deletions | additions       diff --git a/discussion_thermal constraints.tex b/discussion_thermal constraints.tex  index 3d2f7b9..a2c25ad 100644  --- a/discussion_thermal constraints.tex  +++ b/discussion_thermal constraints.tex 
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\subsection{Thermal constraints on fluid flux}  A requirement of the mixing model is that fluid ascent is fast enough such that heat is largely retained in the fluid and temperature can be used as a conservative tracer for the two components.  To a first approximation we can use the estimated temperatures of the fluid end members to constrain the flux of fluid needed to develop a thermal anomaly similar to that observed at Dirtlow Rake. The question is how much fluid and how fast does it have to flow along the fault to (i) heat the rock in the fault zone and (ii) prevent significant heat loss via conduction through the walls of the fault? The problem is illustrated in Figure 8. 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) 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: \[V \cdot \left( {{\Theta _i} - {\Theta _1}} \right) \cdot C_p^w \cdot {\rho _w} = \left[ {({x_1} - {x_2}) \cdot h \cdot \left( {\frac{{{\Theta _1} - {\Theta _2}}}{2}} \right) + \left( {{\Theta _1} - {\Theta _2}} \right) \cdot \left( {{x_1} - {x_2}} \right) \cdot {{\left( {\frac{{kt}}{\pi }} \right)}^{0.5}}} \right] \cdot C_p^r \cdot {\rho _r}\]