Viscous Dissipation Term Research Articles

Emergence of magnetic flux from the convection zone into the corona

Numerical experiments of the emergence of magnetic flux from the uppermost layers of the solar interior to the photosphere and its further eruption into the low atmosphere and corona are carried out. We use idealized models for the initial stratification and magnetic field distribution below the photosphere similar to those used for multidimensional flux emergence experiments in the literature. The energy equation is adiabatic except for the inclusion of ohmic and viscous dissipation terms, which, however, become important only at interfaces and reconnection sites. Three-dimensional experiments for the eruption of magnetic flux both into an unmagnetized corona and into a corona with a preexisting ambient horizontal field are presented. The shocks preceding the rising plasma present the classical structure of nonlinear Lamb waves. The expansion of the matter when rising into the atmosphere takes place preferentially in the horizontal directions: a flattened (or oval) low plasma-β ball ensues, in which the field lines describe loops in the corona with increasing inclination away from the vertical as one goes toward the sides of the structure. Magnetograms and velocity field distributions on horizontal planes are presented simultaneously for the solar interior and various levels in the atmosphere. Since the background pressure and density drop over many orders of magnitude with increasing height, the adiabatic expansion of the rising plasma yields very low temperatures. To avoid this, the entropy of the rising fluid elements should be increased to the high values of the original atmosphere via heating mechanisms not included in the present numerical experiments. The eruption of magnetic flux into a corona with a preexisting magnetic field pointing in the horizontal direction yields a clear case of essentially three-dimensional reconnection when the upcoming and ambient field systems come into contact. The coronal ambient field is chosen at time perpendicular to the direction of the tube axis and thus, given the twist of the magnetic tube, almost anti-parallel to the field lines at the upper boundary of the rising plasma ball. A thin, dome-shaped current layer is formed at the interface between the two flux systems, in which ohmic dissipation and heating are taking place. The reconnection proceeds by merging successive layers on both sides of the reconnection site; however, this occurs not only at the cusp of the interface, but, also, gradually along its sides in the direction transverse to the ambient magnetic field. The topology of the magnetic field in the atmosphere is thereby modified: the reconnected field lines typically are part of the flanks of the tube below the photosphere but then join the ambient field system in the corona and reach the boundaries of the domain as horizontal field lines.

Aerodynamic Entropy Generation Rate in a Boundary Layer With High Free Stream Turbulence

Aerodynamic Entropy Generation Rate in a Boundary Layer With High Free Stream Turbulence

Exact Similarity Solutions of Coupled Nonsteady Navier--Stokes and Energy Equations in Liquids

Exact similarity solutions are obtained for coupled Navier--Stokes and energy equations that govern the time-dependent motion of a gravitation-free viscous liquid with variable density in one- and three-dimensional (1D and 3D) spaces. The 1D case deals with propagation and diffusion of an initial algebraic density hump C/x that is subjected to a constant flow rate at the origin. We demonstrate that the initial temperature distribution is convected without being diffused at very long times. We also demonstrate that two different propagation velocities exist for short and long times. The 3D case addresses the implosion of an insulated closed system with an initial radially symmetric algebraic density hump C/r3 . We demonstrate that if viscous dissipation and liquid compressibility terms are neglected in the energy equation, very strong shock-like pressure distributions may occur that may lead to a black hole within a finite time.A comprehensive analysis is also carried out for density fields with an initi...

EFFECTS OF ELECTRIC DOUBLE LAYER AND VISCOUS DISSIPATION IN MICROCAPILLARY

International Journal of Computational Engineering ScienceVol. 04, No. 02, pp. 243-248 (2003) BioMEMS and MicrofluidsNo AccessEFFECTS OF ELECTRIC DOUBLE LAYER AND VISCOUS DISSIPATION IN MICROCAPILLARYK. T. OOI, C. YANG, C. K. CHAI, T. N. WONG and P. H. ANGK. T. OOISchool of Mechanical and Production Engineering, Nanyang Technological University, Republic of Singapore 639798, Singapore Search for more papers by this author , C. YANGSchool of Mechanical and Production Engineering, Nanyang Technological University, Republic of Singapore 639798, Singapore Search for more papers by this author , C. K. CHAISchool of Mechanical and Production Engineering, Nanyang Technological University, Republic of Singapore 639798, Singapore Search for more papers by this author , T. N. WONGSchool of Mechanical and Production Engineering, Nanyang Technological University, Republic of Singapore 639798, Singapore Search for more papers by this author and P. H. ANGSchool of Mechanical and Production Engineering, Nanyang Technological University, Republic of Singapore 639798, Singapore Search for more papers by this author https://doi.org/10.1142/S1465876303000995Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractIn this study, effects of electric double layer (EDL) near the solid-liquid interface and viscous dissipation on pressure-driven liquid flow characteristics and heat transfer through a microcapillary are analyzed. As both effects were previously postulated to have certain contrary influences on flow characteristics, this analysis aims to study the interaction between the two effects via a control volume method based CFD technique. The Poisson-Boltzmann equation is used to describe EDL field near the channel wall. An additional body force due to the presence of EDL is considered in the Navier-Stokes equation. Temperature fields are explored via the energy equation with consideration of the viscous dissipation term. Variations of thermophysical properties are readily incorporated to induce a thorough observation of any coupling or adjoined effects from the two phenomena. Overall results demonstrate that in a short microchannel, when diameter decreases, EDL effects are significant, resulting in higher fluid temperature and friction, as well as reduced flow rate. Also, the effect increases with decreasing solution concentration. However, when channel length is long and flow rate is high, viscous dissipation effect dominates. It is concluded that in microchannel studies, the two effects are always present and contributing to the flow characteristics. References C. L. Rice and R. Whitehead, Journal of Physical Chemistry 69, 4017 (1965). Crossref, Google ScholarG. M. Mala, D. Li and J. D. Dale, International Journal of Heat and Mass Transfer 40, 3079 (1997). Crossref, Google ScholarG. M. Mala and D. Li, International Journal of Heat and Fluid Flow 20, 142 (1999). Crossref, Google ScholarC. Yang, D. Li and J. H. Masliyah, International Journal of Heat and Mass Transfer 41, 4229 (1998). Crossref, Google ScholarL. Ren, D. Li and W. Qu, Journal of Colloid and Interface Science 23, 12 (2001). Google ScholarH. C. Brinkman, Applied Scientific Research A2, 120 (1951). Google Scholar J.-W. Ou and K. C. Cheng, Viscous dissipation effects on thermal entrance heat transfer in laminar and turbulent pipe flows with uniform wall temperature, ASME Paper No. 74 (1974) HT-50 . Google Scholar S. K. Lim, Microtube flow characteristics, MEng thesis, Nanyang Technological University (2002) . Google Scholar G. M. Mala, Heat transfer and fluid flow in microchannels, Ph. D. Thesis, University of Alberta (1999) . Google Scholar R. B. Bird , W. E. Stewart and E. N. Lightfoot , Transport phenomena ( John Wiley & Sons , New York , 1960 ) . Google ScholarR. C. Weast, CRC handbook of chemistry and physics, 67th edn. (CRC Press, Inc, Boca Raton, Florida, 1986). Google Scholar R. J. Hunter , Principles and Applications ( Academic Press , New York , 1981 ) . Google Scholar S. V. Patankar , Computation of conduction and duct flow heat transfer ( Innovative Research, Inc , USA , 1991 ) . Google Scholar FiguresReferencesRelatedDetails Recommended Vol. 04, No. 02 Metrics History PDF download

Finite element solutions of heat transfer in molten polymer flow in tubes with viscous dissipation

This paper presents the results of finite element analysis of a heat transfer problem of flowing polymer melts in a tube with constant ambient temperature. The rheological behavior of the melt is described by a temperature dependent power-law model. A viscous dissipation term is included in the energy equation. Temperature profiles are obtained for different tube lengths and different entrance temperatures. The results are compared with some similar results in the literature.

A new model for viscous dissipation in porous media across a range of permeability values

In this paper a unified mathematical theory for the viscous dissipation term in the governing Brinkman equation is derived. This term has, unlike other models, the correct asymptotic behaviour in both the fully Darcy and Newtonian fluid flow limits.

Combined Free and Forced Convection in Vertical Channels of Porous Media

In this paper we investigate the combined free and forced convection of a fully developed Newtonian fluid within a vertical channel composed of porous media when viscous dissipation effects are taken into consideration. The flow is analysed in the region of a first critical Rayleigh number in order to interpret the multiple-valued solutions and discuss their validity. The governing fourth-order, ordinary differential equation, which contains the Darcy and the viscous dissipation terms, is solved analytically using perturbation techniques and numerically using D02HBF NAG Library. A detailed investigation of the governing O.D.E. is performed on both clear fluid and porous medium for various values of the viscous dissipation parameter, e, when the wall temperature decreases linearly with height, and the pressure gradient is both above and below its hydrostatic value. Although mathematically the results in all cases show that there are two solution branches, producing four possible solutions, the study of the velocity and buoyancy profiles together with the Darcy effect indicate that only one of the two solutions at any value of the Rayleigh number appears to be physically acceptable. It is shown that the effect of the Darcy number decreases as the critical Rayleigh numbers increase.

Numerical simulation of the high Reynolds number slit nozzle gas–particle jet using subgrid-scale coupling large eddy simulation

Large eddy simulation (LES) model in which the effect of the particle existence on subgrid-scale flows have been taken into account is proposed. The kinetic energy of the subgrid-scale flow to obtain a turbulent viscosity coefficient of the subgrid-scale flow in the LES has been calculated in assuming that the interaction terms between the gas and particles, the turbulent production term and the viscous dissipation term were balanced with each other in the kinetic energy equation of the subgrid-scale turbulent flow. Using this model, three-dimensional Navier–Stokes equations and the Lagrangian particle motion equations are simultaneously solved to describe the high Reynolds number ( Re=10 4) gas–particle jet flow and the effect of particle existence on it. The calculated results of air and particle turbulent characteristics which are mean velocity, turbulent intensity and Reynolds stress distributions are in good agreement with experimental data measured by a laser Doppler velocimeter. The existence of particles usually reduces the grid-scale turbulence in the high Reynolds number developed turbulent jet. On the other hand, the particle existence which is some kind of flow disturbance produces grid-scale fluctuations in the initial and the transitional regions of the jet and then it increases the air turbulent intensity. When particle size is much smaller than the grid size, the particle existence reduces the subgrid-scale turbulence. However, when the product of the gas and particle relative velocity and the particle concentration gradient is very large, the particle existence is able to increase the subgrid-scale turbulence.

Convective Flow and Heat Transfer in an Inclined Composite Porous Medium

An anallttical study of non-Darcian convective flow and heat transfer in an inclined composite porous medium is performed. The JIow is modeled using the Darcy* Lapwood-Brinkman equation. The viscous ancl Darcy dissipation terms are included in the energy equation. The goveming equations are coupled and nonlinear because ofthe inclusion qf dissipation terms and buoyancy force. The equations are solved using a straighforward perturbation method. The effects of various parameters such as porous paramater, inclination angle, Grashoff number, ratios of heights, permeabilities, and thennal conductivities are discussed.

Equivalent-circuit model for the thickness-shear mode resonator with a viscoelastic film near film resonance.

We derive a lumped-element, equivalent-circuit model for the thickness-shear mode (TSM) resonator with a viscoelastic film. This modified Butterworth-Van Dyke model includes in the motional branch a series LCR resonator, representing the quartz resonance, and a parallel LCR resonator, representing the film resonance. This model is valid in the vicinity of film resonance, which occurs when the acoustic phase shift across the film is an odd multiple of pi/2 rad. For low-loss films, this model accurately predicts the frequency changes and damping that arise at resonance and is a reasonable approximation away from resonance. Elements of the parallel LCR resonator are explicitly related to film properties and can be interpreted in terms of elastic energy storage and viscous power dissipation. The model leads to a simple graphical interpretation of the coupling between the quartz and film resonances and facilitates understanding of the resulting responses. These responses are compared with predictions from the transmission-line and Sauerbrey models.

Measurements of Turbulence Statistics and Energy Budgets in a Model Combustor

Simultaneous two-component laser-Doppler-velocimeter measurements were made in an axisymmetric sudden expansion to measure the flow properties of a confined, isothermal flow-field of a research dump combustor. Measurements of mean velocities, Reynolds stresses, and triple products were carried out at axial distances ranging from 0.38 H ( H=step height) to 18 H downstream of the dump plane. Detailed experimental data are provided to help in understanding the behavior of turbulent transport characteristics of the confined shear layer. Data from this study could be used to upgrade or evaluate advanced numerical codes used to predict complex turbulent flows. The turbulent kinetic energy terms (i.e. convection, diffusion, and production terms) were computed directly from the experimental data using central differences, while the viscous dissipation term was obtained from the energy balance equation. Detailed comparison of the present data with similar work shows that the general behavior of the flow-field and energy budget results are in excellent agreement. The shear-layer flow created by sudden expansion enhances combustor performance by serving as a turbulence generator mechanism.

Article

The unsteady flow and heat transfer of an electrically conducting, viscous, incompressible fluid bounded by two parallel nonconducting porous plates are studied taking the Hall effect into consideration. An external uniform magnetic field is applied normal to the plates, and the fluid motion is subjected to a constant pressure gradient and a uniform suction and injection. An analytical solution for the governing equations of motion is obtained and a numerical solution for the energy equation including the Joule and the viscous dissipation terms is developed. The effect of the Hall term on both the velocity and temperature distributions is examined.PACS No.: 47.70

Velocity measurements and turbulence statistics of a confined isothermal swirling flow

A two-component laser Doppler velocimeter was employed to measure the flow properties of a confined, isothermal, swirling flowfield in an axisymmetric sudden expansion research combustor. A free vortex swirler was used to stir the flow at the inlet of the combustor. Measurements of mean velocities, Reynolds normal and shear stresses, and triple products were carried out at axial distances ranging from 0.38 H (step height) to 18 H downstream of the swirler. Detailed experimental data are provided to help in the understanding of the behavior of swirling, recirculating, axisymmetric, and turbulent flows inside dump combustors. A balance of the turbulence energy equation has been performed in order to get a detailed insight into the turbulent shear layer behavior. The turbulent kinetic energy terms: production, diffusion, and convection terms were computed directly from the experimental data using central differences. The viscous dissipation term was obtained from the balance of the kinetic energy equation. The analysis of the data was successful in identifying the various areas of interest in the flowfield where different turbulent transport mechanisms dominate. In addition, the data from this study will be available for upgrading advanced numerical codes. The swirling flow streamlines data are compared with the simple dump flow and it is shown that swirl reduces the size of the corner recirculation region in addition to creating a central toroidial recirculation region. In summary, swirling enhances the production and distribution of turbulence energy in the combustor which, in turn, indicates thorough flow mixing and earlier flow recovery.

A finite element algorithm for the study of nonlinear standing waves

A finite element method (FEM) is presented for the study of nonlinear acoustic standing waves inside a chamber. The method is developed using the Galerkin–Bubnov weighted residual formulation and applied to solve the Lagrangian second-order wave equation, including thermal and viscous dissipation terms. A one-dimensional problem is studied in the frequency domain. Numerical data are compared with analytical results obtained by using a perturbation scheme for the cases of resonance and antiresonance in a rigid-walled tube with one-sided rigid or pressure release boundary condition. The FEM algorithm is shown to be well suited for the study of high-frequency standing wave fields in which the effect of absorption cannot be described by simple analytical expressions.

Thermal dispersion and viscous dissipation effects on non-darcy mixed convection in a fluid saturated porous medium

Mixed convection flow and heat transfer about an isothermal vertical wall embedded in a fluid saturated porous medium with uniform free stream velocity is considered and the effects of thermal dispersion and viscous dissipation in both aiding and opposing flows are analysed. Similarity solution is not possible due to the inclusion of the viscous dissipation term, series solution is obtained, first and second order effects of dissipation revealed that viscous dissipation lowers the heat transfer rate. Observations also revealed that the thermal dispersion effect enhances the heat transfer rate and the effect of viscous dissipation is observed to increase with increasing values of the dispersion parameter.

Thermal Aspects of a Novel Viscous Pump

We have previously introduced a novel method for pumping fluids via a viscous mechanism. The device essentially consists of a cylindrical rotor eccentrically placed in a channel, and it is suited for hauling highly viscous polymers in macroducts, or more common fluids in microducts. Under certain operating conditions, viscous dissipation can be important, and a significant attendant temperature rise can have adverse effects on the pump operation. For this reason, we have conducted a numerical experiment to characterize the associated phenomena. The coupled system of the two-dimensional Navier-Stokes equations, with temperature-dependent viscosity, and the energy equation, with viscous dissipation terms retained, are solved using a finite-volume method. Different types of thermal boundary conditions at the rotor-fluid interface are explored in the numerical scheme. An approximate theoretical model is also developed to analyze flow in the region between the rotor and the nearest plate (for small gaps). The results indicate that although the bulk temperature rise is minimal for typical microscale situations, significantly steep temperature gradients are observed in the region between the rotor and the nearest channel wall where the most intense shear stress occurs. For certain combinations of Re, Ec, and Pr, temperature rises along the channel wall of the order of 30 K were calculated. Moreover, for very small values of this gap, large errors in the computed flowrates and pumping power estimates can arise for large Brinkman numbers, if the effects of viscous dissipation are ignored. Furthermore, the existence of an optimum value of rotor position, such that the bulk velocity is a maximum, is demonstrated. These findings are significant, as they are indicative of trends associated with the flow of highly viscous polymeric liquids, where much larger temperature rises and their attendant degradation in performance are likely to occur.

Hall current effects on the velocity and temperature fields of an unsteady Hartmann flow

The unsteady flow and heat transfer of an electrically conducting, viscous, incompressible fluid bounded by two parallel nonconducting porous plates are studied taking the Hall effect into consideration. An external uniform magnetic field is applied normal to the plates, and the fluid motion is subjected to a constant pressure gradient and a uniform suction and injection. An analytical solution for the governing equations of motion is obtained and a numerical solution for the energy equation including the Joule and the viscous dissipation terms is developed. The effect of the Hall term on both the velocity and temperature distributions is examined.

Effect of viscous dissipation on the generation of shear flow at a plasma edge in the finite gyro-radius guiding center approximation

A numerical simulation is performed to study the effect of a viscous dissipation term on the generation of shear flow at a plasma edge in the guiding center approximation. The guiding center model includes the effects of finite Larmor radius corrections and polarization drift. The numerical code applies the method of fractional steps to the fluid guiding center equations. We attempt to discriminate between the smoothing of the microstructure by a small viscous dissipation term to control numerical instabilities, and the modification of the macroscopic physical results introduced by this small viscous dissipation term. The finite Larmor radius effect allows for a charge separation to exist, which can be further accentuated by the polarization drift. A difference in the viscous term between electrons and ions can add to the charge separation effect at the plasma edge, which can modify the physical results. The numerical calculation is effected using a slab model, periodic in one direction and finite in the other direction, with an inhomogeneous density of guiding centers to simulate a plasma edge. The evolution of the system shows the potential evolving to a shape characterized by the longest wavelength associated with the transverse dimension of the system, an evolution characteristic of an inverse cascade. We present an analysis of the effect of different values of the viscous term on the time evolution of this guiding center system, and on the formation and existence of a charge separation and an electric field at the edge of a plasma and the associated shear in the E × B flow.

Eigenfunction Spectrum Analysis for Self-Organization in Dissipative Solitons

An attractor of dissipative structures in solitons described by the Korteweg-de Vries (K-dV) equation with a viscous dissipation term is investigated, with the use of an eigenfunction spectrum analysis associated with the dissipative dynamical operator [Phys. Rev. E 49 (1994) 5546]. It is shown numerically and quantitatively that the basic procesess for the self-organization of dissipative soliton are spectrum transfer by nonlinear interaction and selective dissipation among the eigenmodes of the dissipative operator. It is quantitatively shown that an interchange between the dominant operators occurs during nonlinear self-organization processes, which leads to a final self-similar coherent structure uniquely determined by the dissipative operator.

HEAT TRANSFER to and TRANSPORT PROPERTIES of WHEAT GLUTEN IN A TUBULAR REACTOR

The design and modeling of a tubular reactor, similar to an extrusion rheometer, which accounts for reacting flow is described. A numerical study (finite differences) of heat transfer to a flowing and reacting biopolymer melt (wheat gluten), similar to extrusion processing, is described and compared to experimental data. the cylindrical wall is nonisothermal in the axial direction, but is adequately characterized by a third‐order polynomial determined experimentally. Convective and viscous dissipation terms are included in the energy equation. the rheological behavior of the melt is described by a power law model, . The consistency coefficient pre‐exponential, m0, is 530,000–2,100,000 Pa‐secn and the power law exponent or flow index, n, is 0.38–0.65 for a 25–30% moisture content range and a 110–209 C temperature range. the flow index decreases with increasing conversion due to polymerization reactions occurring at elevated temperatures. Flow curves, bulk temperatures, and temperature profiles are presented for a variety of cylinder wall temperatures and biopolymer moisture contents.