Asymptotic Solution Of The Thermocapillary Flow In A Thin Annular Pool

The thermocapillary convection induced by interface tension gradient becomes a prominent factor influencing the quality of materials under microgravity condition. The research on the regularity of thermodynamic and hydrodynamic features of thermocapillary convection gives a new theoretical analysis on the technology of crystal growth. It also plays a very important role in the research on physics fluids. With the developing of the computer technology, it has reported much valuable result on thermocapillary convection by using the numerical simulation. However, the development of the computer lead to the numerical simulation methods in recent ten years, but the importance of the analysis solutions can never be neglected. Some perturbation methods'generation in this time may confirm this fact. If the simple accurate solutions can be approximately achieved by some methods, it is easy to research on the each parameter's fluctuation on solution and it can make clear the analysis configuration of velocity and temperature field. It is also used to check the accuracy of the numerical method.A study on the approximate analytical solution of the thermocapillary convection in a thin annular pool by asymptotical way is carried out in the present paper. The effect of different aspect ratio and dimensionless physical parameters on thermocapillary convection is emphasized in the present paper. It containsâ‘ An approximate analytical solution of the thermocapillary convection in the core region of a thin annular pool is obtained by asymptotical way. Expressions of velocity,temperature and pressure field in the core region are given.â‘¡An approximate analytical solution of the thermocapillary convection near the ends of the thin annular pool is obtained by asymptotical way. Expressions of velocity and temperature a field near the ends are given.â‘¢In order to know if the approximate analytical solution is reasonable, we compared the asymptotical solution with the numerical solution. The affect of aspect ratio and some dimensionless physical parameters on asymptotical solution is emphasized by the aid of the comparison.The results show that different aspect ratio and dimensionless physical parameters affect the results of asymptotical solution. It is found that there is a good agreement between asymptotical solution and the numerical solution in the core region for the low Prandtl number fluid, and it also shows that the end region plays an important role in the asymptotical solution. There is a bad agreement between them for the moderate Prandtl fluid. Next solution needs to be taken into account.