3 Steady Heat Conduction

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How can HT be modelled in plane walls?

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  • steady

  • one-dimensional

  • temperature is normally expressed as T(x)

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What is thermal resistance?

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The resistance of a surface against conduction, convection, or radiation. It can be thought of using the analogy of electrical circuits:

  • rate of heat transfer → electrical current

  • thermal resistance → electrical resistance

  • temperature difference → voltage difference

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19 Terms

1
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How can HT be modelled in plane walls?

  • steady

  • one-dimensional

  • temperature is normally expressed as T(x)

2
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What is thermal resistance?

The resistance of a surface against conduction, convection, or radiation. It can be thought of using the analogy of electrical circuits:

  • rate of heat transfer → electrical current

  • thermal resistance → electrical resistance

  • temperature difference → voltage difference

3
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What are the equations for thermal resistance in walls?

  • Rcond = L/kA

  • Rconv = 1/(hA)

  • Rrad = 1/(hradA)

4
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What happens when there is a very large convection coefficient?

Convection resistance tends to zero and so there is no resistance against convection in the surface

5
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What is the temperature drop equation?

where U is the overall heat transfer coefficient

<p>where U is the overall heat transfer coefficient</p>
6
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What is the equation for heat conduction in a cylinder?

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7
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What are the equations for resistance in a cylinder?

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8
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What are the equations for resistance in a sphere?

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9
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What is fin efficiency?

A judgement of how good a fin is working

η = Actual HT from the fin ÷ Ideal HT from the fin if entire fin were at base temperature

10
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What is fin effectiveness?

This is judging if having the fin is better than not having the fin

ε = HT rate from fin ÷ HT rate from surface (w/out fin)

11
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What is thermal contact resistance?

Interfaces between bodies are not always perfectly in contact which leads to thermal contact resistance

12
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What causes the critical radius of insulation in cylinders/spheres?

The additional insulation increases the conduction resistance of the insulation layer, but decreases the convection resistance of the surface due to the increase in outer surface area.

13
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What is the critical radius for cylinders and spheres?

cylinders r =k/h

spheres r =2k/h

14
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Why may fins be added to a design?

If temperatures are fixed, adding fins increases the surface area and thus the heat transfer rate

15
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What makes an effective fin?

  • high k

  • large p/Ac (ratio of perimeter to cross section area)

  • low h

16
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How can you increase heat transfer rate?

  • increase surface area As using fins

  • increase convection coefficient h (using a pump or fan)

17
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Name a dinosaur with fins

stegosaurus used fins to cool its blood

18
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What is the best fin length?

when mL=1 as 76.2% of heat transferred by an infinitely long fin will be transferred and it uses less material

19
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What is the heat transfer circuit analogy?

Heat transfer, like current, is the same everywhere