熱傳導

傅立葉定律

微分形式

${\displaystyle {\overrightarrow {q}}=-k{\nabla }T}$

${\displaystyle {\overrightarrow {q}}}$ 是熱通量密度，單位W·m−2
${\displaystyle {\big .}k{\big .}}$ 是這種材料的熱導率，單位W·m−1·K−1
${\displaystyle {\big .}\nabla T{\big .}}$ 是溫度梯度，單位K·m−1

${\displaystyle q_{x}=-k{\frac {dT}{dx}}}$

積分形式

${\displaystyle P={\frac {\partial Q}{\partial t}}=-k\oint _{S}{{\overrightarrow {\nabla }}T\cdot \,{\overrightarrow {dA}}}}$

• ${\displaystyle {\big .}P={\frac {\partial Q}{\partial t}}{\big .}}$ 是熱傳導功率，即單位時間通過面積S的熱量，單位W，而
• ${\displaystyle {\overrightarrow {dA}}}$ 是面元矢量，單位m2

${\displaystyle {\big .}P={\frac {\Delta Q}{\Delta t}}=-kA{\frac {\Delta T}{\Delta x}}}$

A 是介質的截面積，
${\displaystyle \Delta T}$ 是兩端溫差，
${\displaystyle \Delta x}$ 是兩端距離。

熱導

${\displaystyle {\big .}U={\frac {kA}{\Delta x}},\quad }$

${\displaystyle {\big .}P={\frac {\Delta Q}{\Delta t}}=U\,(-\Delta T).}$

${\displaystyle {\big .}R={\frac {1}{U}}={\frac {\Delta x}{kA}}={\frac {-\Delta T}{P}}.}$

${\displaystyle {\big .}{\frac {1}{U}}={\frac {1}{U_{1}}}+{\frac {1}{U_{2}}}+{\frac {1}{U_{3}}}+\cdots }$

${\displaystyle {\big .}P={\frac {\Delta Q}{\Delta t}}={\frac {A\,(-\Delta T)}{{\frac {\Delta x_{1}}{k_{1}}}+{\frac {\Delta x_{2}}{k_{2}}}+{\frac {\Delta x_{3}}{k_{3}}}+\cdots }}.}$