deletions | additions       diff --git a/discussion_thermal constraints.tex b/discussion_thermal constraints.tex  index 4e5e1a7..ac2c13a 100644  --- a/discussion_thermal constraints.tex  +++ b/discussion_thermal constraints.tex 
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Hydrothermal fluid at an initial temperature $\Theta$_{i} enters the fault at depth \textit{x}_{1} and flows up along the fault to a depth of \textit{x}_{2} where it has cooled to a temperature $\Theta$_{1}. We assume that the heat lost from the fluid (i) heats the immediate fault zone to the temperature of the fluid ($\Theta$_1) $\Theta$_1,  and; (ii) is lost through thermal diffusion perpendicular to the fault walls. For a parallel plate slab we can express this energy balance per metre length of fault as: \[V \cdot \left( {{\Theta _i} - {\Theta _1}} \right) \cdot C_p^w \cdot {\rho _w} = \left[ {({x_1} - {x_2}) \cdot h \cdot \left( {\frac{{{\Theta _1} - {\Theta _2}}}{2}} \right) + \left( {{\Theta _1} - {\Theta _2}} \right) \cdot \left( {{x_1} - {x_2}} \right) \cdot {{\left( {\frac{{kt}}{\pi }} \right)}^{0.5}}} \right] \cdot C_p^r \cdot {\rho _r}\]