1. Home work 2: Thermos

2. 𝑅 𝑙,𝑡𝑜𝑡 = 𝑅 𝑙,𝑖 + 𝑅 𝑙,𝑐𝑎𝑣𝑖𝑡𝑦 + 𝑅 𝑙,𝑒
Home work 2: Thermos
We neglect the heat flux through the glass walls and consider only the cavity
𝑅 𝑙,𝑡𝑜𝑡 = 𝑅 𝑙,𝑖 + 𝑅 𝑙,𝑐𝑎𝑣𝑖𝑡𝑦 + 𝑅 𝑙,𝑒 i e
Inside
𝑅 𝑙,𝑖 = 1 2𝜋 𝑟 1 ℎ 𝑖
Outside
Rl,cavity
radiation
conduction/ convection
Rl,i
Rl,e
𝑅 𝑙,𝑒 = 1 2𝜋 𝑟 2 ℎ 𝑒

3. Home work 2: Thermos Φ 𝐶,12 = 𝑁𝑢 𝑅 𝑙,𝑝𝑖𝑝𝑒 𝐿 𝜃 𝑠1 − 𝜃 𝑠2
Cavity
The total flux by conduction and convective in the cavity is
Φ 𝐶,12 = 𝑁𝑢 𝑅 𝑙,𝑝𝑖𝑝𝑒 𝐿 𝜃 𝑠1 − 𝜃 𝑠2
𝑅 𝑙,𝑝𝑖𝑝𝑒 = ln 𝑟 2 𝑟 𝜋𝜆
Φ 𝐶,12 = 1 𝑅 𝑙,𝑐 𝐿 𝜃 𝑠1 − 𝜃 𝑠2
Rl,cavity
radiation
conduction/ convection
Rl,i
Rl,e
1 𝑅 𝑙,𝐶 = 𝑁𝑢 ln 𝑟 2 𝑟 𝜋𝜆

4. Home work 2: Thermos Φ 𝑅,12 = 2𝜋 𝑟 1 𝐿 𝐶 𝑏 𝐹 𝑇 𝐹 𝑟 𝜃 𝑠1 − 𝜃 𝑠2
Cavity
The total radiative flux
between the surfaces in the cavity is
Φ 𝑅,12 = 2𝜋 𝑟 1 𝐿 𝐶 𝑏 𝐹 𝑇 𝐹 𝑟 𝜃 𝑠1 − 𝜃 𝑠2
Φ 𝑅,12 = 1 𝑅 𝑙,𝑅 𝐿 𝜃 𝑠1 − 𝜃 𝑠2
Rl,cavity
radiation
conduction/ convection
Rl,i
Rl,e
1 𝑅 𝑙,𝑅 = 2𝜋 𝑟 1 𝐶 𝑏 𝐹 𝑇 𝜚 1 𝜀 𝐹 𝜚 2 𝜀 2 𝐴 1 𝐴 2

5. Home work 2: Thermos
Cavity
The total radiative flux
between the surfaces in the cavity is
  𝐹 12 =1
  𝐴 1 =2𝜋 𝑟 1 𝐿
1 𝑅 𝑙,𝑅 = 2𝜋 𝑟 1 𝐶 𝑏 𝐹 𝑇 𝜚 1 𝜀 𝐹 𝜚 2 𝜀 2 𝐴 1 𝐴 2
  𝐴 2 =2𝜋 𝑟 2 𝐿 i e
1 𝑅 𝑙,𝑅 = 2𝜋 𝑟 1 𝐶 𝑏 𝐹 𝑇 𝜚 1 𝜀 𝜚 2 𝜀 2 𝑟 1 𝑟 2

6. Home work 2: Thermos 1 𝑅 𝑙,𝑐𝑎𝑣𝑖𝑡𝑦 = 1 𝑅 𝑙,𝐶 + 1 𝑅 𝑙,𝑅 Cavity
The total flux is parallel series of resistances
1 𝑅 𝑙,𝑐𝑎𝑣𝑖𝑡𝑦 = 1 𝑅 𝑙,𝐶 𝑅 𝑙,𝑅
1 𝑅 𝑙,𝐶 = 𝑁𝑢 ln 𝑟 2 𝑟 𝜋𝜆
1 𝑅 𝑙,𝑅 = 2𝜋 𝑟 1 𝐶 𝑏 𝐹 𝑇 𝜚 1 𝜀 𝜚 2 𝜀 2 𝑟 1 𝑟 2
Rl,cavity
radiation
conduction/ convection
Rl,i
Rl,e

7. Home work 2: Thermos
𝑅 𝑙,𝑖 = 1 2𝜋 𝑟 1 ℎ 𝑖 = 1 2𝜋∗0.05∗ 1000 = 𝑚𝐾 𝑊
𝑅 𝑙,𝑒 = 1 2𝜋 𝑟 2 ℎ 𝑒 = 1 2𝜋 ∗0.1 ∗8 = 𝑚𝐾 𝑊
1 𝑅 𝑙,𝐶 = 𝑁𝑢 ln 𝑟 2 𝑟 𝜋𝜆 = ln 𝜋∗ =0.272 𝑊 𝑚𝐾

8. Home work 2: Thermos
1 𝑅 𝑙,𝑅 = 2𝜋 𝑟 1 𝐶 𝑏 𝐹 𝑇 𝜚 1 𝜀 𝜚 2 𝜀 2 𝑟 1 𝑟 2
𝐹 𝑇 = 𝑇 𝑚 = = 𝐾 3
𝛼+𝜚=1
𝛼=𝜀
𝜀=1−𝜌=1−0.2=0.8
1 𝑅 𝑙,𝑅 = 2𝜋 𝑟 1 𝐶 𝑏 𝐹 𝑇 𝜚 1 𝜀 𝜚 2 𝜀 2 𝑟 1 𝑟 2 = 2𝜋∗0.05∗5.67∗ ∗ =1.514 𝑊 𝑚𝐾

9. Home work 2: Thermos 𝑅 𝑙,𝑖 =0.0032 𝑚𝐾 𝑊 𝑅 𝑙,𝑒 =0.199 𝑚𝐾 𝑊
𝑅 𝑙,𝑖 = 𝑚𝐾 𝑊
𝑅 𝑙,𝑒 = 𝑚𝐾 𝑊
1 𝑅 𝑙,𝐶 =0.272 𝑊 𝑚𝐾
1 𝑅 𝑙,𝑅 =1.514 𝑊 𝑚𝐾
1 𝑅 𝑙,𝑐𝑎𝑣𝑖𝑡𝑦 = 1 𝑅 𝑙,𝐶 𝑅 𝑙,𝑅 = = 𝑊 𝑚𝐾
𝑅 𝑙,𝑐𝑎𝑣𝑖𝑡𝑦 =0.56 𝑚𝐾 𝑊
𝑅 𝑙,𝑡𝑜𝑡 = 𝑅 𝑙,𝑖 +𝑅 𝑙,𝑐𝑎𝑣𝑖𝑡𝑦 +𝑅 𝑙,𝑒 = = 𝑚𝐾 𝑊

10. R (mk/W) no-reflec reflec 1 reflec 2 reflec 1&2 Air 0.76 2.30 1.78
Home work 2: Thermos
R (mk/W)
no-reflec
reflec 1
reflec 2
reflec 1&2
Air
0.76
2.30
1.78
2.61
Vacuum
0.86
5.07
2.96
7.17