Thermocapillary migration of a droplet under thermal radiation with a uniform flux is numerically investigated and theoretically analyzed. By using the front-tracking method, it is observed that thermocapillary droplet migration at small Reynolds numbers and moderate Marangoni numbers reaches a steady process. The steady migration velocity decreases as Marangoni number increases. The time-evolution behavior of temperature fields in the steady migration process is found to be a quadratic function, in which the linear rise of the steady state temperatures with the relative time is a main characteristics. The quadratic function behavior of the temperature fields is further used to derive the steady energy equations. From the steady momentum and energy equations, an analytical result at small Reynolds number and zero Marangoni number is determined by using the method of matched asymptotic expansions. The steady migration velocity decreases as Reynolds number increases, which is in qualitatively agreement with the numerical result.

数值研究和理论分析了液滴在热辐射下具有均匀通量的热毛细管迁移。通过使用前跟踪方法，可以观察到在小的雷诺数和中等的马兰戈尼数下热毛细管液滴迁移达到稳定过程。稳定的迁移速度随着Marangoni数的增加而降低。发现稳态迁移过程中温度场的时间演化行为是二次函数，其中稳态温度随相对时间的线性上升是主要特征。温度场的二次函数行为进一步被用来导出稳态能量方程。根据稳定的动量和能量方程，采用匹配渐近展开法确定了雷诺数为零，Marangoni数为零的解析结果。随着雷诺数的增加，稳定的迁移速度降低，这与数值结果在质量上是一致的。