The Mathematics of Heat Exchangers: Logarithms in Action

摘要

A heat exchanger is used to cool a hot liquid or to heat a cold liquid. An example of a heat exchanger in your home is the water heater, which heats cold water by transferring heat from burning gas or from electrically heated metal. In industry, a liquid product may be hot just after it is made and must be cooled in a heat exchanger before storage. In this paper, we show how mathematics is used in determining the size of the heat exchanger; as the title suggests, logarithms play an important role. Consider a hot product being cooled to room temperature using cold water. Figure 1 shows a typical "shell and tube" heat exchanger. The hot product flows inside the tubes and the cold water flows in the surrounding jacket (or shell) in the opposite direction. In the figure, the product enters from the left and exits to the right, whereas the cooling water enters from the bottom right and exits to the top left. Heat is transferred from the hot product to the cooling water. The driving force for this heat transfer is the temperature difference between the product and the water at any specific point in the heat exchanger.