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Table 1 Distribution of minimum positive root \( \alpha_{1} \) of Eq. 6 at different radii of thermal impacted circle

From: An efficient hybrid model for thermal analysis of deep borehole heat exchangers

\( {{r_{b} } \mathord{\left/ {\vphantom {{r_{b} } {r_{\infty } }}} \right. \kern-0pt} {r_{\infty } }} \)

0.001

0.01

0.02

0.05

0.1

0.2

\( \alpha_{1} r_{\infty } \)

3.832

3.832

3.836

3.860

3.941

4.236