1. FASTRAC Thermal Model Analysis By Millan Diaz-Aguado

2. Overview Sun/Shade and Line of Sight Heat Flux (Earth, Albedo, Sun) –Heat Flux Earth and Albedo and View Factor Simple Example (Thin Disk) Two Square Parallel Surfaces –Conduction through the Solar Panel –Radiation to the Structure –Radiation to EMI Future work and Conclusions

3. Eclipsed vs. Light Find the position of the Sun (Julian Date) and the satellite, and calculate the angle between them (Θ). If θ 1 +θ 2 > Θ then there is Line of Sight

4. Eclipsed vs. Light Example: i=45º Ω=45º ω=0 h=300km on July 21 st 2005

5. Environmental Heat Flux Solar Heat Flux ( W/m 2 ) q=1350 α cos(ψ) –Where ψ is the angle between the normal of the spacecraft surface and the Sun and α is the aborptivity of the surface Earth Blackbody Radiation q=σ (T) 4 α F –Where σ is the Stefan-Boltzmann constant, T is the temperature of Earth’s blackbody, and F is the view factor Earth Albedo q=1350 AF α F cos (θ) –Where θ is the angle between the spacecraft surface and the Sun, AF is the Albedo Factor (~at 90 min orbit) Albedo Factor Inclination 0-30 Inclination 30-60 Inclination 60-90 Hot Case0.280.310.28 Cold Case0.110.16

6. View Factor Shape factor for different angles between the normal of the surface of the spacecraft and its position vector h/R=0.047 Interpolate data if angle lays between the given data

7. Heat Flux for a Orbiting Thin Germanium Circular Disk Altitude 300km, i=0º, α = 0.81

8. Temperature for Thin Disk To calculate the surface temperature we use a simple ODE for radiated thin plate Where ρ is the density, ε is the emissivity, h is the width and T is the temperature of the thin plate

9. Thermal Model of Two Parallel Plates Plate 1 is facing the Earth Plate 2 is facing away from the Earth Radiation patterns will be different View Factor is different as the plates are square Fse=.98 ε=.85 α=.81 Width=175 μm C=0.093 W-hr/(Kg-°C) ρ=5260 Kg/m³

10. Surface Heat Flux A) Plate 1 B) Plate 2

11. Surface Temperatures A) Plate 1B) Plate 2

12. Conductance Through the Solar Panel 1234 k 12 k 23 k 34 The Solar Panel is assumed to have a multilayer wall The temperature of the inner aluminum surface is calculated by: Where t 1 is the temperature of the outer surface, k is the thermal conductivity, Δx is the thickness and q/A is the heat flux

13. Radiation Between Two Parallel Surfaces Radiation between the solar panel with side panel and EMI boxes Where T is the surface temperature, ε is the emissivity and σ is the Stefan-Boltzmann 12

14. Buffed Aluminum Side Panel A) Plate 1B) Plate 2

15. EMI Golden Anodized Aluminum A) Plate 1B) Plate 2

16. Conclusion and Future Work Conduction: –Between aluminum side panel and EMI box –Between solar panel and aluminum side panel –Between structural elements Thruster tank Four other sides of the hexagon, top and bottom sides Inner Heat Production –Subsystems and Thruster Rotation of the satellite MLI