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Limit of thickness of soil layer

Thickness of soil layer providing a thermal resistance equivalent to $h_{amb}$, when the laying depth approaches the radius of the pipe, $L_{cm}$ → $D_{ext}/2$.

Symbol
$e_{limit}$
Unit
m
Formulae
$\frac{D_{ext}}{2} \left(e^{\frac{2k_4}{D_{ext} h_{ext}}}-1\right)$
Related
$D_{ext}$
Overall outer diameter of pipe [m]
$h_{ext}$
External heat transfer coefficient [W/(K.m$^2$)]
$k_4$
Thermal conductivity of soil [W/(m.K)]
Used in
$h_{ground}$
Heat transfer coefficient buried part of wall to soil [W/(K.m$^2$)]