Thermal System

Description

The Thermal System governs the entire spacecraft thermal network, managing all registered Thermal Model instances and resolving power exchange and temperature updates at each simulation step.

It provides the framework for calculating:

• Radiative heat transfer
• Conductive heat transfer
• Radiation to deep space
• Internal power generation and dissipation

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Module Implementation

System Workflow

At each time step, the thermal system performs the following sequence:

1. Reset power flows for all active thermal models.
2. Update lookup models (CSV-based).
3. Compute conduction and radiation between connected models.
4. Compute radiation losses to space.
5. Add internal heat generation.
6. Integrate temperature for each thermal node using the energy balance equation.

Conduction

For two nodes $A$ and $B$ connected via conduction:

$${\dot{Q}}_{\mathrm{cond}}=k_{\mathrm{eff}}A\frac{T_A-T_B}{L_{\mathrm{avg}}}$$

where:

• $k_{\mathrm{eff}}=\frac{k_A+K_B}{2}$ ​​: Effective thermal conductivity [W/m·K]
• $A$: Surface area of contact [m²]
• $L_{\mathrm{avg}}=\frac{L_A+L_B}{2}$​ ​​: Mean wall thickness [m]

This linear form assumes steady-state conduction with no internal heat generation. To prevent instability, conduction power is capped:

$$|{\dot{Q}}_{\mathrm{cond}}|<1000W$$

Radiation Between Components

For two surfaces exchanging thermal radiation:

$${\dot{Q}}_{\mathrm{rad}}=\sigma A{ϵ}_{\mathrm{avg}}(T_A^4-T_B^4)$$

where:

• $\sigma =5.6703\times 10^{-8}W.m^{-2}.K^{-4}$ : Stefan–Boltzmann constant
• ${ϵ}_{\mathrm{avg}}=\frac{{ϵ}_A+{ϵ}_B}{2}$​ ​: Average emissivity

Temperatures are clamped to a maximum $T_{\max }=5800$ K to prevent overflow.

Radiation to Space

Un-occluded surface area $A_{\mathrm{space}}$​ radiates to the background environment:

$${\dot{Q}}_{\mathrm{space}}=\sigma A_{\mathrm{space}}ϵ(T^4-T_{\mathrm{env}}^4)$$

where $T_{\mathrm{env}}$ is either:

• Ambient atmospheric temperature (if an atmosphere model exists), or
• $3K$ (deep-space background).

Temperature Update

Each model’s temperature is updated using the discrete-time formulation:

$$\Delta T=\frac{{\dot{Q}}_{\mathrm{net}}\Delta t}{m\cdot c_p}$$ $$T_{\mathrm{new}}=T_{\mathrm{old}}+\Delta T$$

The derivative of temperature is stored as:

$$\dot{T}=\frac{T_{\mathrm{new}}-T_{\mathrm{old}}}{\Delta T}$$

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Assumptions/Limitations

• All thermal nodes are lumped-mass models with spatially uniform temperature.
• Heat transfer is limited to radiation and solid conduction while convection is neglected assuming vacuum in space.
• The simulation uses explicit Euler integration for thermal state updates.
• Temperature values are bounded between $0.1K$ and $5800K$.
• Radiation losses are assumed one-sided and space does not emit back into the model.
• Thermal contact resistances are not modelled explicitly (ideal conduction).
• The system neglects transient conduction through multi-layered materials.
• Self-shadowing and complex radiation view factors are not considered (isotropic emission assumed).
• The $1000W$ conduction cap introduces non-physical limiting behaviour at large gradients.
• Numerical stability depends on time step size $\Delta T$.

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References

[1] Bergman, Theodore et al. Fundamentals of Heat and Mass Transfer. 8th ed. Wiley, 2017. Web. 29 Oct. 2025.

[2] Howell, J.R., Mengüc, M.P., Daun, K., & Siegel, R. (2020). Thermal Radiation Heat Transfer (7th ed.). CRC Press. https://doi.org/10.1201/9780429327308