1. Ministry of Education and Science of the Russian Federation State Educational Institution of Higher Professional Education National Research Tomsk Polytechnic University Institute of Cybernetics Department : Applied Mathematics Specialization : Applied Mathematics and Informatics COMSOL MULTIPHYSICS SIMULATION OF MARANGONI CONVECTION Student: Ryabikina A.S., Group: 8b90, Scientific advisor: Ogorodnikov A.S., Linguistic advisor: Kuznetsova I.N.

2. OVERVIEW Introduction Introduction Covering equations Covering equations Modeling Modeling Results Results Conclusion Conclusion References References 2

3. Features: Surface tension Surface tension Liquid-air interface Liquid-air interface Modeling technique: MetalsMetals High temperaturesHigh temperatures Real system substitutionReal system substitution Silicone oil fillingSilicone oil filling Known propertiesKnown properties Dependance: Species concentration Species concentration Temperature distribution Temperature distribution INTRODUCTION 3

4. Equations Formulae № Features (1) velocity field, velocity field, pressure distribution pressure distribution (2) fluid heating fluid heating (3) temperature variations temperature variations (4)(4)(4)(4) COVERING EQUATIONS 4

5. MODELING 5 Performance: Diverse scientific tasks Diverse scientific tasks Partial differential equations Partial differential equations Technique of finite elements Technique of finite elements

6. MODELING 5 Fig.1. Mode selection. Modes: Incompressible Navier-Stokes Incompressible Navier-Stokes Convection and Conduction Convection and Conduction Weak Form, Boundary Weak Form, Boundary

7. MODELING 5 Fig.2 The vessel after mesh generation. Basic steps: Subdomain settings Subdomain settings Boundary conditions Boundary conditions Mesh generation Mesh generation Fig.3 Problem solving.

8. RESULTS 6 Fig.4. Temperature and velocity, ∆T = 10 -3 K. ∆T = 10 -3 K: NO temperature & velocity field correlation

9. 6 Fig.5. Temperature and velocity, ∆T = 2K. RESULTS ∆T = 2K: DISTINCT temperature & velocity field correlation

10. CONCLUSION Experimental study difficulties Experimental study difficulties Real system substitution Real system substitution Temperature difference range calculation Temperature difference range calculation Comsol Multiphysics modeling Comsol Multiphysics modeling Direct correlation of temperature and velocity field Direct correlation of temperature and velocity field Marangoni’s effect influence Marangoni’s effect influence 7

11. REFERENCES 8 1.Levich V.G. Physicochemical Hydrodynamics. – New Jersey: Prentice-Hall, 1962. 2.Егоров В.И. Применение ЭВМ для решения задач теплопроводности. Учебное пособие.– СПб: СПб ГУ ИТМО, 2006.- 4с. 3.Огородников А.С. Моделирование в среде Matlab – Comsol 3.5a. Часть 1: учебное пособие. Томск: Изд-во Томского политехнического университета, 2012. 4.Batchelor G.K. An Introduction to Fluid Dynamics. – Cambridge: Cambridge University Press, 1967. 5.Space Science News Archive [Электронный ресурс] / Physical Simulation of Marangoni Convection in Weld Pools. – Режим доступа: http://www.spacescience.spaceref.com/, свободный. – Загл. с экрана. - Яз.англ. 6.Comsol Multiphysics [Электронный ресурс] / Model Gallery. – Режим доступа: http://www.comsol.com/, свободный. – Загл. с экрана. – Яз.англ. 7.Wikipedia, the free encyclopedia [Электронный ресурс] / Navier-Stokes equations. – Режим доступа: http://www.wikipedia.org/, свободный. – Загл. с экрана. – Яз.англ. 8.Physics Forums [Электронный ресурс] / Thermodynamics Energy balance Equation. – Режим доступа: http://www.physicsforums.com/, свободный. – Загл. с экрана. – Яз.англ. 9.Thermopedia [Электронный ресурс] / Archimede’s Force. – Режим доступа: http://www.thermopedia.com/, свободный. – Загл. с экрана. – Яз.англ. 10.Scholarpedia [Электронный ресурс] / Navier-Stokes Equations: Mathematical Properties. – Режим доступа: http://www.scholarpedia.com/, свободный. – Загл. с экрана. – Яз.англ.

12. Ministry of Education and Science of the Russian Federation State Educational Institution of Higher Professional Education National Research Tomsk Polytechnic University Institute of Cybernetics Department : Applied Mathematics Specialization : Applied Mathematics and Informatics COMSOL MULTIPHYSICS SIMULATION OF MARANGONI CONVECTION Student’s contacts: ryabikina11@mail.ru, ryabikina11@gmail.com, as.tomsk@yahoo.com Student: Ryabikina A.S., Group: 8b90, Scientific advisor: Ogorodnikov A.S., Linguistic advisor: Kuznetsova I.N.