A small satellite has a high power data transmitter that it needs to power briefly each...

   

Transcribed Image Text:

A small satellite has a high power data transmitter that it needs to power briefly each time it completes an orbit. The transmitter electronics package has footprint dimensions of 50 mm × 50 mm, and generates 2,000 W of heat for 5 s when it operates. A simple thermal management solution is being considered in which a solid copper plate (same 50 mm × 50 mm footprint) would be mounted to the transmitter. This plate heat sink would absorb the brief heat pulse during operation, and then gradually cool down to a baseline temperature of T₁ = 20°C during the next orbit. All sides of the copper slab, except the heated interface can be assumed insulated. X 11 11 " 0* = 11 "1 11 " T-Ti q" L/k 11 " 11 3 11 11 11 11 LHS a. (8 pts) Sketch (qualitative) temperature profiles through the thickness of the heat sink (x = 0 - LHS) at different times during the 5 s heating period. b. (8 pts) Solve for the required thickness of the heat sink to keep the heated base (at x = 0) below 100°C during the heat-up period. 0*(x*,t*) = t* + The series solution for the 1-D transient conduction problem for: specified heat flux q" at x = 0, insulation at x = L, and uniform initial temperature Ti is: X X x = Fo = t* t* = at L² Copper Heat Sink 2 9 *2 - Q = 2,000 W x + 1 3 π² 11 11 11 11 II n=1 cos(n π x*) n² No heat transfer from sides or top 0* (x*,t*) = (t*) + -exp[−(n ñ)² t*] c. (4 pts) Interestingly, the contribution from the series terms in the solution is almost negligible. Physically, explain what the contributions from the two remaining groups: A and B, below, represent. *2 X (² - x + 1) 2 B A small satellite has a high power data transmitter that it needs to power briefly each time it completes an orbit. The transmitter electronics package has footprint dimensions of 50 mm × 50 mm, and generates 2,000 W of heat for 5 s when it operates. A simple thermal management solution is being considered in which a solid copper plate (same 50 mm × 50 mm footprint) would be mounted to the transmitter. This plate heat sink would absorb the brief heat pulse during operation, and then gradually cool down to a baseline temperature of T₁ = 20°C during the next orbit. All sides of the copper slab, except the heated interface can be assumed insulated. X 11 11 " 0* = 11 "1 11 " T-Ti q" L/k 11 " 11 3 11 11 11 11 LHS a. (8 pts) Sketch (qualitative) temperature profiles through the thickness of the heat sink (x = 0 - LHS) at different times during the 5 s heating period. b. (8 pts) Solve for the required thickness of the heat sink to keep the heated base (at x = 0) below 100°C during the heat-up period. 0*(x*,t*) = t* + The series solution for the 1-D transient conduction problem for: specified heat flux q" at x = 0, insulation at x = L, and uniform initial temperature Ti is: X X x = Fo = t* t* = at L² Copper Heat Sink 2 9 *2 - Q = 2,000 W x + 1 3 π² 11 11 11 11 II n=1 cos(n π x*) n² No heat transfer from sides or top 0* (x*,t*) = (t*) + -exp[−(n ñ)² t*] c. (4 pts) Interestingly, the contribution from the series terms in the solution is almost negligible. Physically, explain what the contributions from the two remaining groups: A and B, below, represent. *2 X (² - x + 1) 2 B

Answer rating: 100% (QA)

Qualitative temperature profiles through the thickness of the heat sink x 0 LHS at different times during the 5 s heating period Time Temperature Prof... View the full answer