# Form factor

The form factor F was introduced by J. Vermeer in the paper: 'A simple formula for the calculation of the convective heat transfer between conductor and sheath in compressed gas insulated (CGI) cables', 1983 as published in Elektra 87.

A different form factor - for single- and three-core PAC/GIL - was introduced by K. Itaka, T. Araki, and T. Hara in the paper: 'Heat Transfer Characteristics of Gas Spacer Cables', 1978.

Symbol
$F_{form}$
Formulae
 $\frac{D_c \left(1-\frac{D_c}{D_{comp}}\right)^{2.167}}{\ln\left(\frac{D_{comp}}{D_c}\right)}$ Vermeer1983 $\frac{1{D_c}^{\frac{3}{4}}}{\left(\ln\left(\frac{D_{comp}}{D_c}\right)+2.2\right) \left(1+\left(\frac{D_c}{D_{comp}}\right)^{\frac{3}{5}}\right)^{\frac{5}{4}}}$ Itaka1978, single-core $\frac{3{D_c}^{\frac{3}{4}}}{\left(\ln\left(\frac{D_{comp}}{2.4D_c}\right)+2.2\right) \left(1+3^{\frac{4}{5}} \left(\frac{D_c}{D_{comp}}\right)^{\frac{3}{5}}\right)^{\frac{5}{4}}}$ Itaka1978, three-core
Related
$D_c$
$D_{comp}$
Used in
$W_{conv,ce}$