Thermal Vacuum Test

What is modelled

A lumped test article of mass m exchanges heat with a cold shroud by radiation and, while gas remains, by conduction through the gas. Pumps with speed S empty a chamber of volume V while outgassing adds a small flow. As the mean free path grows past the gap the gas stops carrying heat and radiation takes over, so the article relaxes to a temperature set by its internal power and emissivity.

Equations

• Radiation q = ε σ (T&sup4; - Ts&sup4;), σ = 5.670374e-8 W/m²K&sup4;; factored form ε σ (T - Ts)(T + Ts)(T² + Ts²).
• Balance m c dT/dt = Qint - A q - A hg (T - Ts); steady vacuum state T = (Q / (ε σ A) + Ts&sup4;)1/4.
• Pump-down dp/dt = -(S/V) p + qout/V, so t = (V/S) ln(p0/p) without outgassing.
• Mean free path λ = k T / (√2 π d² p), d = 0.365 nm (N₂); Knudsen number Kn = λ / L.
• Gas conduction: free-molecular hfm = α (γ+1)/(γ-1) p √(R / (8 π M T)), capped by the continuum value k / L.

Checks run in the page

• The radiative flux against its factored form.
• Pump-down time to 1 Pa from the closed form against numerical integration.
• The vacuum balance temperature against a long integration.
• The linearised radiative time constant against the simulated e-fold time.

Honest simplifications

A single isothermal lump, grey surfaces, one shroud temperature with view factor 1, a fixed 0.5 m conduction gap, constant specific heat 900 J/kg K and a simple blend of the free-molecular and continuum conduction limits. No solar simulation, multilayer insulation, internal gradients, pump staging or real outgassing curves. A teaching model, not a test plan.

• Press Cold shroud and watch the payload cool slowly: while gas remains conduction helps, afterwards only radiation does.
• Press Low emissivity blanket: the same internal heat now holds the payload much warmer.
• Raise the outgassing and see the pressure stop falling at the ultimate pressure q / S.