The heat transfer coefficient of ground is combining the inside film coefficient, heat transfer coefficient of pipe wall and heat transfer coefficient of soil.
The equation acc. Carslaw & Jaegers is used for $h_{buried}$ reaching a limit when $H$ → $D_{ext}/2$ using the quantity $e_{limit}$.
| $\frac{2k_4}{D_{ref}} \frac{1}{\cosh^{-1}\left(1+\frac{2e_{limit}}{D_{ext}}\right)}$ | Carslaw & Jaeger |
| $\frac{2k_4}{D_{ref}} \frac{2}{\beta_b \left(\pi-\beta_b\right)} \frac{C_{g1}}{\sqrt{{C_{g2}}^2-1}} \left(\frac{\pi}{2}-\\arctan\left(\sqrt{\frac{C_{g2}+1}{C_{g2}-1}} tan\left(\frac{\beta_b}{2}\right)\right)\right)$ | Morud & Simonsen $C_{g2}$ > 1 |
| $\frac{2k_4}{D_{ref}} \frac{1}{\beta_b \left(\pi-\beta_b\right)} \frac{C_{g1}}{\sqrt{1-{C_{g2}}^2}} \ln\left(\frac{tan\left(\frac{\beta_b}{2}\right)+\sqrt{\frac{1-C_{g2}}{1+C_{g2}}}}{tan\left(\frac{\beta_b}{2}\right)-\sqrt{\frac{1-C_{g2}}{1+C_{g2}}}}\right)$ | Morud & Simonsen $C_{g2}$ ≤ 1 |
| $\frac{2k_4}{D_{ref}} \frac{1}{\pi \left(1+\frac{\mathrm{Bi}_p}{\mathrm{Bi}_g}\right)} \frac{2\mathrm{Bi}_p sin\left(\beta_0\right) \\arctan\left(\sqrt{\frac{1-K_{par}}{1+K_{par}}}\right)}{\sqrt{1-{K_{par}}^2}}$ | Ovuworie $|K_{par}|$ < 1 |
| $\frac{2k_4}{D_{ref}} \frac{1}{\pi \left(1+\frac{\mathrm{Bi}_p}{\mathrm{Bi}_g}\right)} \mathrm{Bi}_p sin\left(\beta_0\right)$ | Ovuworie $K_{par}$ = 1 |
| $\frac{2k_4}{D_{ref}} \frac{1}{\pi \left(1+\frac{\mathrm{Bi}_p}{\mathrm{Bi}_g}\right)} \frac{2\mathrm{Bi}_p sin\left(\beta_0\right) \tanh^{-1}\left(\sqrt{\frac{K_{par}-1}{K_{par}+1}}\right)}{\sqrt{{K_{par}}^2-1}}$ | Ovuworie $K_{par}$ > 1 |
| $\frac{2k_4}{D_{ref}} \frac{\mathrm{Bi}_p}{\left(\left(1+\frac{\mathrm{Bi}_p}{\mathrm{Bi}_g}\right) \left(1+2\mathrm{Bi}_p\right)\right)^{0.5}}$ | OTC 23033 |
