# Peltier calculation utility

Posted:

## Overview

This program can calculate the performance of a Peltier cooling system. It will take into account the CPU parameters, cold-plate thermal resistance, Peltier parameters and cooler parameters (e.g. water cooling). From this it will calculate CPU temperature, Peltier cold side temperature and hot side temperature. The program can cope with more than one Peltier in a system, as long as they are identical.

The formulae used to calculate these temperatures are:

1. Thot = (Q + (I * V)) * Rcooler
2. (Thot - Tcold)/DTmax = (2I/Imax) - (I/Imax)2)0.8 - ((Q / Qmax) / (I/Imax)0.2)
3. TCPU = Tcold + (Q * Rcoldplate)

2: is an empirically determined formula, so it may not give perfectly accurate results, but I think the error should be very small. I fitted the equation to the 'universal graphs' that manufacturers often supply. When I = Imax, the formula simplifies down to the more familiar DT/DTmax = 1 - (Q / Qmax)

## CPU parameters

The program will calculate the output power of the CPU based on its default settings and the overclocked speed and voltage.

The formula used is:

Poverclocked = Pdefault * (Foverclocked / Fdefault) * (Voverclocked / Vdefault)2

## Cold plate parameters

The thermal resistance of the cold-plate (or whatever is between the Peltier and CPU) can be specified, or it can be calculated from experimental data.

The formula used is:

Rthermal = (Tcooled - Theated) / P

## Peltier parameters

Peltier performance can be calculated at any supply voltage.

I have assumed that Peltier supply voltage is proportional to supply current, whereas in reality the voltage needed for a given current actually varies depending on operating conditions. However, the difference should be small enough to safely ignore.

## Cooler parameters

Treated the same as cold-plate parameters.

The formula used is:

Rthermal = (Tambient - Theated) / P

## Other parameters

To account for the heat leaked in through the insulation, I used the following formula:

Q = PCPU + ((Tambient - TCPU) / Rinsulation)

This is used iteratively: The temperatures are first calculated as normal, then the calculated value of TCPU is used in the above equation to get a new value for Q. This new value is then used to calculate the next value for TCPU, and so on until the difference between successive iterations is too small to show up.

Thanks to DuffMan for giving me the idea for this program.