Viscous dissipation in plastic pipe extrusion

We study the temperature distribution of a power‐law fluid in a pressure‐driven axial flow between eccentric cylinders in bipolar cylindrical coordinates. We begin our analysis by writing the equation of energy in bipolar cylindrical coordinates. We then obtain a dimensionless algebraic analytic solution for temperature profiles under a steady, laminar, incompressible, and fully developed flow for an adiabatic core and an isothermal outer cylinder (Eq. 59 ). We find that the dimensionless temperature profile depends upon the radius ratio of the inner to outer cylinders, the eccentricity, the angular position, and the power‐law exponent n. The temperature is a strong function of the gap between the cylinders. Finally, dimensionless maximum temperatures are plotted to help pipe manufacturing engineers prevent excessive heating during production. POLYM. ENG. SCI., 53:2205–2218, 2013. © 2013 Society of Plastics Engineers     

NONSIMILAR SOLUTIONS FOR HEAT TRANSFER IN WALL JET FLOWS

An analysis is presented to investigate the flow and heat transfer characteristics of a laminar plane wall jet with non-isothermal wall as well as uniform suction and blowing at the surface and a laminar cylindrical wall jet. The approach used is local nonsimilarity method, wherein, the nonsimilanty terms appearing in the momentum and energy equations are retained and simplifications are introduced only in the auxiliary system of equations. To insure the accuracy of the results, solutions are obtained for three levels of truncation of the governing equations. For the case of plane wall jet problem, both a series solution as well as local nonsimilarity solution have been given and the agreement between the two is found to be very good. For the cylindrical wall jet problem, the results obtained by the local nonsimilarity approach in the present paper have been compared with the series solution results. Numerical results for the wall shear stress, velocity distribution, wall heat transfer rate and temperature field are presented.     

Experimental and Numerical Study of the Effect of an Electric Field on a Bunsen-type Flame

The effect of an electric field on the behavior of premixed methane-air flames has been studied. A candle-type flame has been observed experimentally and analyzed for its geometrical proportions under an electric field. A numerical model has been developed to explain some of the experimental observations. The model employs a two-dimensional cylindrical coordinate system and assumes axial symmetry. The mass, momentum, species, and energy conservation equations are solved by an integrated version of the PHOENICS and CHEMKIN computer codes. It is concluded that the effect of the electric field on the flame behavior is mainly due to ionic wind effects.     

INTERFACIAL TRANSPORT PHENOMENA INVITED REVIEW

Interfacial transport phenomena include all effects associated with momentum, energy, and mass transfer at phase interfaces.

I shall begin by examining the nature of the phase interface and associated common lines. I then will develop the general balance equations at each point within a phase, at each point on a dividing surface, and at each point on a common line. Mass conservation, momentum transfer, energy transfer, and mass transfer are treated as special cases.     

Unsteady coupled high flux-mass and momentum transfer with a moving boundary

The simultaneous transient developing mass and momentum boundary layers in a moving-wall (Stefan) problem resulting from the flow of a fluid through a channel with dissolving walls is determined. Two effects which influence the course of the problem are considered: a flux induced velocity, referred to as the Stefan-Nusselt effect, characterized by a parameter called the potential ratio and a velocity due to the density difference between the phases, superimposed on the Stefan-Nusselt velocity, and characterized by a parameter called the density ratio. The changing geometric confines of the problem requires the introduction of a mobile coordinate system in lieu of the conventional Eulerian coordinate system. No known solution by previous authors have considered both these effects in a mobile coordinate system.The boundary equations, considering these effects, are developed in vector form for a wall which is skewed to the coordinates of a conventional x, y coordinate system. The general diffusion equation in terms of moving coordinates is derived from basic principles and shown to contain additional terms which are not obtainable by a chain-rule conversion. The additional terms cancel out in differential form but must be included in finite difference form to ensure conservation. The problem is then solved by finite differences using the vorticity-stream function method.A non-dimensional flux is defined and plots showing the variation of the non-dimensional flux, mass concentration, vorticity and velocity as well as the shape of the channel wall with the governing parameters—Re, Sc, the potential ratio, and the ratio of solid to fluid density are shown as a function of time and distance. The influence of the parameters are discussed.A wave-wall effect, which occurred in some of the problems, is described.The mathematical techniques developed are applicable to solving a class of problems which have heretofore received scanty attention, namely problems in which the important consideration is the shape of the domain for the desired or optimum potential distribution. Moving-wall, separation flow, explosion propagation and free surface problems are in this class.     

INTERFACIAL TRANSPORT PHENOMENA INVITED REVIEW

Interfacial transport phenomena include all effects associated with momentum, energy, and mass transfer at phase interfaces.

I shall begin by examining the nature of the phase interface and associated common lines. I then will develop the general balance equations at each point within a phase, at each point on a dividing surface, and at each point on a common line. Mass conservation, momentum transfer, energy transfer, and mass transfer are treated as special cases.     

Modélisation numérique du transfert de matière dans un écoulement annulaire faiblement tourbillonnaire non-entretenu

Mass transfer and hydrodynamics in a laminar swirling flow induced by a tangential inlet in a cylindrical annulus was investigated. The simplified version of the momentum and convection-diffusion equations using the boundary layer theory, was resolved by an implicit finite difference method. Although the proposed method cannot be applied to vortex flows and recirculating phenomena, the present work identified a relevant problem about the validity of the boundary layer theory for the mass transfer determination at high Schmidt numbers.     

Coupled heat and mass transport phenomena in siliceous aggregate concrete slabs subjected to fire

A mathematical and computational model simulating the coupled heat and mass transfer and related processes in porous media exposed to elevated temperatures has been developed. Taking into account the conservation of mass, momentum and energy, and including the effects of evaporation and dehydration processes on the transport phenomena, a set of three coupled nonlinear differential equations is obtained. Siliceous aggregate concrete slabs subjected to the ASTM E119 standard fire exposure are modeled and validated against test data. Output depicts the coupled relationships between the material's temperature, moisture content, and pore pressure histories and distributions. © 1997 John Wiley & Sons, Ltd.     

MATHEMATICAL MODELING OF HEAT AND MASS TRANSFER IN HOT GAS SPRAY SYSTEMS

A mathematical model is developed to study simultaneous heat and mass transfer in hot gas spray systems. The model is obtained by writing mass, energy, and momentum balances for both continuous and discontinuous phases. Governing equations along with suitable correlations for heat and mass transfer coefficients have been solved numerically. In order to develop a realistic model for such complicated systems, a droplet size distribution was implemented in the model instead of using an average size. A steady state spray-cooling problem is analyzed to illustrate the applicability of the model. To validate the mathematical model for this case, necessary data was collected and measured in commercial cement plants. A good agreement between plant data and the model was noticed in general, and results obtained from the model indicate that size distribution of water droplets and physical dimensions of the spray-cooling system are important parameters. This model is very useful in determining the so-called "critical operation condition" at which sludge formation at the bottom of spray-cooling systems will happen. The predicted parameters in spray-cooling systems both for droplet phase and gas phase aptly illustrate the ability of the model to treat the complex phenomena associated with two-phase flows.     

Mathematical modeling of heat and mass transfer in hot gas spray systems

A mathematical model is developed to study simultaneous heat and mass transfer in hot gas spray systems. The model is obtained by writing mass, energy, and momentum balances for both continuous and discontinuous phases. Governing equations along with suitable correlations for heat and mass transfer coefficients have been solved numerically. In order to develop a realistic model for such complicated systems, a droplet size distribution was implemented in the model instead of using an average size. A steady state spray-cooling problem is analyzed to illustrate the applicability of the model. To validate the mathematical model for this case, necessary data was collected and measured in commercial cement plants. A good agreement between plant data and the model was noticed in general, and results obtained from the model indicate that size distribution of water droplets and physical dimensions of the spray-cooling system are important parameters. This model is very useful in determining the so-called "critical operation condition" at which sludge formation at the bottom of spray-cooling systems will happen. The predicted parameters in spray-cooling systems both for droplet phase and gas phase aptly illustrate the ability of the model to treat the complex phenomena associated with two-phase flows.     

TREATMENT OF THE NONEQUILIBRIUM VAPOR MOTION NEAR AN EVAPORATING INTERPHASE BOUNDARY

Strong evaporation problems are characterized by the nonequilibrium vapor motion near the interphase boundary. The solution of this nonequilibrium region, known as Knudsen layer, requires the use of kinetic theory. Kinetic equations have been solved numerically for a plane evaporation problem. Numerical solutions have led to the establishment or the validity of a simple kinetic theory approach to calculate the jump conditions across the Knudsen layer and the net mass, momentum, and heat fluxes. This approach can be used together with the conventional continuum method to calculate How parameters at the outer edge of the Knudsen layer for heat transfer problems in which evaporation occurs at the interphase boundary.     

Hopf bifurcation and solution multiplicity in a model for destabilized Bridgman crystal growth

Flow instabilities are analyzed within a destabilized vertical Bridgman crystal growth system, first studied experimentally by Kim et al. (J. Electrochem. Soc. 119(1972) 1218), using a distributed-parameter model consisting of balance equations for energy and momentum transport. Numerical solution of the governing equations via a Galerkin finite element method reveals multiple operating states and dynamic phenomena. Bifurcation analysis shows that the onset of time-periodic flows occurs in the model system via a supercritical Hopf bifurcation, consistent with prior experimental observations on the dynamics of flow in similar systems.     

A comprehensive CFD model of anode-supported solid oxide fuel cells

The two-dimensional comprehensive CFD model of anode-supported SOFCs operating at intermediate temperature has been presented. This model provides transport phenomena of gas species with electrochemical characteristics and micro-structural properties, and predicts SOFC performance. The mathematical model solves conservation of electrons and ions, continuity equation, conservation of momentum, conservation of mass, and conservation of energy. A continuum micro-scale model based on statistical properties together with a mole-based conservation model was employed. CFD technique was used to solve the set of governing equations. The cell performance was decomposed with contributions of each overpotential and was presented at several operating temperatures with analysis of effective diffusivity. It was found that the contribution of potential gain due to temperature rising was considerably high. However it became non-significant at high operating temperature due to decreasing of effective diffusivity in AFL. These results showed that the performance and the distributions of current density, overpotentials, and mole fractions of gas species have a strong dependence upon temperature. From these results, it was concluded that the conservation of energy should be accommodated in comprehensive SOFC model. Also the useful information for the effect of parameters on cell performance and transport phenomena was provided.     

Effect of Blockage on Heat Transfer Phenomena of Spheroid Particles at Moderate Reynolds and Prandtl Numbers

Effects of the confining wall or blockage on the heat transfer phenomena of spheroid particles were numerically investigated. The heated spheroid particles were maintained at constant temperature and allowed to sediment in cylindrical tubes filled with Newtonian liquids. In this flow configuration, the heat transfer took place from the heated spheroid particles to the surrounding Newtonian liquid. The governing conservation equations of the mass, momentum, and energy together with appropriate boundary conditions were numerically solved using commercial software based on computational fluid dynamics. A simple correlation for the average Nusselt number of the confined spheroid particles was developed which can be applied in new applications.     

A practical approach to dynamic simulation of two-phase systems

A general method is presented for the dynamic simulation of two-phase flow systems. The analysis is based on the cross section averaged form of the mass, energy and momentum conservation laws. In order to predict the bulk dynamics and to avoid numerical difficulties a quasi-steady-state assumption is used in formulating the overall mass and momentum balances. For the wall shear stress and the void fraction, empirical correlations are used. In each computational step the pressure distribution is predicted solving an ordinary boundary value problem; then, we solve the non-steady enthalpy balances. The method is applied to simulate forced convection flow-boiling phenomena in a furnace.     

Investigation of flow structures and transport phenomena in bubble columns using particle image velocimetry and miniature pressure sensors

The bubble column reactors are usually operated in a heterogeneous regime where the liquid phase turbulence is generated by the bubble motion and the velocity gradients in the mean motion. The turbulent flow comprises of fluid elements moving in a random fashion with different sizes and energies, called ‘flow structures’. Both the large and small scale flow structures within a reactor play an important role in governing the local momentum, heat and mass transfer. The current work is focused on the estimation of the time averaged flow pattern and flow structures. The experimental data has been collected using miniature pressure sensors, PIV+shadowgraphy and LDA. The data was subjected/analyzed to/with multipoint linear stochastic estimation (MLSE), wavelet transforms, image processing and eddy isolation (EIM) to identify the flow structures. Two bubble columns have been used: a narrow rectangular (2D) column and a cylindrical (3D) column. Wavelet transforms (WT) were applied to isolate individual structures from PIV data to get their shape, size and energy in the 2D column. MLSE has been used to obtain the velocity profiles from pressure fluctuation signals. This data, augmented by PIV and LDA data, is subjected to WT and EIM to get the eddy age and its energy distribution. The data of the eddy shape size and energy was used to predict the mass transfer coefficient in the cylindrical bubble column as a test case. Overall, in this work we present a methodology to utilize the experimental data to get a better insight of the dynamics of flow structures, and propose a path forward for the deeper understanding of transport phenomena in bubble columns.     

Forced convection heat transfer to a power-law fluid in arbitrary cross-section ducts

A numerical method is developed to predict the three-dimensional forced convection laminar incompressible flow of a power law fluid in arbitrary cross-section straight ducts. The continuity equation and boundary layer forms of the energy and momentum equations in rectangular coordinates are transformed into new orthogonal coordinates with boundaries coinciding with the coordinate surfaces. The resulting equations are solved using the finite difference technique. The numerical scheme is capable of handling different hydrodynamic and thermal entry boundary conditions but results are only presented for uniform inlet velocity and temperature profiles and isothermal wall. To demonstrate the wider applicability of the method local heat transfer coefficients and pressure drop in square, trapezoidal and regular pentagonal ducts are computed as functions of pertinent thermal and hydrodynamic parameters.     

A Multiphase Model to Analyze Transport Phenomena in Food Drying Processes

The aim of the present work is the development of a theoretical model describing the transport phenomena involved in food drying. A fundamental multiphase approach was utilized to account for the simultaneous presence of both liquid water and vapor within the sample undergoing drying. The transport equations referred to the food were coupled, by a proper set of boundary conditions, to momentum and heat and mass transfer equations referred to the drying air, thus obtaining a general model that did not rely on the specification of any heat and mass transfer coefficient at the food/air interfaces.     

A comprehensive model of functionals for three-dimensional non-isothermal steady flow with molecular and convective diffusion and a chemical reaction of arbitrary order

A mathematical model of diffusion-reaction, velocity and temperature functionals is developed using the calculus of variation and the concept of “local potential”. The diffusion-reaction functional, which involves both molecular and convective diffusion, describes the general case of three-dimensional steady-state diffusion of a single component with a chemical reaction of arbitrary order and complexity while the velocity and temperature functionals cover viscosity, pressure, convection and heat generation terms. The functionals have the feature of being minimum at the stationary state and can, therefore, be minimized and solved for velocity, temperature and concentration. An important feature of the present formulation for the diffusion-reaction problem is that the reaction term is linearized during the course of solution. Such linearization is inherent in the present formulation and makes the functional applicable to reactions of any type and complexity. Furthermore, the convective terms for both diffusion and heat transfer and the viscous and reaction generation terms in the energy equation are also linear and can be handled with relative ease in any numerical solution. The functionals are verified by yielding, upon minimization, the appropriate diffusion-reaction, momentum, continuity and energy equations as their Euler-Lagrange equations. Finally, the developed functionals are independent of the coordinate system and can be applied in any appropriate system of coordinates chosen for convenience.