unisat

Thermal Analysis

Reference: ECSS-E-ST-31C (Thermal Control), ECSS-Q-ST-70-04C (Thermal Testing), NASA-STD-7009A

1. Thermal Environment Definition

1.1 External Heat Sources

Source Nominal Hot Case Cold Case Notes
Solar Radiation (S) 1361 W/m² 1414 W/m² (perihelion) 1322 W/m² (aphelion) AM0 spectrum
Earth Albedo (a*S) 408 W/m² 481 W/m² (a=0.34) 317 W/m² (a=0.24) Varies with surface
Earth IR (OLR) 237 W/m² 258 W/m² (tropical) 218 W/m² (polar) Outgoing longwave
Cosmic Background 2.725 K 2.725 K 2.725 K Negligible flux

1.2 View Factors (3U CubeSat at 550 km)

Earth angular radius: rho = arcsin(R_E / (R_E + h)) = arcsin(6371/6921) = 66.9 deg
Earth solid angle from satellite: Omega = 2*pi*(1 - cos(rho)) = 3.73 sr
View factor to Earth (nadir face): F_nadir = 0.88
View factor to Earth (side faces): F_side = 0.30
View factor to Deep Space: F_space = 1 - F_earth (per face)
Face F_earth F_space Solar Exposure
+Z (nadir) 0.88 0.12 Intermittent
-Z (zenith) 0.02 0.98 Direct sun (SSO)
+X (ram) 0.30 0.70 Depends on attitude
-X (wake) 0.30 0.70 Depends on attitude
+Y (sun-facing, SSO) 0.30 0.70 Continuous in sunlit
-Y (anti-sun) 0.30 0.70 Never direct

2. Thermal Properties of Materials

2.1 Surface Optical Properties

Surface Treatment alpha_s epsilon_IR alpha/epsilon Application
Black anodize (AL) 0.88 0.85 1.04 Structure exterior
Bare aluminum (polished) 0.15 0.05 3.00 Not used (poor radiator)
White paint (AZ-93) 0.14 0.92 0.15 Radiator faces (option)
Solar cell (GaAs + coverglass) 0.91 0.81 1.12 Solar panels
Kapton (gold coated) 0.42 0.63 0.67 MLI outer layer
MLI (10-layer effective) 0.42 0.02 21.0 Blanket insulation

2.2 Material Thermal Properties

Material Conductivity (W/mK) Specific Heat (J/kgK) Density (kg/m³)
AL 6061-T6 (structure) 167 896 2700
FR4 (PCB) 0.3 (through-plane) 1100 1850
Copper (PCB traces) 385 385 8960
Kapton (polyimide) 0.12 1090 1420
Li-ion cell (NCR18650B) 3.0 (axial), 0.5 (radial) 1040 2700
Thermal interface pad 5.0 1000 2600

3. Thermal Node Model

3.1 Lumped-Parameter Node Description

The satellite is divided into 14 thermal nodes for the lumped-parameter analysis:

        +------ Node 6: -Z face (zenith) ------+
        |                                        |
        |   +---Node 10: ADCS Board---+          |
        |   +---Node 9: COMM Board----+          |
  Node  |   +---Node 8: OBC Board-----+    Node  |
  3: +Y |   +---Node 7: EPS Board-----+    4: -Y |
  face   |   +---Node 12: Battery------+    face   |
        |   +---Node 11: Camera-------+          |
        |   +---Node 13: Payload------+          |
        |                                        |
        +------ Node 5: +Z face (nadir) --------+
                                                  
  Node 1: +X face (ram)       Node 2: -X face (wake)
  Node 14: Solar panel (deployable)

3.2 Thermal Conductances Between Nodes

From Node To Node Conductance (W/K) Path Description
Structure faces (1-6) Adjacent faces 0.50 AL frame conduction
Structure (any) Internal boards 0.25 PC/104 standoffs (4x M3 AL)
EPS Board (7) Battery (12) 0.40 Thermal pad + bracket
OBC Board (8) COMM (9) 0.15 PC/104 connector + standoffs
COMM (9) ADCS (10) 0.15 PC/104 connector + standoffs
Battery (12) +X face (1) 0.10 Thermal isolators (Ultem)
Camera (11) +Z face (5) 0.30 AL mounting bracket
Payload (13) Structure 0.20 Mounting screws + interface

3.3 Radiative Couplings

From Node To Node Coupling GR (W/K⁴) Notes
Face 1-6 Deep space epsilon * sigma * A * F Per face, see view factors
Face 5 (+Z) Earth (237 W/m²) F_nadir * A Absorbed Earth IR
Internal boards Adjacent boards Small (< 0.01 W/K⁴) Negligible internal radiation

4. Boundary Conditions

4.1 Hot Case Definition (worst-case hot)

Parameter Value Rationale
Solar constant 1414 W/m² Perihelion (January)
Albedo factor 0.34 Tropical ocean + clouds
Earth IR 258 W/m² Tropical subsolar point
Beta angle 71.6 deg Full sun (no eclipse)
Internal dissipation 6.46 W Science mode (max power)
Attitude +Y sun-pointing Maximum solar input on one face
BOL optical properties Fresh alpha_s = 0.88 No UV degradation yet

4.2 Cold Case Definition (worst-case cold)

Parameter Value Rationale
Solar constant 1322 W/m² Aphelion (July)
Albedo factor 0.24 Polar/ocean (low albedo)
Earth IR 218 W/m² Polar winter region
Beta angle 0 deg Maximum eclipse (35.7 min)
Internal dissipation 1.21 W Safe mode (minimum power)
Attitude Tumbling (worst orientation) Minimum solar input
EOL optical properties Degraded alpha_s = 0.95, epsilon = 0.82 2-year UV/atomic oxygen

5. Temperature Predictions

5.1 Steady-State Equilibrium (Analytical)

For a single isothermal node, energy balance gives:

alpha_s * S * A_proj + epsilon * q_IR * A_earth + Q_int
    = epsilon * sigma * A_total * T^4

T = [ (alpha_s * S * A_proj + epsilon * q_IR * A_earth + Q_int)
      / (epsilon * sigma * A_total) ] ^ (1/4)

Where sigma = 5.67e-8 W/m²K⁴ (Stefan-Boltzmann constant)

5.2 Hot Case Results

Node Component Predicted T (C) Acceptance Limit (C) Margin (C)
3 +Y Face (sun-facing) +72 +100 +28
5 +Z Face (nadir) +48 +100 +52
4 -Y Face (anti-sun) +18 +100 +82
7 EPS Board +52 +70 +18
8 OBC (STM32F4) +55 +75 +20
9 COMM Module +49 +70 +21
10 ADCS Board +47 +70 +23
11 Camera Sensor +53 +50 -3 (VIOLATION)
12 Battery Pack +42 +40 -2 (VIOLATION)
13 Payload +45 +60 +15

Action Items for Hot Case Violations:

5.3 Cold Case Results

Node Component Predicted T (C) Acceptance Limit (C) Margin (C)
1-6 Structure faces -38 to -18 -40 +2 to +22
7 EPS Board -12 -20 +8
8 OBC (STM32F4) -15 -30 +15
9 COMM Module -18 -20 +2
10 ADCS Board -16 -20 +4
11 Camera Sensor -22 -20 -2 (VIOLATION)
12 Battery (heater ON) +2 -5 +7
13 Payload -14 -20 +6

Action Item: Camera requires survival heater or improved thermal coupling to warm boards.

6. Heater Duty Cycle Analysis

6.1 Battery Heater

The battery heater maintains cells above 0C for safe charging.

Heater sizing:
  Q_loss = G_conductive * (T_bat - T_structure) + epsilon * sigma * A * (T_bat^4 - T_env^4)
  
  During eclipse cold case:
    T_structure ~ -25C (248 K)
    T_bat_target = +5C (278 K)
    G_cond = 0.40 W/K (to EPS board) + 0.10 W/K (to structure) = 0.50 W/K
    Q_loss_cond = 0.50 * (278 - 248) = 15.0 W  << This seems high

  Corrected (with thermal isolation):
    G_cond_isolated = 0.08 W/K (Ultem spacers + minimal contact)
    Q_loss = 0.08 * 30 = 2.4 W

  With 2x 1W heaters: P_heater = 2.0 W
  Steady state T_bat = T_structure + P_heater / G_cond = -25 + 2.0/0.08 = 0C (marginal)

6.2 Heater Duty Cycle Profile

Orbit Phase Duration (min) Heater State Power (W) Energy (Wh)
Sunlit (hot case) 62 OFF 0.0 0.0
Sunlit (cold case) 62 ON 30% duty 0.6 0.62
Eclipse (cold case) 34 ON 100% duty 2.0 1.13
Eclipse (nominal) 34 ON 60% duty 1.2 0.68

Average heater power over orbit (cold case): 1.25 W This is accounted for in the power budget eclipse standby mode.

6.3 Thermostat Control Logic

if T_battery < T_ON (0 C):
    heater = ON (PID or bang-bang)
elif T_battery > T_OFF (5 C):
    heater = OFF

Hysteresis band: 5C (prevents rapid cycling)
Thermistor accuracy: +/- 0.5C (NTC, Steinhart-Hart calibration)
Heater response time: ~30 seconds to +1C (low thermal mass heater pad)

7. Component Derating Table

Per ECSS-Q-ST-30-11C (Derating of EEE Components):

Component Qual. Range (C) Derated Range (C) Derating Rule Hot Margin Cold Margin
STM32F427 MCU -40 to +85 -30 to +75 80% of range +20C +15C
NCR18650B Battery -10 to +45 -5 to +40 Charge: 0C to 40C -2C +7C
CC1125 UHF Radio -40 to +85 -30 to +75 80% of range +26C +12C
OV5647 Camera -20 to +60 -15 to +50 75% of range -3C +7C
BMI088 Gyroscope -40 to +85 -30 to +75 80% of range +28C +14C
HMC5883L Magnetometer -30 to +85 -25 to +75 80% of range +28C +10C
MAX-M10S GNSS -40 to +85 -30 to +75 80% of range +26C +15C
Spectrolab UTJ Cells -100 to +100 -80 to +90 90% of range +18C +42C
RFPA5522 S-band PA -40 to +85 -30 to +70 80% of range +21C +12C

Bold values indicate tight margins requiring design action (see Section 5 action items).

8. Thermal Test Plan

8.1 Test Levels (per ECSS-Q-ST-70-04C)

Level Purpose Temperature Range Duration
Qualification Design verification +/- 10C beyond acceptance 4 cycles min
Acceptance Workmanship screening Predicted +/- 5C 8 cycles min
Protoflight Combined qual + acceptance Qual range, acceptance cycles 4 cycles

8.2 Thermal Vacuum Test Profile

Temperature
(C)
 +80 |          ____          ____          ____          ____
     |         /    \        /    \        /    \        /    \
 +60 |        / HOT  \      /      \      /      \      /      \
     |       / DWELL  \    /        \    /        \    /        \
 +20 |      /  (2 hr)  \  /          \  /          \  /          \
     |     /            \/            \/            \/            
   0 |----/                                                       
     |                                                            
 -20 |                                                            
     |                  /\            /\            /\            
 -40 |                 /  \          /  \          /  \           
     |                / COLD\       /    \        /    \          
 -50 |               / DWELL \     /      \      /      \        
     |              /  (2 hr) \   /        \    /        \       
     +----+----+----+----+----+----+----+----+----+----+---> Time
      Cycle 1        Cycle 2       Cycle 3       Cycle 4

Pressure: < 1e-5 mbar (high vacuum)
Ramp rate: 1-2 C/min (max 5 C/min for qualification)
Dwell time: 2 hours at each extreme (functional test during dwell)

8.3 Thermal Cycling (Ambient Pressure)

For board-level screening before integration:

Parameter Value
Hot limit +75C
Cold limit -30C
Ramp rate 5C/min
Dwell time 15 min per extreme
Number of cycles 20
Functional test Every 5th cycle

8.4 Pass/Fail Criteria

Test Criterion
Thermal balance (TVAC) Model correlation within +/- 5C of prediction
Functional (hot dwell) All subsystems operational, telemetry nominal
Functional (cold dwell) All subsystems operational, battery charging
Heater verification Battery temp maintained > 0C during cold dwell
Survival (cold, unpowered) No damage after 2 hr at -50C, resume operation
Post-test inspection No delamination, cracking, or discoloration

9. Thermal Design Improvements (Trade Study)

Option Mass Impact Power Impact Thermal Benefit Priority
White paint on -Y face Negligible None -10C hot case reduction High
MLI on battery module +15 g None +8C cold case improvement High
Copper thermal strap (bat-radiator) +20 g None -5C hot case for battery Medium
Camera duty-cycle limit None Software Prevents camera overheat High
Additional heater (camera) +10 g +0.5 W +5C cold case for camera Medium
Thermal gap filler (all boards) +8 g None Better board-to-frame coupling Low

10. References

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