关键词: 发汗, 数学分析, 热传导, 微分方程, 差分方程

Abstract: A solution of transpiration control equation is investigated in this paper. It is found that the equation can be classified as the classic heat transfer equation under certain conditions by means of variable alternation and then the analytic solution can be obtained. A numerical calculation of the analytic solution by a computer has proved the existence, uniqueness and stability of the solution. The theoretical problem of this sort of control system applied in the engneering is preliminarily ascertained. A finite difference numerical calculation has shown that the smaller the difference step is, the faster the difference solution approaches the analytic one. Because of limitation of the difference method, the steady numerical solution can be gotten in the region surrounded by R=0, BT=0 and R·BT=βτ/4h. The main conclusion of reference [2] is verified again.

Key words: transpiration, mathematical analysis, heat transfer, differential equation, difference equation