用Mathematica解热量传递过程中的数学问题

The application of Mathematica to the solving of the mathemalical problems in the process of heat transfer

本文建议用数学软件Mathematica计算热量传递过程,包括用符号运算功能推导保温层临界直径,用曲线拟合法处理传热实验数据,用积分法求取传热系数为温度函数时的换热面积,用Solve等命令求解换热和保温过程所产生的非线性方程,用DSolve命令求解非稳态传热过程产生的微分方程等等。同时绘制出有关函数图形,准确、形象地展示计算过程和结果,方便教师讲解和学生理解,避免复杂、繁琐、耗时的手工计算,提高学生利用计算机解决热量传递问题的能力。

This paper has proposed a method for processing some calculations about heat transfer process by mathematical software Mathematica, including the use of symbol calculation deriving the critical diameter of insulating layer, curve fitting approach to heat transfer experimental data, solving nonlinear equations from heat transfer by ＂Solve＂ function and the differential equations from non- steady-state heat transfer process by ＂ DSolve＂ function without complex, cumbersome and time-consuming manual process. Through drawing function graphics, calculation process and results can be displayed intuitively and figuratively, so that it is easier for the students to understand. Student＇s capacity using computer to solve heat transfer problems will be improved greatly by using Mathematica.