具有热源的二维稳态温度起伏模型  

Two-dimensional Temperature Fluctuation Model in a Molten Liquid with Heat Source

作　　者：苏培[1] 史英英[2] 孙仁济[1] 陈明文[1] 王自东[3] 

机构地区：[1]北京科技大学数学力学系,北京100083 [2]烟台师范学院数学与信息学院,山东烟台264025 [3]北京科技大学材料科学与工程学院,北京100083

出　　处：《烟台师范学院学报（自然科学版）》2006年第1期3-9,共7页Yantai Teachers University journal(Natural Science Edition)

基　　金：国家重大基础研究项目(G20000672061)基金资助

摘　　要：对一个具有对流和热源的二维晶体生长的温度场进行了分析,建立了热传导问题的数学模型,给出了模型的精确解析解,证明了解的唯一性和稳定性,并通过实例计算说明当横向对流存在时,温度场的解在与界面垂直的方向上呈指数型震荡衰减.A model of two-dimensional heat transfer equation with fluid convection and heat source is analyzed. By a specific method an accurate analytical solution is obtained, the stability and the uniqueness of this solution are also proved. Calculation of an example shows that under the confluence of the convection, the temperature will occur to be oscillatory and exponential decaying along the direction that is perpendicular to the boundary.

关 键 词：晶体生长 偏微分方程 常微分方程 傅立叶级数 

分 类 号：O175.2[理学—数学]