From d959b34541f5b1d18d0e3ebf18f8c24096bf860d Mon Sep 17 00:00:00 2001 From: Ray Speth Date: Sat, 14 Dec 2013 00:18:00 +0000 Subject: [PATCH] [Doc] Fix typos in documentation of reactor model Resolves Issue 191. --- doc/sphinx/reactors.rst | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/doc/sphinx/reactors.rst b/doc/sphinx/reactors.rst index 04774b66b..103a412bf 100644 --- a/doc/sphinx/reactors.rst +++ b/doc/sphinx/reactors.rst @@ -106,8 +106,8 @@ for `dm/dt`, the equation for each homogeneous phase species is: .. math:: - m \frac{dY}{dt} = \sum_{in} \dot{m}_in (Y_{k,in} - Y_k)+ - \dot{m}_{k,gen} - Y_k \dot{m}_{gen} + m \frac{dY}{dt} = \sum_{in} \dot{m}_{in} (Y_{k,in} - Y_k)+ + \dot{m}_{k,gen} - Y_k \dot{m}_{wall} Energy Conservation ------------------- @@ -117,7 +117,7 @@ for an open system: .. math:: - \frac{dU}{dt} = - p \frac{dV}{dt} - Q + + \frac{dU}{dt} = - p \frac{dV}{dt} - \dot{Q} + \sum_{in} \dot{m}_{in} h_{in} - h \sum_{out} \dot{m}_{out} Ideal Gas Reactor @@ -141,9 +141,9 @@ temperature: .. math:: - m c_v \frac{dT}{dt} = - p \frac{dV}{dt} - Q + m c_v \frac{dT}{dt} = - p \frac{dV}{dt} - \dot{Q} + \sum_{in} \dot{m}_{in} \left( h_{in} - \sum_k u_k Y_{k,in} \right) - - p V \sum_{out} \dot{m}_{out} - \sum_k \dot{m}_{k,gen} u_k + - \frac{p V}{m} \sum_{out} \dot{m}_{out} - \sum_k \dot{m}_{k,gen} u_k While this form of the energy equation is somewhat more complicated, it significantly reduces the cost of evaluating the system Jacobian, since the @@ -168,7 +168,7 @@ Noting that `dp/dt = 0` and substituting into the energy equation yields: .. math:: - \frac{dH}{dt} = - Q + \sum_{in} \dot{m}_{in} h_{in} + \frac{dH}{dt} = - \dot{Q} + \sum_{in} \dot{m}_{in} h_{in} - h \sum_{out} \dot{m}_{out} The species and continuity equations are the same as for the general reactor @@ -193,5 +193,5 @@ temperature: .. math:: - m c_p \frac{dT}{dt} = - Q - \sum_k h_k \dot{m}_{k,gen} + m c_p \frac{dT}{dt} = - \dot{Q} - \sum_k h_k \dot{m}_{k,gen} + \sum_{in} \dot{m}_{in} \left(h_{in} - \sum_k h_k Y_{k,in} \right)