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\subsection{Thermal constraints on fluid flux}  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 $\Theta$_{1} $\Theta$_{i}  enters the fault at depth X_{1} and flows up along the fault to a depth of X_{2} where it has cooled to a temperature $\Theta$_{2}. $\Theta$_{1}.  We assume that the  heat lost  from the fluid is lost to heating (i) heats  the immediate  fault zone to the temperature of the fluid and ($\Theta$_1) and; (ii) is lost  through thermal diffusion. diffusion perpendicular to the fault walls.  We can express the this  energy balance as: \[V \cdot \left( {{\Theta _i} - {\Theta _1}} \right) \cdot C_p^w \cdot {\rho _w} = \left[ {({x_1} - {x_2}) \cdot h \cdot \left( {\frac{{{\Theta _1} - {\Theta _2}}}{2}} \right) + \left( {{\Theta _1} - {\Theta _2}} \right) \cdot \left( {{x_1} - {x_2}} \right) \cdot {{\left( {\frac{{kt}}{\pi }} \right)}^{0.5}}} \right] \cdot C_p^r \cdot {\rho _r}\]