# Electrical heating of a pipe

## Input(s)

$$\mathrm{R}$$: Radius $$(\mathrm{m})$$

$$\kappa$$: Ratio of Inner Radius to Outer Radius $$\left(\mathrm{m}^{2} \mathrm{~kg} \mathrm{~s}^{-2} \mathrm{~K}^{-1}\right)$$

L: Length $$(\mathrm{m})$$

$$\mathrm{T}_{\kappa}$$: Desired Temperature $$(\mathrm{K})$$

$$\mathrm{T}_{\mathrm{a}}$$: Ambient Air Temperature (K)

$$\mathrm{k}$$: Thermal Conductivity $$(\mathrm{W} / \mathrm{m} \mathrm{K})$$

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

## Output(s)

P: Electrical Power (Watt)

## Formula(s)

$\mathrm{P}=\frac{\pi * \mathrm{R}^{2} *\left(1-\kappa^{2}\right) * \mathrm{~L} *\left(\mathrm{~T}_{\kappa}-\mathrm{T}_{\mathrm{a}}\right)}{\left(1-\kappa^{2}\right) * \frac{\mathrm{R}}{2 * \mathrm{~h}}-\frac{(\kappa * \mathrm{R})^{2}}{4 * \mathrm{k}} *\left(1-\frac{1}{\kappa^{2}}-2 * \ln (\kappa)\right)}$

## Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 10, Page: 325.

## Related

### Surface temperature of a heating coil

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