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$$ 
  C_e \rho_e \frac{\partial T_e}{\partial t} = 
  \bigtriangledown (\kappa_e \bigtriangledown T_e) - 
  g_p (T_e - T_a) + g_s T_a' + \theta (x-x_{surface})I_0 \exp(-x/l_{skin})
$$

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