Thermal resistances adding formula

In summary, the conversation discusses proving a rule for adding thermal resistances in series and parallel. The book suggests that in series, the total resistance is the sum of the individual resistances, while in parallel, the inverse of the total resistance is the sum of the inverses of the individual resistances. The concept of heat current and temperature difference is introduced as the thermodynamic analog of electrical current and voltage.
  • #1
LinearMan
5
0

Homework Statement


Prove a rule for adding of Thermal resistances
for: A)R1 and R2 in Series
B)R1 and R2 in Parallel

Homework Equations


The Attempt at a Solution


According to the book the result should be :
A) R = R1 + R2
B) 1/R = 1/R1 + 1/R2

So i thought we can get some ideas from the theory of Electrical resistance because these formulas are similar for example here: http://www.grc.nasa.gov/WWW/k-12/airplane/ohmrser.html .
However, I don't know how to start (in Thermodynamics there is no Electric current etc., so we can hardly use Ohm´s formula like in previous case).
Thanks for help
 
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  • #2
The thermodynamic analog of current is the Heat Current defined as the rate of flow of heat through the material and the analog of voltage is temperature difference
 
  • #3
OK, thank you.
 
  • #4
I get it
 
  • #5
in Thermodynamics there is no Electric current etc., so we can hardly use Ohm´s formula like in previous case

Not exactly but...

heat flow = ΔT/Thermal Resistance

which is similar to

Current = ΔV/Electrical Resistance

I'll let you work out the units.
 

What is the formula for calculating thermal resistances?

The formula for calculating thermal resistances is Rtotal = R1 + R2 + R3 + ... + Rn, where Rtotal is the total thermal resistance and R1, R2, R3, ..., Rn are the individual thermal resistances.

How do thermal resistances add together?

Thermal resistances add together in series, meaning that the total thermal resistance is the sum of the individual thermal resistances. This is because heat must pass through each thermal resistance in order to reach the other side.

What is the purpose of calculating thermal resistances?

The purpose of calculating thermal resistances is to determine the overall thermal resistance of a system or material. This is important in understanding how heat is transferred and can help in designing more efficient systems or choosing the right materials for a specific application.

Can thermal resistances be added together in parallel?

No, thermal resistances cannot be added together in parallel. In a parallel circuit, the total resistance is less than the individual resistances. However, in thermal systems, heat flows through all resistances simultaneously, so they cannot be added in the same way as electrical resistances.

What units are used for thermal resistances?

Thermal resistances are typically measured in units of degrees Celsius per watt (°C/W) or Kelvin per watt (K/W). These units represent the temperature difference across the resistance for a given amount of heat flow. Other common units include meters squared Kelvin per watt (m2K/W) and hours square feet degrees Fahrenheit per BTU (hft2°F/BTU).

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