# Heat conduction in a cooling fan

## Input(s)

z: Distance from Start of Fan (cm)

L: Length of Fan $$(\mathrm{cm})$$

B: Breadth of Fan $$(\mathrm{cm})$$

$$\mathrm{h}$$: Heat Transfer Coefficient $$\left(\mathrm{J} / \mathrm{s} \mathrm{m}^{2} \mathrm{~K}\right)$$

k: Thermal Conductivity (W/cm K)

$$T_{w}$$: Temperature of Wall (K)

$$T_{a}$$: Ambient Temperature of Air (K)

## Output(s)

$$\xi$$: Dimensionless Distance (dimensionless)

N: Dimensionless Heat Transfer Coefficient (dimensionless)

$$\Theta$$: Dimensionless Temperature (dimensionless)

T: Temperature at Distance $$\mathrm{Z}$$ from Wall at the Fan $$(\mathrm{K})$$

## Formula(s)

$\begin{gathered} \xi=\frac{\mathrm{z}}{\mathrm{L}} \\ \mathrm{N}=\left(\frac{\mathrm{h} *\left(\mathrm{~L}^{2}\right)}{\mathrm{k} * \mathrm{~B}}\right)^{0.5} \\ \Theta=\frac{\cosh (\mathrm{N} *(1-\xi))}{\cosh (\mathrm{N})} \\ \mathrm{T}=\mathrm{T}_{\mathrm{a}}+\Theta *\left(\mathrm{~T}_{\mathrm{w}}-\mathrm{T}_{\mathrm{a}}\right) \end{gathered}$

## Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 10, Pages: 308, 309.

## Related

### Heat flux distribution in a wall

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