# Calculating the thermal coefficient between the insulated interior of a telescope instrument package and the cold ambient air outside

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• Erwinux
In summary, the conversation discusses building an insulated chamber to protect a sensitive instrument from freeze temperatures in the winter. A digital PID thermostat is used to maintain a safeguard temperature, and the power consumed is recorded on a remote server. The conversation also suggests using a simple model and surface energy balance to estimate the outside minimum temperature the heater will maintain.
Erwinux
I've built an insulated chamber to protect a sensitive instrument at freeze temperatures in the winter. The instrument is mounted on a telescope, so the heat inside the chamber will slowly dissipate in the ambient. A digital PID thermostat is used to keep the temperature at a safeguard level. The outside and inside temperature and the duty cycle of the thermostat are recorded on a remote server, so I know the power consumed at a certain difference of temperature, anytime.

How to calculate the outside minimum temperature the heater will maintain the safeguard temperature inside insulated chamber?

A simple model will work pretty well here for steady state solutions. The power your heater makes will be proportional to the temperature difference it creates. This should be a linear relationship in normal stable systems (not true if you have things that change state like water freezing/melting) so twice the heat flow (power) will create twice the temperature difference. Also, the temperature difference won't depend much on the temperature values within "normal" temperature ranges.

So, you should be able to get a good estimate by collecting some power-temperature data and then extrapolate to maximum heater power and the minimum desired temperature.

jrmichler

So you have something like that above.

I think you can apply surface energy balance to the interior/exertion walls to get in the ball park for a steady state solution. Its a bit hand wavy, but it shouldn't be that bad:

Take ## A_s ## to be the exterior surface area of the enclosure
## k ## is the thermal conductivity of the insulation
##L## is the insulation thickness
## h_{int}## is the average convection coefficient inside the enclosure maybe ## 10 \rm{ \frac{W}{m^2 K}}##
## h_{ext}## is the average convection coefficient outside the enclosure could be as high as ## 200\rm{ \frac{W}{m^2 K}}##
## q ## is the maximum output power rating for the heater

Then you get ## T_{int} ## from solving the following relation:

$$q = A_s \frac{T_{int} - T_{\infty}}{ \frac{1}{h_{int}} + \frac{L}{k} + \frac{1}{h_{ext}} }$$

let me know if you have any questions.

## 1. What is the thermal coefficient and why is it important in telescope instrument packages?

The thermal coefficient is a measure of the rate at which heat is transferred between two materials. In telescope instrument packages, it is important because it determines how quickly the interior of the package will change in temperature when exposed to the cold ambient air outside.

## 2. How is the thermal coefficient calculated?

The thermal coefficient is calculated by measuring the temperature difference between the two materials and dividing it by the time it takes for the temperature to equalize. This is known as the thermal time constant.

## 3. What factors can affect the thermal coefficient in telescope instrument packages?

The thermal coefficient can be affected by the type of insulation used, the thickness of the insulation, the materials used in the construction of the package, and the temperature difference between the interior and exterior of the package.

## 4. How can the thermal coefficient be optimized in telescope instrument packages?

The thermal coefficient can be optimized by using high-quality insulation materials, increasing the thickness of the insulation, and using materials with low thermal conductivity. Additionally, minimizing the temperature difference between the interior and exterior of the package can also help improve the thermal coefficient.

## 5. Can the thermal coefficient change over time in telescope instrument packages?

Yes, the thermal coefficient can change over time due to factors such as wear and tear on the insulation, changes in the materials used, and changes in the temperature difference between the interior and exterior of the package. Regular maintenance and monitoring can help ensure that the thermal coefficient remains at an optimal level.

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