The Museum of HP Calculators

# Newton's Law of Cooling for the HP 42S

This program is by Ron Ross and is used here by permission.

This program is supplied without representation or warranty of any kind. Ron Ross and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

## Overview

Newton’s Law of Cooling My favorite program actually makes use of the solver in the 42s. I used this program often when I was an instrument tech for a chemical plant. I normally used it to determine how good of condition or well the heat exchangers were working and if they needed cleaning. Right after an exchanger was cleaned or worked on, I would check it out by using Newton’s Law of Cooling to find out its heating constant. Since this is a two stage problem the solver is better than a program for this type of application.

I would take temperature readings at 5 minutes, find the time constant and predict the time for 10 minutes out (to verify my time constant). Every couple of weeks I would recheck the time constant of the reactor and if it started to degrade or slow in its heating cycle, I knew the Heat exchanger was failing. This allowed the maintenance dept. a better cycle of repair than just a 6 month cycle, fix it whether it needed it or not (which is what was used before). Often the heat exchanger would degrade after 4 months but sometimes they might last 8-12 months, but maintenance did not want to fix what wasn’t broke. Documentation always made the crew feel better, knowing the system they were going to fix, needed fixing. I myself worked on these systems located in a pit a couple times. NO ONE wanted to fix a working heat exchanger!

The Solver allows for any temperature and/or time scale (just stay in the same units). It works great at predicting future temperatures or time constants. And the 42s allows long variable names, which is great for looking at this program years later and still knowing what each variable is for.

Here is the formula listed:
(Ti-TA)e^(K x TIME) + TA = TF

## Listing

```LBL”COOL”
MVAR”TF”		FINAL TEMP
MVAR”Ti”		INITIAL TEMP
MVAR”TA”		AMBIENT “surrounding or supplied” TEMP
MVAR”K”			TIME CONSTANT
MVAR”TIME”		TIME
RCL”Ti’
RCL”TA”
-
RCL”K”
RCL”TIME”
X
E^X
X
RCL”TA”
+
RCL”TF”
-
END
```