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Numerical Heat Transfer And Fluid Flow

Advanced models of fuel droplet heating and evaporation

The major methods of mathematical modelling of solidification and melting problems are reviewed in this paper. Different analytical methods, nowadays still used as standard references to validate numerical models, are presented. Various mathematical formulations to numerically solve solidification and melting problems are categorized. Relative merits and disadvantages of each formulation are analysed. Recent advances in modelling solidification and melting problems associated with convective motion of liquid phase are discussed. Based on this comprehensive survey, basic guidelines are outlined to choose a correct mathematical formulation for solving solidification and melting problems.

https://iopscience.iop.org/article/10.1088/0965-0393/4/4/004/pdf

Mathematical modelling of solidification and melting: a review

A simple, but comprehensive model of heat transfer and solidification of the continuous casting of steel slabs is described, including phenomena in the mold and spray regions. The model includes a one-dimensional (1-D) transient finite-difference calculation of heat conduction within the solidifying steel shell coupled with two-dimensional (2-D) steady-state heat conduction within the mold wall. The model features a detailed treatment of the interfacial gap between the shell and mold, including mass and momentum balances on the solid and liquid interfacial slag layers, and the effect of oscillation marks. The model predicts the shell thickness, temperature distributions in the mold and shell, thickness of the resolidified and liquid powder layers, heat-flux profiles down the wide and narrow faces, mold water temperature rise, ideal taper of the mold walls, and other related phenomena. The important effect of the nonuniform distribution of superheat is incorporated using the results from previous three-dimensional (3-D) turbulent fluid-flow calculations within the liquid pool. The FORTRAN program CONID has a user-friendly interface and executes in less than 1 minute on a personal computer. Calibration of the model with several different experimental measurements on operating slab casters is presented along with several example applications. In particular, the model demonstrates that the increase in heat flux throughout the mold at higher casting speeds is caused by two combined effects: a thinner interfacial gap near the top of the mold and a thinner shell toward the bottom. This modeling tool can be applied to a wide range of practical problems in continuous casters.

http://ccc.illinois.edu/pdf files/publications/03_mtb_meng_con1d_reprint_post.pdf

Heat-transfer and solidification model of continuous slab casting: CON1D

Numerical investigation of a PCM-based heat sink with internal fins

A generalized temperature boundary condition coupling strategy for the modeling of conventional casting processes was implemented via experiments and numerical simulations with commercial purity aluminum, aluminum alloy, and tin specimens in copper, graphite, and sand molds. This novel strategy related the heat transfer coefficient at the metal-mold interface to the following process variables: the size of the air gap that forms at the metal-mold interface, the roughness of the mold surface, the conductivity of the gas in the gap, and the thermophysical properties of both the metal and mold. The objective of this study was to obtain, apply, and evaluate the effect of incorporating an experimentally derived relationship for specifying transient heat transfer coefficients in a general conventional casting process. The results are presented in two parts. Part I details the implementation of a systematic experimental approach not limited to a specific process to determine the heat transfer coefficient and characterize the formation of the air gap at the metal-mold interface. The heat transfer mechanisms at the interface were identified, and seen to vary in magnitude during four distinct stages, as the air gap formed and grew. A semiempirical inverse equation was used to characterize the heat transfer coefficient-air gap relationship, across the various stages, for experimental data from the literature and this study.

Finding boundary conditions: A coupling strategy for the modeling of metal casting processes: Part I. Experimental study and correlation development

Development of a heat transfer dimensionless correlation for spheres immersed in a wide range of Prandtl number fluids

This article focused on the effects of surface roughness and temperature on the heat-transfer coefficient at the metal mold interface. The experimental work was carried out in a unique and versatile apparatus, which was instrumented with two types of sensors, thermocouples, and linear variable differential transformers (LVDTs). The monitoring of the two types of sensors was carried out simultaneously during solidification. The concurrent use of two independent sensors provided mutually supportive data, thereby strengthening the validity of the interpretations that were made. With this type of instrumentation, it was possible to measure temperature profiles in mold and casting, as well as the air gap at the metal mold interface. Commercial purity aluminum was cast against steel and high carbon iron molds. Each type of mold had a unique surface roughness value. Inverse heat-transfer analysis was used to estimate the heat-transfer coefficient and the heat flux at the metal mold interface. A significant drop in the heat-transfer coefficient was registered, which coincided with the time period of the air gap formation, detected by the LVDT. An equation of the form \(h\, = \,\frac{1} {{b^{\ast}A + c}}\, + \,d\) was found to provide excellent correlation between the heat-transfer coefficient and air gap size. In general, an increase in mold surface roughness results in a decrease in the heat-transfer coefficient at the metal mold interface. On the other hand, a rise in liquid metal temperature results in a higher heat-transfer coefficient.

The Effects of Surface Roughness and Metal Temperature on the Heat-Transfer Coefficient at the Metal Mold Interface

In Part II of this article, the experimental findings of Part I are incorporated into a numerical model to complete the coupling technique. Presenting the data in a generalized nondimensional form, the effect of surface roughness was observed to be pronounced at small relative gap sizes, reducing the heat transfer coefficient at least one order of magnitude below that predicted for perfectly flat surfaces. The effect was observed to progressively diminish with increasing gap sizes and approached an analytical “perfectly flat” solution for larger gap sizes. A simplified viscoelastic plastic numerical model was developed for a cylindrical coordinate system to predict the growth of the air gap. The model’s predictions of the gap growth compared well with the experimental measurements for each system examined. Application of the correlation via coupling with the energy equation was seen to improve the accuracy of an uncoupled casting model, bettering the predicted air gap formation and eliminating the previously existing time lag for initial formation of the gap.

Stavros A. Argyropoulos

Papers

Mathematical modelling of solidification and melting: a review

Finding boundary conditions: A coupling strategy for the modeling of metal casting processes: Part I. Experimental study and correlation development

Development of a heat transfer dimensionless correlation for spheres immersed in a wide range of Prandtl number fluids

The Effects of Surface Roughness and Metal Temperature on the Heat-Transfer Coefficient at the Metal Mold Interface

Finding boundary conditions: A coupling strategy for the modeling of metal casting processes: Part II. Numerical study and analysis