0
$\begingroup$

I have been reading on the topic of thermal resistance and I came across these two different definitions multiple times.

The first one: $R = \Delta T/\dot{Q} = L/kA $

and the second one $R = \Delta T/\dot{q} = L/k$

I am just guessing the definition will change depending on what we use to solve the problem, either q or Q. But it strikes me as odd, since in electric circuits the units are always Ohms.

$\endgroup$
2
  • $\begingroup$ Thermal resistance, a concept relying on a daft analogy, really only finds good use in the case of composite walls and such like. Then the thermal resistances are in series. engineeringenotes.com/thermal-engineering/heat-conduction/… $\endgroup$
    – Gert
    Dec 1, 2021 at 19:31
  • $\begingroup$ In the above definitions, you failed to consider that $\dot{Q}=\dot{q}A$. $\endgroup$ Dec 1, 2021 at 20:09

1 Answer 1

0
$\begingroup$

As already noted by @Chet Miller, $\dot Q=\dot q A$. Therefore the first equation can be written as

$$R=\frac{\Delta T}{\dot Q}=\frac{\Delta T}{\dot q A}=\frac{L}{kA}$$

making it identical to the second equation when multiplying each side by $A$.

But it strikes me as odd, since in electric circuits the units are always Ohms.

$R$ in these equations is thermal resistance with units of Kelvins per watt ($K/W$). The electrical analog for steady heat transfer through a wall is Ohms law which gives the relationship between current ($I$) voltage ($V$) and resistance ($R$), where $R$ is electrical resistance with units of Ohms ($\Omega$).

With regard to the electrical analogs for the other parameters:

  1. $k$ is thermal conductivity with units watts per meter Kelvin ($W/(m\cdot K$)). The electrical analog is electrical conductivity with units ohm meters ($\Omega\cdot m$).

  2. $\Delta T$ is the temperature difference between the two walls in degrees Kelvin ($K$). The electrical analogy is potential difference if volts ($V$), or Joules per Coulomb ($J/C$)

  3. $\dot Q$ is heat transfer rate in watts, or Joules per second ($J/s$). The electrical analogy is current in amperes ($A$) or Coulombs per second ($C/s$)

  4. $\dot q$ is heat flux in watts per square meter ($W/m^2$). The electrical analog is current density in amperes per square meter ($A/m^2$).

Hope this helps.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.