# Convection heat transfer conductor-enclosure

Radiation heat transfer from conductor surface to inner wall of the GIL enclosure.

According to Elektra 87, the amount of heat $Q_c$ per unit length that is transmitted by convection between two horizontal coaxial cylinders can formally be described by the formula $Q_c=2\pi h_c(\theta_c-\theta_{encl})/\mathrm{ln}(D_{encl}/D_c)$.

Symbol
$W_{conv_{ce}}$
Unit
W/m
Formulae
 $F_{form} K_{0} \left(\Delta \theta_{gas}^{2} p_{comp}\right)^{0.667}$ Vermeer1983 $\Delta \theta_{gas}^{1.25} F_{form} K_{0} p_{comp}^{0.6}$ Itaka1978 $D_{c} h_{c} \pi \left(\theta_{c} - \theta_{gas}\right)$ Eteiba2002, conductor to gas, $W_{conv_c}$ $D_{comp} h_{encl} \pi \left(- \theta_{encl} + \theta_{gas}\right)$ Eteiba2002, gas to enclosure, $W_{conv_{encl}}$ $\Delta \theta_{gas} F_{form} F_{pt} K_{vermeer}$ Vermeer1983, non-linear formula
Related
$D_{c}$
$D_{comp}$
$\Delta \theta_{gas}$
$F_{form}$
$h_{encl}$
$p_{comp}$
$\theta_{c}$
$\theta_{encl}$
$\theta_{gas}$
Gas temperature [$^{\circ}$C]
Used in
$T_{1}$
$T_{conv_{ce}}$
Choices
IdMethodInfo
0Cableizer based on Vermeer1983The calculation method of the convective heat transfer between conductor and enclosure is an extension of Vermeer1983. The factors $c_{gas}$ were recalculated and extended with the factors for CO2 and dry air, which were calculated in the same way. Calculation is allowed for mixtures of two gases from SF6, N2, and CO2. Dry air contains approx. 20% of N2 and cannot be mixed further.
1Vermeer1983The calculation method of the convective heat transfer between conductor and enclosure is based on the paper 'A simple formula for the calculation of the convective heat transfer between conductor and sheath in compressed gas insulated (CGI) cables' by J. Vermeer, published 1983 in Elektra 87. A generally applicable formula was derived for the convective heat transfer in the gas of CGI cables. The non-linear formula is based on a publication from 1966 by J. Lis who investigated SF6, N2, and mixtures of these gases. The formula was linearized within the application range, that is for temperatures between 30$^{\circ}$C and 90$^{\circ}$C and for gas pressures between 2 and 6 bars for SF6 and 10 and 20 bars for N2. The method can be applied to all practical cases with two horizontal coaxial cylinders.
2Itaka1978The calculation method of the convective heat transfer between conductor and enclosure is based on the paper 'Heat Transfer Characteristics of Gas Spacer Cables', by K. Itaka et al, published 1978. The formula includes a constant \$K_{0}, the value of which was determined by experiment and given as 24.4 for SF6 and 14.9 for N2. In addition to Vermeer1983, the method allows to calculate single- and three-core cables but is limited to SF6 and N2 and cannot be extended to other gases without further measurements.
3Eteiba2002The calculation method of the convective heat transfer between conductor and enclosure is based on the paper 'Steady State and Transient Ampacities of Gas-Insulated Transmission Lines', by M. B. Eteiba, published 2002. The method is based on calculation of the heat transfer coefficients by use of Nusselt numbers between conductor and gas, and between gas and enclosure as published 1976 by T. H. Kuehn and R. J. Goldstein. It could be used to calculate with any gas and mixtures thereof. Implementation was done for unmixed gases only.