# 热传导

（重定向自导热性

## 傅立叶定律

### 微分形式

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

${\displaystyle {\overrightarrow {q}}}$  是热通量密度，单位W·m−2
${\displaystyle {\big .}k{\big .}}$  是这种材料的热导率，单位W·m−1·K−1
${\displaystyle {\big .}\nabla T{\big .}}$  是温度梯度，单位K·m−1

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

### 积分形式

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

• ${\displaystyle {\big .}P={\frac {\partial Q}{\partial t}}{\big .}}$  是热传导功率，即单位时间通过面积S的热量，单位W，而
• ${\displaystyle {\overrightarrow {dA}}}$  是面元矢量，单位m2

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

A 是介质的截面积，
${\displaystyle \Delta T}$  是两端温差，
${\displaystyle \Delta x}$  是两端距离。

## 热导

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

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

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

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

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