Constant Physical Properties Research Articles

Numerical modeling of coupled phenomena in a mechanically stirred molten-glass bath heated by induction

A mechanically stirred molten-glass bath heated by direct induction in a cold crucible was numerically modeled. The aim of the study was to develop numerical tools to understand thermal, hydrodynamic and electromagnetic phenomena that occur in the bath. Models and coupling between these phenomena are described. This coupling and the high content of elements in the 3D mesh result in a long calculation time. The study demonstrates how to couple programs to yield the highest degree of accuracy in the shortest calculation time possible. Numerical studies are also used to characterize the fluid dynamic behavior and heat transfer in an industrial-size tank. Classical correlations commonly used to characterize stirrer efficiency and heat transfer for fluids with constant physical properties were adapted for molten glass. The power number N p and the Nusselt number Nu are used as macroscopic indicators. The results of these global studies will be useful for the operation and optimization of the vitrification facilities.

Mixed Convection in an Enclosure with Different Inlet and Exit Configurations

A numerical analysis is carried out to study the performance of mixed convection in a rectangular enclosure. Four different placement configurations of the inlet and outlet openings were considered. A constant flux heat source strip is flush-mounted on the vertical surface, modeling an integrated circuit chips affixed to a printed circuit board, and the fluid considered is air. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh elements by a nonlinear parametric solution algorithm. Results are obtained for a range of Richardson number from 0 to 10 at Pr = 0.71 and Re = 100 with constant physical properties. At the outlet of the computational domain a convective boundary condition (CBC) is used. The results indicate that the average Nusselt number and the dimensionless surface temperature on the heat source strongly depend on the positioning of the inlet and outlet. The basic nature of the resulting interaction between the forced external air stream and the buoyancy-driven flow by the heat source is explained by the heat transfer coefficient and the patterns of the streamlines, velocity vectors and isotherms.

Thermal storage and nonlinear heat-transfer characteristics of PCM wallboard

For the materials with constant thermophysical properties, the thermal performance of wallboards (or floor, ceiling) can be described by decrement factor f and time lag φ. However, the phase change material (PCM) may charge large heat during the melting process and discharge large heat during the freezing process, which takes place at some certain temperature or a narrow temperature range. The behavior deviates a lot from the material with constant thermal physical properties. Therefore, it is not reasonable to analyze the thermal performance of PCM wallboard by using the decrement factor f and time lag φ. How to simply and effectively analyze the thermal performance of a PCM wallboard is an important problem. In order to analyze and evaluate the energy-efficient effects of the PCM wallboard and floor, two new parameters, i.e., modifying factor of the inner surface heat flux ‘ α’ and ratio of the thermal storage ‘ b’, are put forward. They can describe the thermal performance of PCM external and internal walls, respectively. The analysis and simulation methods are both applied to investigate the effects of different PCM thermophysical properties (heat of fusion H m, melting temperature T m and thermal conductivity k) on the thermal performance of PCM wallboard for the residential buildings. The results show that the PCM external wall can save more energy by increasing H m, decreasing k and selecting proper T m ( α < 1); that the PCM internal wall can save more energy by increasing H m and selecting appropriate T m, k. The most energy-efficient approach of applying PCM in a solar house is to apply it in its internal wall.

A generalised mean temperature difference method for thermal design of heat exchangers

A Generalised Mean Temperature Difference (GMTD) method instead of the Logarithmic Mean Temperature Difference (LMTD) method for heat exchangers is proposed. Unlike the LMTD method, the GMTD method allows the performance analysis of heat exchangers with distributed physical properties. GMTD is calculated by a new method to take fluid temperature profiles as a function of heat load. Mathematical proof is made that the formula of the LMTD can be derived from that of the GMTD, in the case of constant physical property. The GMTD method is applied to experiments of a hot water supplier with supercritical carbon dioxide as a heating media that works through its pseudo-critical point where specific heat behaves anomalously. The empirical correlations of the local Nusselt number and pressure loss coefficient based on the GMTD gives an accurate prediction of the overall heat transfer coefficient, with a 5% error rating, whilst an error two times larger appears in the case of the LMTD.

Modeling Temperature-Dependent Properties of Water via Response Modeling Methodology (RMM) and Comparison with Acceptable Models

Response Modeling Methodology (RMM) is a new empirical modeling methodology, recently developed. In this paper, a new structured procedure to compare relational models, in terms of goodness-of-fit and stability, is developed and applied to evaluate three types of models: Those obtained by TableCurve2D (a dedicated software for relational modeling), acceptable models recommended by DIPPR (a widely used database for constant and temperature-dependent physical properties), and models derived by RMM. For four pure substances (oxygen, argon, nitrogen, and water), model comparison had been conducted on 14 temperature-dependent physical and thermodynamic properties. Summary tables of ranking the various models are provided. Detailed results are reported in this paper for water. The three variations of the RMM model (two-, three- and four-parameter models) compare favorably with others, both in terms of goodness-of-fit and stability. The unique desirable properties of RMM models are discussed.

Boundary-layer model of mantle plumes with thermal and chemical diffusion and buoyancy

SUMMARY We present a boundary-layer model for mantle plumes driven by thermal and chemical diffusion and buoyancy. The problem is solved for a Boussinesq, Newtonian fluid with infinite Prandtl number and constant physical properties. We focus on axisymmetric mantle plumes, but also solve 2-D plumes due to line-sources for comparison. The results show that chemical plumes are much thinner than thermal plumes because of small chemical diffusivity in the mantle. When pressure-release partial melting occurs in a thermal-chemical plume, at least two mantle components may be involved: one from the chemical plume and one from the ambient mantle. A buoyant chemical boundary layer in the plume source region tends to cause narrow and strong plumes. A dense chemical source would have the opposite effect. The effects of chemical buoyancy diminish as the Lewis number, the ratio of thermal to chemical diffusivity, increases. For fully developed mantle plumes, the effects of chemical buoyancy may be insignificant. The physical parameters of mantle plumes may be estimated using surface information deduced from swell models. The total heat input from the Hawaiian plume source is about 1.3 x lo1' W, nearly 5-10 per cent of the total heat loss from the core. The depth of the Hawaiian plume source is constrained to be near the core-mantle boundary. Our results show that 2-D plumes are generally stronger than axisymmetric plumes.

A Numerical Computation of Heat and Fluid Flow in L-Shaped Curved Channels

A numerical analysis of steady, hydrodynamically and thermally fully developed, incompressible laminar flow with constant physical properties is presented. Two different geometrical cases of L-shaped channels are considered: right-curved and left-curved. The solution of the discretized continuity, momentum, and energy equations was obtained by using an elliptic Fortran program based on the SIMPLE algorithm. Solutions are obtained for Dean number ranges from 4.1 to 210.6 with dimensionless radius of curvature of 100, and Prandtl number of 0.7. The secondary flow streamlines, the isotherms, average Nusselt numbers, and friction factors are presented depending on Dean number and L-shaped channel orientation. As a result, it is observed that the secondary flows resulting from centrifugal forces change the distribution of the velocity and the temperature fields. In addition, it is determined that channel orientation has a profound effect on the flow and temperature fields.

Steady-state performance of a two-phase natural circulation loop

Using both HEM and TEDFM the steady-state behaviour of a rectangular uniform cross section two-phase closed NCL has been studied through one-dimensional approach. Uniform heat flux for heating as well as cooling has been considered along with the constant physical properties, uniform pressure inside the loop and water-steam as the working fluid. For the given operating range and loop geometry, the circulation velocity lies in the turbulent regime. The flow rate monotonically increases with the loop height. However, with heat flux it initially increases, reaches maximum and then falls. This implies that the surface heat flux should match the loop geometry and other operating parameters to produce the maximum flow rate. It has also been observed that the cooling and heating lengths and the temperature of the liquid at the entry of the heating section have to be selected optimally to generate the maximum mass flow rate.

Ideal thermophysical properties for free-cooling (or heating) buildings with constant thermal physical property material

Free-cooling is understood as a means to store outdoors coolness during the night, to supply indoors cooling during the day in summer, while free-heating is understood as a means to store the solar radiation during daytime, to supply indoors heating during the night in winter. In principle, free-cooling or free-heating can make the indoor air temperature in the comfortable region all the year if the thermophysical properties of building envelope material are in the desired range (defined as ideal thermophysical properties in this paper). Those properties are obviously related to the outdoor climate condition, internal heat source intensity, building configuration, ventilation mode etc. For a given region and a given building, the critical values of those ideal thermal physical properties can be determined through modeling and simulation. Two parameters, I win and I sum, are defined to describe the overcool degree in winter and the overheat degree in summer, respectively. To illustrate, the critical values of thermophysical properties of building envelope of a building located in Beijing are obtained through modeling and simulation. The simulated results are validated with experiments. The model, the methodology and the results are helpful for selection of suitable building envelope materials and for design of energy efficient buildings.

Heat transfer in laminar flow of non-Newtonian fluids in ducts of elliptical section

Laminar forced convection inside tubes of various cross-section shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumption used in this work is a laminar flow of a power flow inside elliptical tube, under a boundary condition of first kind with constant physical properties and negligible axial heat diffusion (high Peclet number). To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as Sturm–Liouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number and the average Nusselt number for various cross-section aspect ratios.

Liquid crystalline behaviour of N-cetyl N, N, N,-trimethyl ammonium bromide: An experimental study

Ultrasonic velocity, dielectric constant, specific conductance, viscosity, density and other related physical properties of a lyotropic liquid crystal namely N-cetyl N, N, N-trimethyl ammonium bromide (CTAB) in aqueous solution at various compositions have been studied. Solutions of different concentrations of CTAB in NaCl have been prepared. The change in miceller aggregation of the liquid crystal is indicated by the variation in the physical parameters within a range of concentration. Results have been used to elucidate the liquid crystalline behaviour of the compound in the solution.

Coolant film flow over the edge of a nozzle in a rarefied gas

The flow of a thin liquid film over the nozzle wall under the action of tangential friction and pressure gradient is considered. For the slow flow of the film with constant thermal physical properties, analytical dependences of the film thickness and temperature at the interface on the coordinate along the nozzle edge are derived. The flow of the film over the variable-curvature nozzle edge when the gas expands into vacuum is considered. At the initial section of the curvilinear edge, the film thickness increases in inverse proportion to the root of the friction stress at the interface. Near the end point of the nozzle, the film thickens drastically because of a decrease in the friction and, consequently, the curvature of the interface diminishes. As a result, the deceleration of the liquid by the Laplace pressure gradient drops, which causes an additional sharp growth of the thickness of the film with the possibility of its dynamic and thermal disintegration and, eventually, contamination of the spacecraft surface.

Improved formulation of electron kinetic theory approach for laser ultra-short-pulse heating

The formulation of energy transport in electron and lattice sub-systems due to the laser ultra-short-pulse heating of metallic surface is carried out using an electron kinetic theory model. The rate of electron energy gain from the irradiated field and its dissipation through the collisional process are taken into account in the analysis. The constant and variable physical properties are introduced in the numerical simulations. The two-equation and electron kinetic theory models formulated previously are also employed for the comparison purposes. It is found that the improved electron kinetic theory formulation predicts relatively lower lattice site temperatures as compared to the two-equation and electron kinetic theory models formulated previously. The results of the improved formulation is similar to that obtained for the hyperbolic heating model.

FORCE ON A DROPLET IN ANOTHER LIQUID WITH ARBITRARY ARRANGEMENT OF THE GRAVITY AND THERMAL GRADIENT

The steady-state force on the droplet released in another liquid subjected to the gravitational field and imposed thermal gradient in the case of vanishingly small Re and Ma is derived using the general solution given by Lamb. A solution to a transitional thermocapillary-type droplet migration is thereby obtained for the case of constant physical properties, which corresponds to the well known YGB result as t → ∞. These can be employed to investigate the interactions between droplets in a host solution under the gravitational and thermal influences, and further to explore deposition and migration of a droplet cluster in the corresponding fields.

Numerical simulation of laminar natural convection in a laterally heated vertical cylindrical enclosure: application to crystal growth

Laminar natural convection has been studied in a laterally heated vertical cylindrical enclosure with a free insulated surface and a centrally located constant temperature wall at the top. These conditions are a simplification of the conditions existing in a Czochralski crystal pulling system. The laminar, axisymmetric flow of a Newtonian, constant physical properties fluid under Boussinesq’s approximation has been considered. Governing equations in primitive variable form are solved numerically by control volume method. SIMPLE algorithm due to Patankar has been used for the numerical simulation. The effects of the constant wall heat flux boundary condition at the side wall have been investigated whereas the bottom wall is considered to be insulated. Streamlines and isotherms are presented for various Rayleigh numbers and Prandtl numbers. Heat flux vectors through the melt are plotted for selected cases. The axial velocity and temperature variations at different horizontal sections of the crucible have been presented graphically to explain the transport processes inside the crucible. It has been observed that in case of low Pr and high Ra, flow separation occurs at the vertical wall of the crucible which leads to an oscillatory flow as Ra increases. The investigation has been extended to the oscillatory regime of flow in the zone of supercritical Rayleigh numbers and some unsteady results are also presented. Finally a heat transfer correlation has been developed for steady-state case.

ポリオールプロセスを用いたＬ１０‐ＦｅＰｔナノ粒子直接合成における添加剤効果

Partially ordered L10-FePt nanoparticles synthesized in tetraethylene glycol by using polyol process is mostly polycrystalline in nature. In this paper, we attempted the preparation of single crystal L10-FePt nanoparticles by introducing nucleating and complexing agents during the synthesis. Though the synthesis of L10-FePt particles with constant physical properties was possible by using hexachloroplatinate (H2PtCl6) as the nucleating agent, particles remained polycrystalline in nature. However, when carboxylic acid was used along with H2PtCl6 FePt nanoparticles with more than 50 % ordering was realized under the optimum experimental conditions of Fe:Pt initial mole ratio of 52.5:47.5, 1 at% H2PtCl6 and five equivalent weight of Fe of carboxylic acid. The superlattice reflection lines of (001) and (110) in XRD pattern and the sextets from the Mossbauer spectroscopy at room temperature confirmed the presence of L10 phase. The coercivity and anisotropy field of these particles were 5. 6 kOe and more than 40 kOe, respectively.

Thermally Developing Forced Convection of Non-Newtonian Fluids Inside Elliptical Ducts

Laminar-forced convection inside tubes of various cross-section shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumptions used in this work are a non-Newtonian fluid, laminar flow, constant physical properties, and negligible axial heat diffusion (high Peclet number). Most of the previous research in elliptical ducts deal mainly with aspects of fully developed laminar flow forced convection, such as velocity profile, maximum velocity, pressure drop, and heat transfer quantities. In this work, we examine heat transfer in a hydrodynamically developed, thermally developing laminar forced convection flow of fluid inside an elliptical tube under a second kind of a boundary condition. To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as Sturm-Liouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform, where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number, and the average Nusselt number for various cross-section aspect ratios.

Roof cooling effect with humid porous medium

A method of laying a layer of humid porous medium on roof to gain free cooling effect by passive water evaporation is proposed. Numeric model for simulating cooling effect is built with the help of experimental results of physical properties for humid porous medium, which shows advantage over analytical solutions because of the supposition of constant physical properties in the latter. Through the comparison between simulated and experimental results, the model is validated. And the method of evaporation cooling effect with humid porous medium on the roof is tested to be feasible.

Numerical analysis of laminar heat transfer in entrance region of a horizontal channel with transverse fins

In the present work, a numerical investigation of the laminar fluid flow and heat transfer in the entrance region of a two dimensional horizontal channel, with in-line ribs, is carried out. The computations are based on the Finite Volume method and the SIMPLE algorithm has been implemented. Both sides of the channel are assumed at a constant temperature and physical properties of the fluid are assumed as constant. Computations are performed for the Reynolds number in the range of 100 to 500, Prandtl number of 0.7 and blockage ratio of 0.1, 0.2 and 0.3. The present results show that the ribs interrupt the boundary layers. Flow detaches from the channel wall and it forms a recirculation zone in front of the rib. The reattachment point has the maximum local Nusselt number. The precise location of periodically fully developed region depends on the Reynolds number from the third to the sixth rib. Increasing the rib pitch causes a marginal increase in the local Nusselt number and a decrease in the friction factor. Increasing the blockage ratio results in a moderate decrease in the local Nusselt number.

Thermal entry flow for a viscoelastic fluid: the Graetz problem for the PTT model

A theoretical study of the entrance thermal flow problem is presented for the case of a fluid obeying the Phan-Thien and Tanner (PTT) constitutive equation. This appears to be the first study of the Graetz problem with a viscoelastic fluid. The solution was obtained with the method of separation of variables and the ensuing Sturm–Liouville system was solved for the eigenvalues by means of a freely available solver, while the ordinary differential equations for the eigenfunctions and their derivatives were calculated numerically with a Runge–Kutta method. The scope of the present study was quite wide: it encompassed both the plane and axisymmetric geometries for channel and tube flows; two types of thermal boundary conditions with either an imposed wall temperature or an applied heat flux; inclusion of viscous dissipation; and elastic (through the Weissenberg number) and elongational (through the PTT parameter ϵ) effects. The main underlying assumptions were those of constant physical properties, negligible axial heat conduction, and fully developed hydrodynamic conditions. The results are discussed in terms of the main effects brought about by viscoelasticity and viscous dissipation on the Nusselt number variation and the bulk temperature.