# 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.

The equivalent thermal resistance of the soil per unit surface, representing convection, is equal to a value of 0.20 K.m$^2$/W, refer to CIGRE Guide 218 or Electra 125 'Calculation of the continuous rating of three core, rigid type, compressed gas insulated cables in still air and buried'.

Symbol
$h_{tr}$
Unit
W/(K.m$^2$)
Formulae
 $\frac{\mathrm{Nu}_L k_{gas}}{L_{char}}$ Kutateladze $9$ Multi-layer backfill (R. de Lieto Vollaro et al. 2014) $5$ Kenelly (CIGRE Guide 218) $20$ channel (Heinhold)
Used in
$d_{im}$
$T_{surf}$