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\mbox{if} \, z < z_f  \Rightarrow T_b(t,z) = T_f + (T_G(z) - T_f) \cdot \frac{2}{\sqrt{\pi}} \int_0^{(z_f -z)/\sqrt{4at}} e^{-\xi^2} d\xi



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\mbox{if} \, z_f \leq z \leq z_f + h_f  \Rightarrow T_b(t,z) = T_f



LaTeX Math Block
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\mbox{if} \, z > z_f + h_f  \Rightarrow T_b(t,z) = T_f + (T_G(z) - T_f) \cdot \frac{2}{\sqrt{\pi}} \int_0^{z/\sqrt{4at}} e^{-\xi^2} d\xi



See Also

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Geology / Geothermal Temperature Field / Geothermal Temperature Profile

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