The functions F(p,θ) and F(p) were 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.
For the conditions prevailing CGI-cables and GIL filled with SF6 or with N2, that is for temperatures between 30°C and 90°C and for gas pressures between 2 and 6 bars for SF6 and 10 and 20 bars for N2, it can be shown that the functional relation $F_{pt} can be linearized.
$c_{Kc} p_{\mathrm{comp}}^{0.667}$ | Vermeer1983, linearized function of pressure |
$\left(\frac{c_{p comp}}{\nu_{\mathrm{gas}}^{2}} k_{\mathrm{gas}}^{2} \rho_{\mathrm{gas}}^{2}\right)^{0.333}$ | Vermeer1983, function of pressure and temperature |