1 \documentstyle[12pt
]{article
}
6 U^
{cond
} =
\displaystyle\sum_{i=
1}^
{N
} u_
{i
}^
{cond
} \\
7 U^
{mech
} =
\displaystyle\sum_{i=
1}^
{N
} u_
{i
}^
{mech
} \\
8 U^
{chem
} =
\displaystyle\sum_{i=
1}^
{N
} u_
{i
}^
{chem
} \\
9 U =
\displaystyle\sum_{i=
1}^
{N
} (u_
{i
}^
{cond
} + u_
{i
}^
{mech
} + u_
{i
}^
{chem
}) \\
10 \theta_{avg
} = (
\frac{1}{N
}\displaystyle\sum_{i=
1}^
{N
} \frac{1}{\theta_{i
}})^
{-
1} \\