顺逆流换热器部分冷热流体温度凸凹变化的数学解析

Mathematical Solutions of the Temperature Variations of Hot and Cooled Fluids for the Simple Parallel and Cross Heat Exchanger

针对传热学教学中换热器中冷热流体温度变化,建立冷热流体温度沿流动面积变化的数学模型,此模型给出冷热流体温度沿换热面积的显示表达式,及其对流程方向的一阶导数、二阶导数,针对冷热流体热容量大小,完整给出顺、逆流换热器的温度变化曲线凸凹性的条件。这部分内容是对现有换热器教学内容的有益补充,也强化培养学生的物理问题数学思维。

Mathematical models of the hot and cooled fluids are built for the simple parallel and cross heat exchanger. The solutions of temperature of the hot and cooled fluids are drawn on the areas. Its 1-order and 2-order derivative are given simultaneously. The concave-convex properties of the hot and cooled fluids are explained completely. The mathematical interpretation strengthen the mathematical thinking for the physical problem.