Thermal Resistance
Consider a layer with thickness \(L\) and surface area \(A\) as shown in Figure . If there is a temperature difference across this layer, there will be conduction heat transfer from its high temperature side to its low temperature side. Fourier’s law gives the magnitude of this conduction heat transfer rate as
\[
\dot{Q}_{\text{cond}}=kA\frac{T_1-T_2}{L}
\]
or
\[
\dot{Q}_\text{cond}=\dfrac{T_1-T_2}{L/kA}
\]
we can rewirte this equation as
\[
\quad\dot{Q}_{\text{cond}}=\dfrac{T_1-T_2}{R_{\text{cond}}}
\]
where,
\[
R_{cond} = L/kA
\]
where \(R_{\text{cond}}\) is called conduction thermal resistance and is measured with the unit °C/W.
Thermal resistances concept can also be applied to convection and radiation heat transfer.
For convection heat transfer
\[
\dot{Q}_\text{conv}=hA(T_s-T_\infty)
\]
it can be rewrite as
\[
\dot Q_\text{conv}=\dfrac{T_s-T_\infty}{R_\text{conv}}
\]
For radiation heat transfer
\[
\quad\dot Q_{\text{rad}}=h_{\text{rad}}A(T_s-T_{\text{surr}})
\]
it can be rewrite as
\[
\dot{Q}_{\text{rad}}=\dfrac{T_s-T_{\text{surr}}}{R_{\text{rad}}}
\]