The total aerobic counts were 6.62 cfu/g for TO and 8.62 cfu/g for LO and lactic acid bacteria (LAB) was 6.58 cfu/g for TO and 7.87 cfu/g for LO and were lower in samples with the root. Coliforms, 2.68 cfu/g (TO) and 2.70 cfu/g (LO) and yeasts and moulds were not significantly different (p≤0.05) and were 1.57 cfu/g for TO and 1.69 cfu/g for LO. Yeasts and mould counts from the gourd swabs were high, 4.78 cfu/g. The LAB identified belonged to the genera Lactobacillus (Lb.), Leuconostoc (Leuc.), Lactococcus (Lact.) and Streptococcus (Strep.). The LAB species identified were Lb. plantarum, Lb. lactis subsp. lactis, Leuc. lactis, Leuc. citreum, Lact. lactis subsp. lactis, Lact. lactis subsp. diacetylactis and Strep. thermophillus. The results indicated that Omukunzi root plays a positive role in the quality of value added Omashikwa in terms of improving consistency, sensory quality and controlling microbial profile which could finally help to increase income, create jobs and improve food security and nutrition to the rural communities. Key words: Boscia albitrunca, fermentation, buttermilk, Omashikwa, viscosity, INTRODUCTION Omashikwa, a traditional fermented buttermilk is produced by the Owambo and Herero tribes living a community life in Namibia. In the absence of cooling facilities, fermented milk products are [...]

We investigate models of future finite-time singularities in f(T) theory, where T is the torsion scalar. The algebraic function f(T) is the teleparallel term, T, plus an arbitrary function, g(T). A suitable expression for the Hubble parameter is assumed and constraints are imposed to provide an expanding universe. Two parameters, [beta] and [H.sub.s], that appear in the Hubble parameter are relevant in specifying the types of singularities. Differential equations of g(T) are established and solved, leading to algebraic f(T) models for each type of future finite-time singularity. Moreover, we take into account the viscosity in the fluid and discuss three interesting cases: constant viscosity, viscosity proportional to [square root of (-T)], and the general one where the viscosity is proportional to [(-T).sup.n/2], where n is a natural number. We see that for the first and second cases, in general, the singularities are robust against the viscous fluid, while for the general case, the Big Rip and the Big Freeze can be avoided from the effects of the viscosity for some values of n. PACS Nos.: 95.36.+x, 04.50.Kd, 66.20.-d. Nous analysons la theorie des modeles de singularites de temps futur fini, f(T)ou T est le scalaire de torsion. La fonction algebrique est posee comme etant le terme teleparallele de T plus une fonction g(T). Nous supposons une expression adequate pour le parametre de Hubble et nous imposons des contraintes de facon a avoir un univers en expansion. Les deux parametres [beta] et [H.sub.s] qui apparaissent dans l'expression pour le parametre de Hubble sont pertinents pour specifier les types de singularite. Nous etablissons et solutionnons les equations differentielles pour g(T), menant aux modeles algebriques f(T) pour chaque type de singularite de temps futur fini. Nous tenons egalement compte de la viscosite du fluide et discutons trois cas interessants: viscosite constante, viscosite proportionnelle a [square root of (-T)] et un cas general ou la viscosite est proportionnelle a [(-T).sup.n/2], ou n est un entier naturel. Pour les deux premiers cas, generalement les singularites sont robustes devant la viscosite du fluide, alors que pour le cas general, la viscosite correspondant a certaines valeurs de n permet d'eviter la Grande Dechirure et le Grand Gel. [Traduit par la Redaction], 1. Introduction Recent observations of type Ia supernovae (SNIa) and Wilkinson microwave anisotropy probe (WMAP) [1, 2] indicate that our universe is currently undergoing an accelerating expansion, which confronts the [...]

A marked anisotropy in viscosity develops in Earth's mantle as deformation strongly aligns the crystallographic axes of the individual grains that comprise the rocks. On the basis of geodynamic simulations, processes significantly affected by viscous anisotropy include post-glacial rebound (1,2), foundering of lithosphere (3) and melt production above subduction zones (4). However, an estimate of the magnitude of viscous anisotropy based on the results of deformation experiments on single crystals (5) differs by three orders of magnitude from that obtained by grain-scale numerical models of deforming aggregates with strong crystallographic alignment (6-8). Complicating matters, recent experiments indicate that deformation of the uppermost mantle is dominated by dislocation-accommodated grain-boundary sliding (9), a mechanism not activated in experiments on single crystals and not included in numerical models. Here, using direct measurements of the viscous anisotropy of highly deformed polycrystalline olivine, we demonstrate a significant directional dependence of viscosity. Specifically, shear viscosities measured in high-strain torsion experiments are 15 times smaller than normal viscosities measured in subsequent tension tests performed parallel to the torsion axis. This anisotropy is approximately an order of magnitude larger than that predicted by grain-scale simulations. These results indicate that dislocation-accommodated grain-boundary sliding produces an appreciable anisotropy in rock viscosity. We propose that crystallographic alignment imparts viscous anisotropy because the rate of deformation is limited by the movement of dislocations through the interiors of the crystallographically aligned grains. The maximum degree of anisotropy is reached at geologically low shear strain (of about ten) such that deforming regions of the upper mantle will exhibit significant viscous anisotropy., Many geodynamic processes are directly affected by the development of viscous anisotropy (VA) in Earth's mantle. Numerical simulations indicate that appreciable VA in mantle rocks greatly modifies melt production from [...]

The viscosities of dimethyl ether (DME, [C.sub.2][H.sub.6]O) and of the fluorinated propene isomers 2,3,3,3-tetrafluoroprop-1-ene (R1234yf, [C.sub.3][H.sub.2][F.sub.4]) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) were measured in a combined temperature range from 242 K to [...]

Melt viscosity is a key indicator of product quality in polymer extrusion processes. However, real time monitoring and control of viscosity is difficult to achieve. In this article, a novel 'soft sensor' approach based on dynamic gray-box modeling is proposed. The soft sensor involves a nonlinear finite impulse response model with adaptable linear parameters for real-time prediction of the melt viscosity based on the process inputs; the model output is then used as an input of a model with a simplefixed structure to predict the barrel pressure which can be measured online. Finally, the predicted pressure is compared to the measured value and the corresponding error is used as a feedback signal to correct the viscosity estimate. This novel feedback structure enables the online adaptability of the viscosity model in response to modeling errors and disturbances, hence producing a reliable viscosity estimate. The experimental results on different material/ die/extruder confirm the effectiveness of the proposed 'soft sensor' method based on dynamic gray-box modeling for real-time monitoring and control of polymer extrusion processes. POLYM. ENG. SCI., 52:1332-1341, 2012. [C] 2012 Society of Plastics Engineers, INTRODUCTION Extrusion is a widespread practical method in polymer processing, but controlling the quality of an extrudate material and hence the final product, presents various problems. The feed materials can [...]

The effect of alumina nanoparticles on the viscosity and curing behavior of a bisphenol E cyanate ester monomer suspension was investigated by rheometry and differential scanning calorimetry. The viscosity was found to increase with solids content and was fit well by the Mooney equation. Cure experiments indicate that alumina particles catalyze the curing of the suspensions. The viscosity reduction achieved at high particle loadings by the addition of benzoic acid was also investigated by nuclear magnetic resonance. POLYM. ENG. SCI., 51:1409-1417, 2011. © 2011 Society of Plastics Engineers, INTRODUCTION Bisphenol E cyanate ester (bis(4-cyanatophenyl)-l,l-ethane) or BECy is a low viscosity monomer with a reported viscosity of 0.09-0.12 Pa s [1]. As shown in Fig. 1 [2], BECy cures [...]

Assuming that the matter in the background geometry is a free gas and that no phase transitions were occurring in the early Universe, we discuss the thermodynamics of this closed system using classical approaches. We find that essential cosmological quantities, such as the Hubble parameter H, the scaling factor a, and the curvature parameter k, can be derived from this simple model, which on one hand fulfills and entirely obeys the laws of thermodynamics, and on the other hand, its results are compatible with the Friedmann-Robertson-WaLker model and the Einstein field equations. Including a finite bulk viscosity coefficient leads to important changes in all these cosmological quantities. Accordingly, our picture about the evolution of the Universe and its astrophysical consequences seems to undergoing a radical revision. We find that k strongly depends on the thermodynamics of background matter. The time scale at which negative curvature might take place depends on the relation between the matter content and the total energy. Using quantum and statistical approaches, we introduce expressions for H and the bulk viscosity coefficient ξ. PACS Nos: 98.80.Es, 98.80.Cq, 12.38.Mh, 25.75.-q Supposant que la matiere dans la geometrie de fond de l'univers est un gaz libre et qu'aucune transition de phase ne s'est produite dans l'univers primordial, nous etudions la thermodynamique de ce systeme ferme en utilisant une approche classique. Nous trouvons que les quantites cosmologiques essentielles, comme le parametre de Hubble H, le facteur d'echelle a et le parametre de courbure k peuvent (etre obtenu de ce simple modele qui satisfait et obeit completement aux lois de la thermodynamique. De plus, les resultats sont compatibles avec le modele de Robertson-Walker et avec les equations de champ d'Einstein. L'introduction d'un coefficient fini de viscosite volumique (bulk) amene d'importants changements dans toutes ces quantites cosmologiques. Par consequent, notre vision de revolution de l'Univers et ses consequences astrophysiques semblent devoir etre modifiees de facjon radicale. Nous trouvons que k depend fortement de la thermodynamique de la matiere du fond. L'echelle de temps, a laquelle une courbure negative peut s'etablir, depend de la relation entre le contenu en matiere et l'energie totale. Utilisant des approches quantiques et statistiques, nous introduisons des expressions pour H et le coefficient de viscosite volumique ξ. [Traduit par la Redaction], 1. Introduction We assume that the cosmological background geometry filled with matter or radiation can be characterized by well-known physical laws, such as equations of state and thermodynamics. It leads [...]

Floral nectars of bird-pollinated plants are relatively dilute. One hypothesis proposed to explain this concerns the difficulty for birds of drinking nectar of high viscosity. We examined the effects of viscosity, separately from those of sugar concentration, on feeding by captive whitebellied sunbirds (Cinnyris talatala). Viscosities of artificial nectar (sucrose solutions ranging in concentration from 0.25 to 1.5 mol/1) were altered with Tylose, an inert polysaccharide. Food consumption was measured over 3 h, and lick frequency and duration were recorded using photodetection devices on feeding apertures too small for the bill but large enough for the extended tongue. Volumetric intake rates (ml/s) were inversely proportional to nectar viscosity, and were similar over the range of sucrose concentrations when viscosity was held constant. Sucrose intake rates (mg/s) remained the same on pure sucrose solutions, but they decreased with increasing viscosity at a constant sucrose concentration. Lick frequencies and tongue loads were reduced at high viscosities, and lick duration increased, which confirms that sunbirds take longer to ingest viscous solutions. Licking behavior was remarkably similar in birds feeding on different sucrose concentrations if viscosity was held constant. Nectar ingestion rate is determined by viscosity; however, total food intake is mainly modulated by sugar concentration. Similar effects of food viscosity have been observed in insects that suck nectar. nectarivory; sugar concentration doi: 10.1152/ajpregu.00208.2010.

The ability of eddy-viscosity models to simulate the turbulent wake produced by cross-flow separation over a curved body of revolution is assessed. The results obtained using the standard k - [omega] model show excessive levels of turbulent kinetic energy k in the vicinity of the stagnation point at the nose of the body. Additionally, high levels of k are observed throughout the wake. Enforcing laminar flow upstream of the nose (which replicates the experimental apparatus more accurately) gives more accurate estimates of k throughout the flowfield. A stress limiter in the form of Durbin's T-limit modification for eddy-viscosity models is implemented for the k - [omega] model, and its effect on the computed surface pressures, skin friction, and surface flow features is assessed. Additionally, the effect of the T-limit modification on both the mean flow and the turbulent flow quantities within the wake is also examined. The use of the T-limit modification gives significant improvements in predicted levels of turbulent kinetic energy and Reynolds stresses within the wake. However, predicted values of skin friction in regions of attached flow become up to 50% greater than the experimental values when the T-limit is used. This is due to higher values of near-wall turbulence being created with the T-limit. [DOI: 10.1115/1.4001967]

A method is presented to obtain reduced-order models of multiparametric, steady, transonic aerodynamic flows around two-dimensional airfoils. The method is based on proper orthogonal decomposition and appropriate projection on the proper orthogonal decomposition manifold of the governing equations and boundary conditions, and it includes various ingredients that are new in this field. Proper orthogonal decomposition modes are obtained from a set of snapshots calculated by computational fluid dynamics based on the compressible Navier-Stokes equations and a turbulence model, but projection on the proper orthogonal decomposition manifold is made using the inviscid Euler equations, which makes the method independent of the computational fluid dynamics scheme; projection is made using only a limited number of mesh points, obtaining quite good results. Shock waves are treated specifically in the proper orthogonal decomposition description, to avoid the need of using a too-large number of snapshots. The method is checked and discussed on a specific aerodynamic problem. DOI: 10.2514/1.J050153

An analysis is performed to study the effect of variable viscosity and variable thermal conductivity on the flow and heat transfer of a thin viscoelastic liquid (obeying Walters' liquid B model) film on a horizontal unsteady stretching sheet taking into account the effect of viscous dissipation. The fluid viscosity is assumed to decrease exponentially with temperature but the thermal conductivity is assumed to vary as a linear function of temperature. Numerical solutions are obtained for some representative values of the viscosity and thermal conductivity variation parameters, unsteadiness parameter, and Eckert number. Typical temperature and velocity profiles, dimensionless film thickness, free-surface velocity and temperature, local skin-friction coefficient, and the local surface heat flux are obtained for a wide range of governing parameters. In general, it is found that a viscoelastic fluid is more sensitive to the variable fluid properties effect than a Newtonian fluid. Also, for constant and (or) variable fluid properties, the film thickness and the local surface heat flux of a viscoelastic fluid is small compared to that of a Newtonian fluid. For all values of the variable viscosity parameter and for both viscoelastic and Newtonian fluid films, the viscous dissipation effect increases the free-surface temperature significantly whereas it reduces the heat transfer rate markedly. However, viscous dissipation does not influence the velocity profiles of both Newtonian and viscoelastic liquid films impressively although the film thickness changes noticeably. PACS No: 47.15.gm Nous etudions l'effet d'une viscosite variable et d'une conductivite thermique variable sur l'ecoulement et le transfert de chaleur d'une couche mince de liquide viscoelastique (qui obeit au modele liquide B de Walters) sur une surface horizontale instable extensible, tenant compte d'une dissipation visqueuse. La viscosite du fluide est presumee decroitre exponentiellement avec la temperature, mais la conductivite thermique est supposee etre une fonction lineaire de la temperature. Nous obtenons des solutions numeriques pour des valeurs representatives des parametres de variation de la viscosite et de la conductivite; thermique, du parametre d'instabilite et du nombre d'Eckert. Nous obtenons des profils types de temperature et de vitesse, ainsi que l'eepaisseur adimensionnee de la couche, la temperature et la vitesse en surface libre, le coefficient de friction de peau local et le flux thermique local de surface. En general, nous observons qu'un fluide viscoelastique est plus sensible aux effets des proprietes variables du fluide qu'un fluide Newtonien. Egalement, pour des proprietes constantes/variables du fluide, l'eepaisseur de la couche et le flux thermique local du viscoelastique sont faibles compares au fluide Newtonien. Pour toutes les valeurs du parametre de viscosite variable et pour les deux types de couche de fluide, viscoelastique et Newtonien, l'effet de dissipation visqueuse augmente de facon significative la temperature de la surface libre, alors qu'il reduit de facon marquee le taux de transfert de chaleur. Cependant, la dissipation visqueuse n'influence pas beaucoup les profiles de vitesse des couches de fluide viscoelastique et Newtonien, mais l'epaisseur de la couche change de facon notable. [Traduit par la Redaction], 1. Introduction In recent years the analyses of the flow of a thin liquid film have attracted the attention of a number of researchers because of the possible applications in [...]

Problem statement: Oil well cleaning is the ability of a drilling fluid to suspend and transport drilled cuttings from the down hole (bit face) to the surface. The cleaning performance was affected by many factors such as fluid viscosity, annular flow velocity, angle of inclination and drill cuttings size and shape and. Approach: Navier-Stoke equations, the continuity equation and the power law of non-Newtonian viscosity model were adopted to establish the mathematical model of the cutting transport process in the annulus of the well. The constants of the power law model were evaluated experimentally for three different mud types. The CFD simulation to solve the governing equations was carried out by using FLUENT commercial code. The specifications of the particles, the pumping head and feeding conditions were obtained from a drilling site in Sudan. Results: Simulation of the mud flow in the annulus had shown that in spite of the laminar nature of the flow, the velocity profile was flattening over wide area of the annulus. Such condition was referred to as fog flow and was preferable to produce uniform drag distribution to lift the particles without rotation during the transportation process. The analysis had been conducted for various mud charging rates ranging from 600-900 GPM, in 30[degrees] diverted orientation well. The investigation of cuttings size was conducted for 2.54, 4.45 and 7 mm. Also, the effect of the cuttings shape with 1, 0.9 and 0.85 was investigated and it was found that higher sphereicity have better cleaning efficiency. Conclusion: The analyses revealed that for 30[degrees] diverted orientation; the effective cleaning performance was achieved when the drilling mud charging was higher than 800 GPM for all types of tested cuttings. The simulation results revealed that there was a significant effect of the cuttings size on the cuttings transport. Fine particles are the easiest to clean out. Key words: CFD, well cleaning, cutting particles, simulation, two-phase flow, non-Newtonian fluids, INTRODUCTION Hole cleaning is the ability of a drilling fluid to suspend and transport drilled cuttings from down hole (bit face) to the surface. Inadequate/poor hole cleaning is a major [...]

There is an increasing need to identify the effect of mix composition on the rheological properties of cementitious grouts using minislump, Marsh cone, cohesion plate, washout test, and cubes to determine the fluidity, the cohesion, and other mechanical properties of grouting applications. Mixture proportioning involves the tailoring of several parameters to achieve adequate fluidity, cohesion, washout resistance and compressive strength. This paper proposes a statistical design approach using a composite fractional factorial design which was carried out to model the influence of key parameters on the performance of cement grouts. The responses relate to performance included minislump, flow time using Marsh cone, cohesion measured by Lombardi plate meter, washout mass loss and compressive strength at 3, 7, and 28 days. The statistical models are valid for mixtures with water-to-binder ratio of 0.37-0.53, 0.4-1.8% addition of high-range water reducer (HRWR) by mass of binder, 4-12% additive of silica fume as replacement of cement by mass, and 0.02-0.8% addition of viscosity modifying admixture (VMA) by mass of binder. The models enable the identification of underlying factors and interactions that influence the modeled responses of cement grout. The comparison between the predicted and measured responses indicated good accuracy of the established models to describe the effect of the independent variables on the fluidity, cohesion, washout resistance and the compressive strength. This paper demonstrates the usefulness of the models to better understand trade-offs between parameters. The multiparametric optimization is used to establish isoresponses for a desirability function for cement grout. An increase of HRWR led to an increase of fluidity and washout, a reduction in plate cohesion value, and a reduction in the Marsh cone time. An increase of VMA demonstrated a reduction of fluidity and the washout mass loss, and an increase of Marsh cone time and plate cohesion. Results indicate that the use of silica fume increased the cohesion plate and Marsh cone, and reduced the minislump. Additionally, the silica fume improved the compressive strength and the washout resistance. DOI: 10.1061/(ASCE)MT.1943-5533.0000026 CE Database subject headings: Cement; Grouting; Compressive strength; Plates; Viscosity; Admixture; Binders, materials. Author keywords: Compressive strength; Minislump; Cohesion plate; Silica fume; High-range water reducer; Viscosity modifying admixture; Water/binder.

We describe an experiment involving a mass oscillating in a viscous fluid. The mechanical oscillator is tracked using a simple webcam, and an image processing algorithm records the position of the geometrical center as a function of time. Interesting information can be extracted from the displacement-time graphs, in particular, for the underdamped case. For example, we use these oscillations to determine the viscosity of the fluid. Our mean value of 1.08 [+ or -] 0.07 mPa s for distilled water is in good agreement with the accepted value at 20[degrees]C. The experiment has been successfully employed in an introductory laboratory setting. [c] 2010 American Association of Physics Teachers. [DOI: 10.1119/1.3298370]

Complete wetout of the dry fiber reinforcement by the liquid resin depends strongly on the fiber volume fraction and the resin viscosity of the part being manufactured by rein injection pultrusion. High fiber volume fractions and high resin viscosity values yield high pressures in the tapered resin injection chamber; this work investigates the use of a an injection chamber detached from the pultrusion die in order to lower the resin pressures inside the injection chamber caused by the injection chamber tapering. A 3D finite volume technique was developed to simulate the flow of resin through the glass rovings for a variety of resin viscosities and fiber volume fractions. The results illustrate the impact of the tapering of the injection chamber walls on the minimum injection pressure necessary to achieve complete fiber matrix wetout and the resin pressure induced inside the tapered injection chamber. The results provide important injection chamber design information. [DOI: 10.1115/1.4001138] Keywords: pultrusion manufacturing, resin injection, reinforcement wetout, polymer composites

Coextrusion is widely used to fabricate multilayered products with each layer providing a separate functionality, including barrier resistance to gases, strength, and printability. Here an analytical model of the coextrusion die flow of two incompressible, viscoplastic fluids in a slit die, subject to nonlinear wall slip and under fully developed and isothermal conditions, is developed to allow the prediction of the steady-state velocity and shear stress distributions and the flow rate versus pressure gradient relationship. The resulting model is applied to the coextrusion of two layers of viscoplastic fluids in a thin rectangular slit die (slit gap, h ≪ slit width, W). The analytical solution recognizes a number of distinct flow conditions (eleven cases) that need to be treated separately. The solutions for all eleven cases are provided along with an apriori identification methodology for the determination of the applicable case, given the shear viscosity and wall slip parameters of the two viscoplastic fluids, the slit geometry and the flow conditions. Simplifications of the model would provide the solutions for the fully developed and isothermal coextrusion flows of any combination of Hershel-Bulkley, Bingham, power-law and Newtonian fluids with or without wall slip at one or both walls of the slit die. POLYM. ENG. SCI., 50:652-664, 2010. [C] 2009 Society of Plastics Engineers, INTRODUCTION Multilayered coextrusion involves the bringing together of two or more fluids (1) to generate layered products with structural distributions and ultimate properties that depend on the properties of the [...]

In this investigation, the flexible string algorithm (FSA), used before for inverse design of subsonic and supersonic ducts in compressible flows with and without normal shock, is developed and applied for inverse design of 2D incompressible viscous internal flow with and without separation. In the proposed method, the duct wall shape is changed under an algorithm based on deformation of a virtual flexible string in flow. At each modification step, the difference between current and target wall pressure distributions is applied to the string. The method is an iterative inverse design method and utilizes the analysis code for the flow field solution as a black-box. Some validation test cases and design examples are presented here, which show the robustness and flexibility of the method in handling complex geometries. In cases with separated flow pressure distribution, a unique solution for inverse design problem does not exist. The design algorithm is a physical and quick converging approach and can efficiently utilize commercial flow analysis software. [DOI: 10.1115/1.4001072] Keywords: inverse design, 2D ducts, viscous incompressible flows, flexible string algorithm

On the basis of the special tensile test results under various loading histories, the rate-dependent behaviors of three polymer geosynthetics due to their viscous properties have been investigated. All the investigated polymer geosynthetics show significant loading rate effects, creep deformation, and stress relaxation. Except for the polyester geogrid showing the combined viscosity, all the investigated polymer geosynthetics exhibit the isotach viscosity. An elasto-viscoplastic constitutive model described in a nonlinear three-component model framework is developed to simulate the rate-dependent behaviors of polymer geosynthetics. The developed constitutive model is verified by comparing its simulated results with the experimental data of polymer geosynthetics presented in this study and those available from the literature. The comparison indicates that the developed model can reasonably interpret the rate-dependent behaviors of polymer geosynthetics under arbitrary loading histories, including the step-changed strain rate loading, creep, and stress relaxation applied during otherwise mono-tonic loading (ML). POLYM. ENG. SCI., 50:550-560, 2010. [C] 2009 Society of Plastics Engineers, INTRODUCTION Polymer geosynthetics are increasingly used as reinforcements in many civil, geotechnical, and traffic engineering including retaining structures, roads, railroads, and airfields. The viscosity is viewed as a significant property [...]

Several magnetic force models were developed to interpret various phenomena of a soft ferromagnetic beam plate subjected to a uniform external magnetic field with different incident angles. In this paper, a new transverse magnetic force model for the interface between a ferromagnetic material and the air is derived with the continuation of magnetoelastic stress across the material boundary. It is noted that both the normal and the tangential components of magnetic field on the material boundary are considered in this model. By applying such a transverse magnetic force and the effect of magnetic viscous damping, a new theoretical model is constructed in this study to predict the natural frequency of a soft ferromagnetic beam plate placed in an in-plane magnetic field. The numerical results of the present study are displayed graphically and compared with the experimental data, which appeared in literature to assure the exactness of the present work. [DOI: 10.1115/1.3168602] Keywords: magnetic viscous damping, magnetic force model magnetoelasticity

Regular and Mach reflections of shock waves from the symmetry plane in a steady Mach 4 flow of a monatomic gas have been numerically studied with the use of the continuum (Navier--Stokes) and kinetic (direct simulation Monte Carlo) simulations. Results of the computations demonstrate a prominent effect of flow viscosity and heat conduction in the vicinity of the shock intersection, where the flow parameters depart from the values prescribed by the inviscid theoretical solutions. The reasons for these discrepancies are discussed.

A constitutive model for rate-dependent and thermomechanically coupled plasticity at finite strains is presented. The plasticity model is based on a [J.sub.2] model and rate-dependent behavior is included by use of a Perzyna-type formulation. Adiabatic heating effects are handled in a consistent way and not, as is a common assumption, through a constant conversion of the internal work rate into rate of heating. The conversion factor is instead derived from thermodynamic considerations. The stored energy is assumed to be a function of a single internal variable which differs from the effective plastic strain. This allows a thermodynamically consistent formulation to be obtained which, as shown, can be calibrated by use of simple procedures. Choosing 100Cr6 steel in two differently heat treated conditions as prototype material, experimental tests are performed, enabling the model to be calibrated. Significant differences in deformation behavior are noted as the differently heat treated specimens are compared. In addition, the local stress-updating procedure is reduced to a single scalar equation, permitting a very efficient numerical implementation of the model. The constitutive formulation proposed was employed in an explicit finite element solver, illustrative simulations of a high-velocity metal forming process being performed to demonstrate the capabilities of the model and certain characteristic traits of the materials that were studied. CE Database subject headings: Constitutive models; Viscoelasticity; Continuum mechanics; Experimentation; Deformation; Velocity.

An experimental study was conducted to identify the influence of the breakup regime on the droplet sizes produced by a splash-plate nozzle. Sprays formed by splash-plate atomizers were categorized according to the different types of breakup regimes of a spreading liquid sheet. Mean droplet sizes of various splash-plate nozzles were determined and they were correlated to liquid viscosity, nozzle diameter, and flow velocity. Various mixtures of corn syrup and water were used to obtain viscosities in the range of 1-140 mPa x s. Three different splash-plate nozzles of 0.5, 1, and 2 mm with a constant plate angle of 55 deg were tested. A phase Doppler particle analyzer was used to determine the droplet sizes generated at various operating conditions. The results indicated that the droplet-size correlations for a splash. plate atomizer depend on the liquid-sheet breakup regime. The effect of viscosity based on power-law correlation was changed by about 2 orders of magnitudes in the exponent when the breakup regime changed from the Rayleigh-Taylor instability regime with stable rim to the sheet perforation regime.

Viscous fibers, including [beta]-glucan in oat bran, favorably affect satiety as well as postprandial carbohydrate and lipid metabolism. However, effects of fiber viscosity on modulation of satiety-related gut hormone responses are largely unknown. We examined the effects of modified oat bran, with or without its natural viscosity, on sensations of appetite and satiety-related gastrointestinal (GI) hormone responses to establish the relevance of viscosity of [beta]-glucan in oat bran. Twenty healthy, normal-weight participants (16 female, 4 male, aged 22.6 [+ or -] 0.7 y) ingested 2 isocaloric (1250 kJ) 300-mL oat bran beverages with low or high viscosity (carbohydrates, 57.9 g; protein, 7.8 g; fat, 3.3 g; fiber, 10.2 g) after a 12-h fast in randomized order. Viscosity of the low-viscosity oat bran beverage was reduced by [beta]-glucanase treatment. Blood samples were drawn before and 15, 30, 45, 60, 90, 120, and 180 min after beverage consumption. The oat bran beverage with low viscosity induced a greater postprandial increase in satiety (P = 0.048) and plasma glucose (P < 0.001 ), insulin (P = 0.008), cholecystokinin (P = 0.035), glucagon-like peptide 1 (P = 0.037), and peptide YY (P = 0.051) and a greater decrease in postprandial ghrelin (P = 0.009) than the beverage with high-viscosity oat bran. Gastric emptying as measured by paracetamol absorption was also faster (P = 0.034) after low-viscosity oat bran beverage consumption. In conclusion, viscosity differences in oat [beta]-glucan in a liquid meal with identical chemical composition strongly influenced not only glucose and insulin responses, but also short-term gut hormone responses, implying the importance of food structure in the modulation of postprandial satiety-related physiology.

The shape of a single Newtonian liquid drop moving freely under gravity in quiescent non-Newtonian liquid (visco-inelastic and visco-elastic) has been studied. Strong effect of fluid elasticity on the shape of Newtonian liquid drop has been observed. Based on experimental observations, a shape regime graph has been suitably modified for elastic fluids. Correlations have also been proposed for the prediction of eccentricity of the Newtonian liquid drop moving through a non-Newtonian visco-elastic liquid. [DOI: 10.1115/1.3054284] Keywords: drop shape, eccentricity, Newtonian-non-Newtonian liquid, visco-elastic fluid

Ferrofluids can be used to make deformable mirrors having highly interesting characteristics (e.g., extremely large strokes and low costs). Until recently, such mirrors were thought to be restricted to corrections of frequencies lower than 10 Hz, thus limiting their usefulness. We present counterintuitive results that demonstrate that the limiting operational frequency can be increased by increasing the viscosity of the ferrofluid. We tested the response of ferrofluids having viscosities as high as 494 cP, finding that they could allow an adaptive optics correction frequency as high as 900 Hz. We also demonstrate that we can counter the amplitude loss due to the high viscosity by overdriving the actuators. The overdriving technique combines high current, short duration pulses with ordinary driving step functions to deform the mirror. The integration of a FDM in a complete closed-loop adaptive optics system running at about 500 Hz thus appears to be a realistic goal in the near future. OCIS codes: 220.1000, 220.1080, 230.3810.

A homogeneous model for prediction of the longitudinal distributions of pressure, velocity, and void fraction for two-phase bubbly flow in horizontal pipes is presented. The mixture flow is described by a system of two nondimensional ordinary differential equations that can be integrated numerically to yield the distributions of the flow variables along the pipe. The viscosity of the two-phase mixture is assumed to vary with the void fraction according to a polynomial form. Experimental data were obtained for a range of air-water bubbly flow in a horizontal pipe. Prediction of pressure distributions along the pipe compares favorably with experimental data, while prediction of void fraction distributions can be achieved with moderate accuracy. [DOI: 10.1115/1.2953226] Keywords: bubbly flow, homogeneous model void fraction, pressure distribution, mixture viscosity

Rotation and curvature (RC) effects on turbulence are expected to impact losses and flow structure in turbomachines. This paper examines two recent eddy-viscosity-model corrections devised to account for these effects: the Spalart and Shur (1997, 'On the Sensitization of Turbulence Models to Rotation and Curvature,' Aerosp. Sci. Technol., 1(5), pp. 297-302) correction to the model of Spalart and Allmaras (1994, 'A One-Equation Turbulence Model for Aerodynamic Flows,' Rech. Aerosp., I, pp. 5-21) and the correction of Cazalbou et al. (2005, 'Two-Equation Modeling of Turbulent Rotating Flows,' Phys. Fluids., 17, p. 055110) to the (k, [epsilon]) model. The method of verification and validation is applied to assess the impact of these corrections on the computation of a centrifugal-compressor test case. First, a review of RC effects on turbulence as they apply to centrifugal compressors is made. The two corrected models are then presented. Second, the Radiver open test case (Ziegler K. U., Gallus, H. E., and Niehuis R., 2003, 'A Study on Impeller Diffuser Interaction Part 1: Influence on the Performance,' ASME J. Turbomach, 125, pp. 173-182) is used as a basis for the assessment of the two corrections. After a physical-consistency analysis, the Richardson extrapolation is applied to quantify the numerical errors involved in all the calculations. Finally, experimental data are used to perform validation for both global and local predictions. The consistency analysis shows that both corrections lead to significant changes in the turbulent field, in perfect agreement with the underlying theoretical considerations. The uncertainty analysis shows that the predictions of the global performances are more sensitive to grid refinement than they are to RC turbulence modeling. However, the opposite conclusion is drawn with regard to the prediction of some local flow properties: Improvements are obtained with the RC corrections, the best results being observed for the RC-corrected (k, [epsilon]) model. [DOI: 10.1115/1.2953231]

Quartz crystal impedance analysis has been developed as a technique to assess whether room-temperature ionic liquids are Newtonian fluids and as a small-volume method for determining the values of their viscosity-density product, p[eta]. Changes in the impedance spectrum of a 5-MHz fundamental frequency quartz corstal induced by a water-miscible room-temperature ionic liquid, 1-butyl-3-methylimiclazolium trifluoromethylsulfonate ([C4mim][OTf]), were measured. From coupled frequency shift and bandwidth changes as the concentration was varied from 0 to 100% ionic liquid, it was determined that this liquid provided a Newtonian response. A second water-immiscible ionic liquid, 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide [[C.sub.4]mim][NT[f.sub.2]], with concentration varied using methanol, was tested and also found to provide a Newtonian response. In both cases, the values of the square root of the viscosity--density product deduced from the small-volume quariz crystal technique were consistent with those measured using a viscometer and density meter. The third harmonic of the crystal was found to provide the closest agreement between the two measurement methods; the pure ionic liquids had the largest difference of ~10%. In addition, 18 pure ionic liquids were tested, and for 11 of these, good-quality frequency shift and bandwidth data were obtained; these 12 all had a Newtonian response. The frequency shift of the third harmonic was found to vary linearly with square root of viscosity-density product of the pure ionic liquids up to a value of [check]([rho][eta]) [approximately or equal to] 18 kg [m.sup.-2] [s.sup.-1/2], but with a slope 10% smaller than that predicted by the Kanazawa and Gordon equation. It is envisaged that the quartz costal technique could be used in a high-throughput microfluidic system for characterizing ionic liquids.

The deacetylation of xanthan increases the viscosity of xanthan and guar mixtures in dilute aqueous solutions. The intermolecular binding was observed between the disordered segments of xanthan and guar gum in aqueous solution.

An upper division undergraduate laboratory module to study Brownian motion was developed using polystyrene microspheres suspended in a sample liquid cell that was isolated from its surroundings. The dependence of the Brownian motion of the microspheres on their radius, the time, the viscosity of the suspension liquid, and the temperature were measured using a CCD camera interfaced with a frame grabber and a computer. The motion of each particle was monitored for 5 minutes and was found to be consistent with the Langevin formula for Brownian motion. [DOI: 10.1119/1.2386163]

When an armature slides between a pair of rails under the influence of Lorentz forces, the material at the interface will experience steep increase in temperature due to frictional and Joule heating. Experiments show condensed metal deposits on the rail, which indicates melting of the interface layer. As the temperature increases, the interface material progressively changes phase from solid to liquid and later ionizes to become a plasma. The charge transport from the rail to the armature has to occur through this layer and, hence, the magnetofluid mechanics (MFM) of this layer will affect essential railgun parameters, such as the inductance gradient. Initially, the armature will translate as a solid body. As an interface layer liquefies (and later becomes plasma), it will translate with the armature; it will also experience rotational motion through shear at the wall and through magnetic stirring by the j x B forces. The velocity field will influence the railgun through viscous dissipation and through V x B fields. In order to analyze and understand these phenomena, a model is proposed here. The armature is assumed to translate with an interface layer composed of aluminum liquid. A 1-D diffusing field with closed-form expressions for the magnetic potentials, fields, and current densities is imposed, enabling calculation of the accelerations and velocities of the armature. The secondary flow induced in the interface layer composed of liquid aluminum due to shear at the wall is calculated using MFM equations. The viscous dissipations are calculated and compared to Joule heating. Index Terms--Couette flow, magnetofluid dynamics, magnetofluid mechanics (MFM), rail-armature interface, viscous dissipation.

The effect of friction is analyzed to understand turbulence and temperature dependence of viscosity of the ideal working fluid and for this the optimal motion of a piston to complete a process in finite time is sought and the optimal motion is compared to a sinusoidal motion. Results reveal that in the externally dissipative mode optimizing power or frictional losses are equivalent, while in the internally dissipative mode the optimal motions are different.