Heat transfer coefficient

The heat transfer coefficient (or film coefficient) is the proportionality constant between the heat flux q and the temperature difference $\Delta T$ as the thermodynamic driving force for the flow of heat: $h_{tr}=\frac{q}{\Delta T}$. It is used in calculating the heat transfer, typically by convection.

Calculation of $h_{tr}$ is based on the paper 'Calculation of cable thermal rating considering non-isothermal earth surface' from 2014 by S. Purushothaman, F. de León, and M. Terracciano which uses the Fourier transformation to convert the two-dimensional problem for horizontal plates into a simple one-dimensional problem.

Typical values for the equivalent thermal resistance of the soil per unit surface, representing convection, is given in various sources such as

$\frac{\mathrm{Nu}_L k_{gas}}{L_{char}}$Kutateladze
$5$Kennelly (CIGRE Guide 218)
$9$Multi-layer backfill (R. de Lieto Vollaro et al. 2014)
$20$channel (Heinhold)