Getting a error in the following code “! Missing delimiter (. inserted).”

$$\eta_{TEG}=\frac{P_{elec}}{\dot{\mathrm{m}} C_{p ex}\left(T_{in}-T_{out})\right} \label{eq:tege}$$

• you need a delimiter after \right either \right) or \right. if you want nothing – David Carlisle May 3 '19 at 7:50
• but you do not want \left or \right as there is no need to stretch the delimiters so just use (...) – David Carlisle May 3 '19 at 7:51

You have written

\left(...)\right


but the correct syntax is

\left(...\right)


However, in your particular case such rescaling of brackets is completely unnecessary.

\documentclass{article}

\begin{document}
$$\eta_{\mathrm{TEG}}=\frac{P_{\mathrm{elec}}}{\dot{\mathrm{m}} C_{p\,\mathrm{ex}}\left(T_{\mathrm{in}}-T_{\mathrm{out}}\right)} =\frac{P_{\mathrm{elec}}}{\dot{\mathrm{m}} C_{p\,\mathrm{ex}}(T_{\mathrm{in}}-T_{\mathrm{out}})} \label{eq:tege}$$
\end{document}


Incidentally, I have made most of your subscripts \mathrm, but do not have enough context to know whether this is appropriate for the C_{p ex}. If there really is a space in this subscript, then probably you want a thin space \, before the C too.