Space Calc
Doing the math, so you don't have to.

## Introduction

Waste heat accumulates quickly. An average adult produces 100 Joules of it every second, just doing nothing. Computer banks, nuclear reactors, laser weapons, etc. all add much more.

In space, this is a big problem. There is essentially no medium present to conduct or convect away waste heat. Only heat radiation is relevant. Therefore, spacecraft must have radiators: devices designed to radiate heat.

This calculator simulates the properties of several kinds of radiators. An answer of NaN means that no solution is possible for the requested quantity. A negative power means that the radiator is actually absorbing energy from its environment (this is possible if the radiator is somehow colder than space).

This kind of radiator is just a panel that is (evenly) hot. This is most-easily done by piping hot liquid through small channels in the panel. The liquid transfers heat to the panel, which radiates it away, providing the cooling effect. As seen on the space shuttle and ISS! Simple and effective.

The radiation to and from space is via the Stefan–Boltzmann Law:

$\Phi_e = A_d \cdot \epsilon \cdot \sigma_{sb} \cdot T^4$

Specifically, the radiant power $\Phi_e$ is related to the radiating (or absorbing) surface area $A_d$, the emissivity/absorptivity $\epsilon$ (a material property), and the absolute temperature $T$, in kelvins. The $\sigma_{sb} \approx 5.670373 \times 10^{-8} \cdot \text{W} \cdot \text{m}^{-2} \cdot \text{K}^{-4}$ is a (derived; see link for details) constant.

Quantity Value Solve For
Surface Area: (one side)
(both sides)
Emissivity:
(space radiative; typical: CMBR 2.72548 K)

This kind of radiator just shoots droplets of a hot liquid directly into space and catches them some time later, after they've cooled off (and possibly, solidified). One advantage is that there's no giant fin to be damaged by space debris or bad guys. One disadvantage is that it's much-less efficient (although by leveraging the heats of fusion/vaporization (energy associated with phase change), one can make it less-inefficient, and also reduce engineering costs; see here).

Quantity Value
Droplet Size: (emission diameter; typical: 100μm–200μm)
Region of Droplets: (region area)
(droplets' centers' avg. separation)
(droplet mutual occlusion factor (typical: 0.001))
(time of flight)
(avg. number of droplets)
(mass of droplets)
(mass flow rate)
(volume of droplets)
(volumetric flow rate)
Droplet Material:
Standard materials Custom material (no phase change!) Custom material (phase change(s))
(coming soon?) (emissivity) (emissivity)
(SHC[note]) (SHC (solid))
(SHC (liquid))
(melting point)
(boiling point)
(heat of fusion)
(heat of vaporization)
(density) (density)
[note]Specific heat capacity (SHC). Typical metals: 0.1–0.4 kJ kg⁻¹ K⁻¹.
Temperatures and Energy: (droplets' start temperature[note])
(droplets' end temperature)
(per-droplet energy loss per flight)
[note]If using standard or custom phase-changing material and this is equal to the material's melting point or boiling point,
the droplet's thermal energy is assumed to be on the hot side of the phase transition. Cannot be greater than boiling point,
as gaseous droplets do not make sense.