傅里叶热传导定律
Fourier’s Law of Heat Conduction
热通量Heat Flux 表达式
其中
$ \pmb q $ 是单位面积上的热通量， $W·m^{−2}$,
$k$ 是材料的热传导系数， $W·m^{−1}·K^{−1}$,
$\nabla T$ 是温度梯度，$K·m^{−1}$.
$q_x$物理的意义：在x方向上单位面积的热通量，可以表达为
其中
$k$是材料的热传导系数， $W·m^{−1}·K^{−1}$,
$ T$是物体的温度, $K$
$ x $是长度, $m$
1.直角坐标系($ x, y, z $)
| 直角坐标系Cartesian coordinates ($\textit { x,y,z }$): | NO. |
|---|---|
| $q_x=-k\dfrac {\partial T}{\partial x}$ | 1-1 |
| $q_y=-k\dfrac {\partial T}{\partial y}$ | 1-2 |
| $q_z=-k\dfrac {\partial T}{\partial z}$ | 1-3 |
2.圆柱坐标系（$r,\theta, z$)
| 圆柱坐标系Cylindrical coordinates coordinates ($\textit {r, $\theta$, z }$): | NO. |
|---|---|
| $q_r=-k\dfrac {\partial T}{\partial r}$ | 2-1 |
| $q_\theta=-k \dfrac {1}{r} \dfrac {\partial T}{\partial \theta}$ | 2-2 |
| $q_z=-k\dfrac {\partial T}{\partial z}$ | 2-3 |
3.球坐标系（$r, \theta, \phi $)
| 球坐标系Spherical coordinates（$\textit {r, $\theta$, $\phi$ }$): | NO. |
|---|---|
| $q_r=-k\dfrac {\partial T}{\partial r}$ | 3-1 |
| $q_\theta=-k \dfrac {1}{r} \dfrac {\partial T}{\partial \theta}$ | 3-2 |
| $q_\phi=-k \dfrac {1}{r sin \theta} \dfrac {\partial T}{\partial \theta}$ | 3-3 |
参考文献
- R. Byron Bird, Warren E. stewart, Edwin N. Lightfoot. Transport phenomena:Revised second edition John Wiely &Sons, Inc.