{"title":"固定坩埚中熔体液面下降对契诃夫法对流换热的影响","authors":"V. S. Berdnikov, V. V. Vinokurov","doi":"10.1134/S086986432404005X","DOIUrl":null,"url":null,"abstract":"<div><p>In the regimes of mixed convection, the Czochralski method investigates numerically the effect of a melt layer height on hydrodynamics and convective heat transfer in the range of relative heights of the heptadecane layer 0.1 ≤ ≤ H/<i>R</i><sub>C</sub> ≤ 2.0 with a step of 0.1. Calculations were performed using the finite difference method at a fixed rate of crystal rotation corresponding to the Reynolds number Re = 95, with the Grashof, Marangoni and Prandtl numbers Gr = = 1215, Ma = 2930, Pr = 40.35 for the ratio of crucible radius to crystal radius <i>R</i><sub>C</sub> /<i>R</i><sub>S</sub> = 1.94. In this range of parameters, the flow has a laminar, steady and axisymmetric character. The evolution of the spatial flow shape, velocity and temperature fields, radial distributions of local heat fluxes, and integral heat transfer is studied depending on the relative heights of the heptadecane layer.</p></div>","PeriodicalId":800,"journal":{"name":"Thermophysics and Aeromechanics","volume":"31 4","pages":"669 - 684"},"PeriodicalIF":0.5000,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Effect of the melt level drop in a stationary crucible on convective heat transfer in the Czochralski method\",\"authors\":\"V. S. Berdnikov, V. V. Vinokurov\",\"doi\":\"10.1134/S086986432404005X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the regimes of mixed convection, the Czochralski method investigates numerically the effect of a melt layer height on hydrodynamics and convective heat transfer in the range of relative heights of the heptadecane layer 0.1 ≤ ≤ H/<i>R</i><sub>C</sub> ≤ 2.0 with a step of 0.1. Calculations were performed using the finite difference method at a fixed rate of crystal rotation corresponding to the Reynolds number Re = 95, with the Grashof, Marangoni and Prandtl numbers Gr = = 1215, Ma = 2930, Pr = 40.35 for the ratio of crucible radius to crystal radius <i>R</i><sub>C</sub> /<i>R</i><sub>S</sub> = 1.94. In this range of parameters, the flow has a laminar, steady and axisymmetric character. The evolution of the spatial flow shape, velocity and temperature fields, radial distributions of local heat fluxes, and integral heat transfer is studied depending on the relative heights of the heptadecane layer.</p></div>\",\"PeriodicalId\":800,\"journal\":{\"name\":\"Thermophysics and Aeromechanics\",\"volume\":\"31 4\",\"pages\":\"669 - 684\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2025-03-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Thermophysics and Aeromechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S086986432404005X\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ENGINEERING, AEROSPACE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Thermophysics and Aeromechanics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S086986432404005X","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, AEROSPACE","Score":null,"Total":0}
Effect of the melt level drop in a stationary crucible on convective heat transfer in the Czochralski method
In the regimes of mixed convection, the Czochralski method investigates numerically the effect of a melt layer height on hydrodynamics and convective heat transfer in the range of relative heights of the heptadecane layer 0.1 ≤ ≤ H/RC ≤ 2.0 with a step of 0.1. Calculations were performed using the finite difference method at a fixed rate of crystal rotation corresponding to the Reynolds number Re = 95, with the Grashof, Marangoni and Prandtl numbers Gr = = 1215, Ma = 2930, Pr = 40.35 for the ratio of crucible radius to crystal radius RC /RS = 1.94. In this range of parameters, the flow has a laminar, steady and axisymmetric character. The evolution of the spatial flow shape, velocity and temperature fields, radial distributions of local heat fluxes, and integral heat transfer is studied depending on the relative heights of the heptadecane layer.
期刊介绍：
The journal Thermophysics and Aeromechanics publishes original reports, reviews, and discussions on the following topics: hydrogasdynamics, heat and mass transfer, turbulence, means and methods of aero- and thermophysical experiment, physics of low-temperature plasma, and physical and technical problems of energetics. These topics are the prior fields of investigation at the Institute of Thermophysics and the Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences (SB RAS), which are the founders of the journal along with SB RAS. This publication promotes an exchange of information between the researchers of Russia and the international scientific community.
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