Electrical heating of a pipe

Input(s)

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

κ\kappa: Ratio of Inner Radius to Outer Radius (m2 kg s2 K1)\left(\mathrm{m}^{2} \mathrm{~kg} \mathrm{~s}^{-2} \mathrm{~K}^{-1}\right)

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

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

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

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

h: Heat Transfer Coefficient (W/(m2 K))\left(\mathrm{W} /\left(\mathrm{m}^{2} \mathrm{~K}\right)\right)

Output(s)

P: Electrical Power (Watt)

Formula(s)

P=πR2(1κ2) L( TκTa)(1κ2)R2 h(κR)24k(11κ22ln(κ))\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.


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