# 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

• 5.0 W/(K.m$^2$) in the CIGRE Technical Brochure 218 'Gas insulated transmission lines (GIL)' as well as in Electra 125 'Calculation of the continuous rating of three core, rigid type, compressed gas insulated cables in still air and buried'
• 9.0 W/(K.m$^2$) in the paper by R. de Lieto Vollaro et.al 'Experimental study of thermal field deriving from an underground electrical power cable buried in non-homogeneous soils', 2014, which is the reference for our multi-layer backfill method.
• 20.0 W/(K.m$^2$) in the book 'Kabel und Leitungen für Starkstrom' by L. Heinhold, 5th edition 1999 (in German) used when calculating rating of cables in unventilated, shallow-buried channels.

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