![Figure 1.0: A two-body system in a nodal analysis with formulas for nodal conductance (top) and conductive coupling (bottom) [2]](https://s3-us-west-2.amazonaws.com/secure.notion-static.com/f44f9832-dfa4-4dc3-8833-d4eb68ae8d31/Screen_Shot_2021-08-06_at_11.12.31_PM.png)
By: Darton Li, Matthew Ong, and Edwin Giang
Date: August 7, 2021
<aside> ❗ Will need to be verified and be continuously edited (for corrections, new knowledge or simplifications). Most explanations have been simplified and may be underestimating prerequisite or content knowledge.
</aside>
In Low Earth Orbit, a CubeSat will be subjected to extreme temperature changes as well as be in sight of various energy sources from space. Thermodynamics is the study of the conversion and flow of heat that can help inform simulations and tests whether it is as accurate as real life conditions. Since thermodynamics is a vast subject, the brief will only cover conduction, radiation and other thermal considerations to allow for verification and the experimental analyses with the recommended softwares.
Thermodynamics is the study of the relationships between heat (thermal energy) and other energy as well as the transformation or conversion of thermal energy [1]. Thermal energy is the energy generated by moving or vibrating molecules; the more the molecules vibrate, the higher the temperature and the more heat will be outputted. It is important to distinguish heat and temperatures as two separate, yet related, entities in thermodynamics. Heat is the energy transferred between systems due to temperature (dictated by the vibration of molecules) [1].
While there are various topics that pertain to thermodynamics, a thermal study of a CubeSat primarily only takes into account conduction and radiation [2]. As such, this brief will only cover a subset of thermodynamics that is relevant to verifying and conducting thermals simulations for the 3U CubeSat to give an accurate description of what will occur in Earth Low Orbit conditions. Nonetheless, an understanding of how thermal energy flows in the context of an operating CubeSat will be important for the safety of the internal components as well as to prevent unwanted changes in mechanical properties.
By definition, thermal conduction is the diffusion of thermal energy within a material or with another material in contact [3]. The mechanism of thermal conduction is in the movement of the material's energetic particles (characterized by a higher temperature) resulting in collisions with low-energy particles (characterized by a lower temperature) [2]; the energy transfer from the collision is known as thermal conduction. Since conduction depends on the movement of energetic particles, the rate of thermal conduction is thusly dependent on the geometry, thickness and material make-up of the object (defined as the medium) as well as its temperature difference [2].
Considering a steady state model — where the driving temperature difference is constant and where the object is one homogenous system — the rate of conduction, Q , is "proportional to the temperature difference across the layer," ΔT in in microKelvin, and "heat transfer area but is inversely proportional to the thickness of the layer", Δx. This is known as Fourier's Law of Heat Conduction:
$Q = KA(T_1-T_2)/Δx$
or expressed as a rate of change
$Q = -KA(dT/dx)$
or in words
Rate of conduction (W/s) = -[Thermal Conductivty (W/m*K) * Cross-sectional area (m^2) * Temperature gradient (K)] / Thickness (m)
From this, the direction of heat conduction is proportional to the temperature gradient in that direction or that higher temperatures will conduct towards lower temperatures.
In thermal analyses, each part of a system is quantized (or reduced into) as several nodes where conductive heat transfer can occur and a coupled model can be applied. Conductive coupling between two nodes, $G*L_x$ , can be found using Figure Y where G is the conductance of a node.
Figure 1.0: A two-body system in a nodal analysis with formulas for nodal conductance (top) and conductive coupling (bottom) [2]
If two solid bodies/systems are in contact with one another, thermal contact conductance will take place wherein heat will flow from the hotter system (the one with a higher peak temperature) to the colder body [2].The rate of heat flow, Q in watts, is closely related to the steady state model with proportionality in the temperature differences. However, the temperature difference is between the highest temperature and lowest temperature and the denominator takes into account the different thermal constants, thicknesses and the thermal contact conductance ($h_c$). The temperature drop occurs in the contact surface.
![Figure 2.0: Thermal contact conductance visualization and the rate of heat flow formula [2]](https://s3-us-west-2.amazonaws.com/secure.notion-static.com/a9008351-be96-4aba-b196-d72acd5b17ca/Screen_Shot_2021-08-06_at_11.12.22_PM.png)
Figure 2.0: Thermal contact conductance visualization and the rate of heat flow formula [2]