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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