Finding the Pinch — Targeting Minimum Utilities5 / 17
The Problem Table Algorithm
The temperature-interval cascade that finds the pinch and the minimum hot and cold utility requirements by arithmetic alone.
12 min read · Jacob Willis, Net Zero Lead · Last reviewed July 2026
The composite-curve picture from the last lesson is intuitive, but you don't need to draw it precisely to get an exact answer. The problem table algorithm finds the pinch temperature and the minimum hot and cold utility requirements through nothing but addition and subtraction: a cascade of numbers down a temperature scale. This lesson works it through in full, on a small two-stream example, so every step is visible.
In this lesson
- 01The process
- 02Step 1: shift the temperatures
- 03Step 2: mark out the temperature intervals
- 04Step 3: find the net heat surplus or deficit in each band
- 05Step 4: cascade the heat downward
- 06Step 5: the most negative value is your minimum hot utility
- 07Step 6: re-run the cascade with that utility added
- 08Reading off the answer
- 09Sources and further reading