Heat transfer model processing

This paper will discuss the formulation of the simulator for the filament winding process which describes the temperature and extent of cure in a cross-section of a composite part. The model consists of two parts the kinetic model to predict the curing kinetics of the polymeric system and the heat transfer model which incorporates the kinetic model. A Galerkin finite element code was written to solve the specially and time dependent system. The program was implemented on a microcomputer to minimize computer costs. 

Finite Element Modeling of Polymer Flow and Heat Transfer in Processing Equipment... 

In this chapter the simulation examples are presented. They are preceded by a short description of simulation tools and the MADONNA program in particular. As seen from the Table of Contents, the examples are organised according to thirteen application areas Batch Reactors, Continuous Tank Reactors, Tubular Reactors, Semi-Continuous Reactors, Mixing Models, Tank Flow Examples, Process Control, Mass Transfer Processes, Distillation Processes, Heat Transfer, Biological Process Examples and Environmental Process Examples. There are aspects of some examples that make them relevant to more than one application area, and this is usually apparent from their titles. Within each section, the examples are listed in order of their degree of difficulty. 

With the above-described heat transfer model and rapid solidification kinetic model, along with the related process parameters and thermophysical properties of atomization gases (Tables 2.6 and 2.7) and metals/alloys (Tables 2.8,2.9,2.10 and 2.11), the 2-D distributions of transient droplet temperatures, cooling rates, achievable undercoolings, and solid fractions in the spray can be calculated, once the initial droplet sizes, temperatures, and velocities are established by the modeling of the atomization stage, as discussed in the previous subsection. For the implementation of the heat transfer model and the rapid solidification kinetic model, finite difference methods or finite element methods may be used. To characterize the entire size distribution of droplets, some specific droplet sizes (forexample,.D0 16,Z>05, andZ)0 84) are to be considered in the calculations of the 2-D motion, cooling and solidification histories. 

Any on-line process control model used for computer-aided manufacturing of high-performance composite laminates must include a thorough treatment of void stability and growth as well as resin transport. These two key components, along with a heat transfer model and additional chemorheological information on kinetics and material properties, should permit optimized production of void-free, controlled-thickness parts. A number of advances have been made toward this goal. 

Heat transfer models of the autoclave process are the most accurate and well understood of all the process models. Much of this understanding is because the models are so easily verified through thermocouple measurements. Thermocouples are the most common part-sensing technique used in production. The challenging aspects are the incorporation of the affects of resin flow, resin kinetics, and autoclave position on heat transfer properties. The importance of incorporating resin kinetic models is to properly predict conditions that may lead to exotherms, especially for thick laminates [17]. 

Heat transfer models are a powerful tool for developing autoclave process cycles. They are especially useful in aiding tool designers in choosing tooling materials, thicknesses, and thermocouple locations. Models can also be used to determine if a tooling concept would be detrimental in a specific position in the autoclave and the types of tools that should be processed together to optimize the cure cycle. 

The discussion above explains why basic information on sorption and diffusion under the reaction conditions, especially at elevated pressures, is required for kinetic and mass- and heat- transfer modelling of catalytic polymerization reactors. If such information is sufficiently available, one should be able, for example, to compare the kinetics of gas-phase and slurry-processes directly by taking into account both gas solubilities in swollen polymers and the hydrocarbons used in slurry processes. 

From the extensive experimental and model development work performed at CSM (during a period of over 15 years), it has been demonstrated that a heat transfer controlled model is able to most accurately predict dissociation times (comparing to laboratory experiments) without any adjustable parameters. The current model (CSMPlug see Appendix B for details and examples) is based on Fourier s Law of heat transfer in cylindrical coordinates for the water, ice, and hydrate layers, and is able to predict data for single- and two-sided depressurization, as well as for thermal stimulation using electrical heating (Davies et al 2006). A heat transfer limited process is controlled by the rate of heat supplied to the system. Therefore, a measurable intermediate (cf. activated state) is not expected for heat transfer controlled dissociation (Gupta et al., 2006). 

The data shown in Fig. 3 indicate a complex effect of particle diameter on the underlying heat transfer processes. Of practical interest is the maximum in U found at intermediate particle sizes ( i6 mm). The solid curves are predictions of the heat transfer model given in the second part of this paper. The model is able to predict this complex behaviour quite well. 

The second and the third components become significant only at high temperatures (> 700°C) and low solids concentrations (< 30 kg/m3). In fast fluidized beds, the motion of the particles plays an overriding role in the heat transfer process, since the solids particles have larger heat capacity and higher thermal conductivity. Most of the heat transfer models reported in the literature give emphasis to particle convective transfer. 

Bongers, P.M.M. (2006)d Heat Transfer model of a scraped surface heat exchangerfor Ice Cream, Proc. 16th European Symposium on Computer Aided Process Engineering... 

Liu et al. (2004, 2005) examined a three-dimensional non-linear coupled auto-catalytic cure kinetic model and transient-heat-transfer model solved by finite-element methods to simulate the microwave cure process for underfill materials. Temperature and conversion inside the underfill during a microwave cure process were evaluated by solving the nonlinear anisotropic heat-conduction equation including internal heat generation produced by exothermic chemical reactions. 

E.M. Nunes et al., A volume radiation heat transfer model for Czochralski crystal growth processes. J. Cryst. Growth 236(4), 596-608 (2002). 

The three-phase nonequilibriimi model developed in our laboratory which includes kinetics, mass transfer and heat transfer models [6] is used to predict the yield and selectivity of EGME from the reaction of ethanol and EO. The model predicts fliat die conversion of EO would reach 94 % and 99 % selectivity to EGME at an operating pressure of 235 kPa and a reflux ratio of 2. The model predictions are in excellent agreement with experimental data (Table 2). This result shows that our three-phase non-equilibrium model could be used for the prediction of yield and selectivity in a CD process. 

The lumped thermal mass equation also describes the heating-up process of flat face or clamp flanges, where the failure mode is, however, the loss of tightness and consequent secondary leak and fire. It should be noted that when the limped thermal mass heat transfer model was used for the calculation of time-to-failure of flanges engulfed by fire, the results agreed well with the full scale tests in Ref 4. 

To evaluate the potential of carbon formation in a steam reformer, it is therefore essential to have a rigorous computer model, which contains kinetic models for the process side (reactor), as well as heat transfer models for the combustion side (furnace). The process and combustion models must be coupled together to accurately calculate the process composition, pressure, and temperature profiles, which result from the complex interaction between reaction kinetics and heat transfer. There may also be a temperature difference between bulk fluid, catalyst surface, and catalyst interior. Lee and Luss (7) have derived formulas for this temperature difference in terms of directly observable quantities The Weisz modulus and the effective Sherwood and Nusselt numbers based on external values (8). 

Single Particle Heat Transfer Modeling for Expanded Shale Processing... 

The coupled furnace-reactor simulation requires an accurate description of the heat transfer from the furnace to the reactor. The global radiative heat transfer from the furnace to the reactor was calculated by the zone method (Fig. 12.5.A-2, Left) proposed by Hottel and Sarofim [1967], To take into account the local influence of radiative heat transfer, CFD simulations of the furnace were carried out using a radiative heat transfer model for short distances [De Marco and Lockwood, 1975], Knowledge of the local flue gas composition is required to calculate the heat release by combustion in each flue gas volume element and the absorption coefficients for radiation. Coupled CFD simulations of the reactor tubes and furnace predict the process gas conversion and the product yields, as well as coke formation rates. 

The processes we have considered thus far - extrusion, wire coating, and injection and compression molding - are dominated by shear between confined surfaces. By contrast, in fiber and film formation the melt is stretched without confining surfaces. It is still possible to gain considerable insight from very elementary flow and heat transfer models, but we must first parallel Section 2.2 and develop some basic concepts of extensional flow. The remainder of the chapter is then devoted to an analysis of fiber formation by melt spinning. 

Denys, S., van Loey, A.M., and Hendrickx, M.E. (2000) A modelling approach for evaluation process uniformity during batch high hydrostatic pressure processing combination of a numerical heat transfer model and enzyme inactivation kinetics. Innovative... 

---