A technique for measuring the heat transfer coefficient inside a Bridgman furnace

Rosch, W.; Jesser, W. A.; Debnam, W. J.; Fripp, A. L.; Woodell, Glenn A.; Pendergrass, T.K.

doi:10.1016/s0022-0248(07)80121-7

Cited by 8 publications

(7 citation statements)

References 1 publication

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“…Regardless, the data provided from the experiments are sufficient to establish the veracity of the simulations provided that any assumptions, such as the magnitudes of the heat transfer coefficients, are within acceptable limits. Albeit adjustable parameters, there are established ranges for their magnitudes and, for the scenario under consideration here, adequate agreement was found when hhot=300 W/(m 2 • C) and hcold=40 W/(m 2 • C) which are acceptable values based on the literature [32,33]. Figure 4 shows the cooling curve measured during the experiments by thermocouples at steady state during the pulling stage.…”

Section: Comparison With Experimental Datamentioning

confidence: 60%

“…Several simulations were performed, with different heat transfer coefficients, since their precise measurements were not available. hhot and hcold were varied in a realistic range of values (last two columns of Table 1) for Bridgman furnaces within an argon atmosphere based on the literature [32,33]. A parametric study was carried out simulating the Bridgman solidification process for a range of conditions aimed to gain knowledge with respect to the relative influence of each of the important dimensionless parameters, along with several key aspects of the solidification process, such as the temperature evolution, shape of the mushy zone and its position in the furnace.…”

Section: Conditions For Comparison With Experimental Datamentioning

confidence: 99%

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Numerical simulation of Bridgman solidification of binary alloys

Battaglioli

McFadden

Robinson

2017

International Journal of Heat and Mass Transfer

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A transient 2D axisymmetric numerical model for the Bridgman solidification process for a stationary furnace and moving sample is presented. The model is able to predict the evolution of temperature and solid fraction of binary alloys in cases where buoyancy induced convection is negligible, such as in microgravity conditions. A dimensionless form of the governing equations was derived in order to identify the dimensionless parameters that characterize the process, those being the Stefan, Péclet, and Biot numbers. The problem was solved using a finite volume method and an explicit time stepping scheme. To test the efficacy of the model, simulated results were compared with experimental data from the literature and acceptable agreement was obtained. Finally, a parametric analysis was performed for understanding the influence of the process parameters on solidification. One key feature of this study was the inclusion of a term describing the advection of latent heat due to the translation of the mushy zone with varying solid fraction. This thermal transport mechanism was shown to be significant, since its magnitude was comparable to the advection of sensible heat. It was also found that when small Biot numbers were due to low values of the heat transfer coefficients at the surface of the sample, rather than to small sample radii, advective mechanisms were enhanced resulting in more convex shapes of the liquidus isotherm. This highlighted the importance of considering both axial and radial heat fluxes when describing the process.

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Section: Comparison With Experimental Datamentioning

confidence: 60%

Section: Conditions For Comparison With Experimental Datamentioning

confidence: 99%

Numerical simulation of Bridgman solidification of binary alloys

Battaglioli

McFadden

Robinson

2017

International Journal of Heat and Mass Transfer

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“…Such variation of the slopes of isothermal surfaces with β also affects the heat transfer rates between the material sides and the inner periphery of the ampoule which, in principle, controls the thermal stresses at the boundary during the growth of the crystal. The Bi number has also been found to be effective on the slope of the isothermal surfaces, especially for Bi values between 1.0 to 0.1, which is the range in the real growth processes for quartz ampoule calculated with h values proposed in [31,32]. The magnitude of the slope is inversely proportional to the Bi number as indicated in the figure.…”

Section: Resultsmentioning

confidence: 86%

Numerical simulation of heat conduction for the growth of anisotropic layered GaSe crystals

Taşarkuyu

Akinoglu

2004

Cryst. Res. Technol.

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In this report, we present the usage of a second rank cylindrical conductivity tensor which we derived to simulate the crystal growth processes of a layered compound GaSe in a cylindrical enclosure by directional solidification. Use of such a tensor is inevitable in the simulations of the growth of highly anisotropic crystals having layered structure, since the crystallographic orientation of the grown material is not necessarily aligned with the ampoule symmetry. Using the finite difference control volume approach in 3D, we solved transient heat conduction equation for a highly anisotropic solid in a cylindrical enclosure. We obtained sloped thermal fields and isothermal surfaces and the magnitudes of the slopes are strong functions of both azimuthal angle and growth orientation. The results showed that the orientation of the crystallographic axes of GaSe in the enclosure is quite effective in the steady and the transient fields, isotherms, and axial and radial temperature gradient within the material. Increase of Bi number decreases the magnitude of the slope of isothermal surface. Anisotropy of the conductivity seems to be effective in the orientation of the growth direction of the resulting crystal within the cylindrical ampoule.

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“…(1) and by Rosch et al [10], the magnitude of the furnace heat transfer coefficient (at the crucible circumference) should increase in proportion to a function temperature cubed. However, this behaviour is not clearly apparent in the results presented here.…”

Section: Heat Transfer Coefficient At the Circumference Of The Cruciblementioning

confidence: 99%

“…An experimental study by Rosch et al [10] combined radiation and convection heat fluxes to estimate an overall heat transfer coefficient in a Bridgman furnace. The radiation heat flux was linearised with respect to temperature difference as,…”

Section: Literature Reviewmentioning

confidence: 99%

An experimental–numerical method for estimating heat transfer in a Bridgman furnace

Mooney

McFadden

Gabalcová

et al. 2014

Applied Thermal Engineering

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Direct measurement of heat flux and heat transfer coefficients in a Bridgman furnace is not always possible using traditional methods. This study characterised a vertical tubular Bridgman furnace using experimental data so that the estimated heat flux and heat transfer coefficients may be used in simulations of future experiments using the same furnace. An experimental-numerical method is presented where a discrete proportional integral derivative controller manipulates the radial heat flux in a front tracking solidification model so that the output temperature profile matches experimental data. The method is applicable for other experimentalists and modellers and its usefulness is demonstrated by example. Highlights A combined experimental-numerical method to estimate heat flux and heat transfer coefficients in a Bridgman furnace is outlined in detail.  The inverse heat transfer problem is solved using a discrete proportional integral derivative controller in series with a front tracking solidification model.  The usefulness of the method is demonstrated by example.

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A technique for measuring the heat transfer coefficient inside a Bridgman furnace

Cited by 8 publications

References 1 publication

Numerical simulation of Bridgman solidification of binary alloys

Numerical simulation of Bridgman solidification of binary alloys

Numerical simulation of heat conduction for the growth of anisotropic layered GaSe crystals

An experimental–numerical method for estimating heat transfer in a Bridgman furnace

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