## 3 Passive Thermal Control Methods  
### Multi-Layer Insulation  
Thermal insulation is crucial for cryogenic and infrared satellite missions. Multi-layer insulation (MLI) blankets are the most efficient insulation material for space applications [18]. The MLI blanket is in general comprised of a number of low-emittance sheets  
Figure 1: Payload configuration.  
combined with low-conduction netting layers to control the heat transfer for low temperature applications such as cryogenic instruments. Thermal insulation performance is quantified as effective emissivity (\(e^{*}\)) and is dependent on the number of inner layers as well as geometric considerations (number of bends, holes, etc.). Effective emissivity is defined as in Equation (3) [19]  
\[e^{*}=\frac{Q_{Total}}{\sigma(T_{hot}^{4}-T_{cold}^{4})} \tag{3}\]  
where, \(e^{*}\)--Effective emissivity; \(Q\)--Total incoming heat flux (W/m\({}^{2}\)); \(\sigma\)--Stefan-Boltzmann constant (5.670374419 \(\times\) 10\({}^{-8}\) W/m\({}^{2}\)\(\cdot\)K\({}^{4}\)); T\({}_{hot}\)--Temperature of the MLI hot side (K); \(T_{cold}\)--Temperature of the MLI cold side (K). Typical values for \(e^{*}\) are closer to in the range 0.0150 to 0.03 [19].  
MLI in satellites is widely used for the following reasons [20].  
1. To prevent excessive thermal flux from/to various satellite components
2. To minimize thermal gradients through out the components
3. To reduce temperature variations due to change in orbital environment conditions.  
Thermal conduction across the thickness of the MLI is very sensitive to the layer compression. To minimize the MLI conduction heat transfer, any compressive pressure or bending of blankets must be avoided [19]. This conduction term is defined as the total temperature difference (\(\Delta T\)) between the outer blanket layer and the inner blanket layer divided by the total number of layers. Assuming that the temperature distribution is uniform throughout the blankets, the conduction heat transfer per unit area is given by Equation (4) [21]. MLI efficiency reduces as the size decreases because heat transfer at the blanket edges increases and hence MLI generally does not perform well on small satellite platforms [10].  
\[q_{c}=\frac{k_{c}\Delta T}{n} \tag{4}\]  
where, \(q_{c}\)--MLI conduction heat load per unit area (W/m\({}^{2}\)), \(k_{c}\)--Conductance of a single MLI layer (W/m\({}^{2}\)K), \(\Delta T\)--Temperature difference across the MLI layer (K), \(n\)--Number of MLI layers. Heat flux due to conduction can be reduced by increasing the number of inner layers and this reduction is linear with increasing layer numbers. Conductive heat transfer is typically negligible and ignored in MLI blankets. Unlike conductive heat transfer, radiation heat transfer is considered and is given in Equation (5) [21].  
\[q_{r}=2.835\times 10^{-5}\epsilon\frac{T_{hot}^{4}-T_{cold}^{4}}{n} \tag{5}\]  
\(q_{r}\)--MLI radiative heat flux (W/m\({}^{2}\)), \(\epsilon\)--Emissivity of MLI outer layers, \(T_{hot}\)--Temperature of the MLI hot side (K), \(T_{cold}\)--Temperature of the MLI cold side (K), \(n\)--Number of MLI layers. From both conduction and radiation terms, it can be proven that the total heat flux is minimized when the number of MLI layers are increased.