We showed in Section 11.5.1 that for a counterflow heat exchanger, the log-mean temperature difference was:

\[\Delta T_{l m, c o u n t e r}=\left[\frac{\left(T_{h i}-T_{c o}\right)-\left(T_{h o}-T_{c i}\right)}{\ln \left(\frac{T_{h i}-T_{c o}}{T_{h o}-T_{c i}}\right)}\right]\]

Using the analysis from the section to describe the temperature difference between the hot and cold streams and the overall heat exchanged, show that for a co-flow heat exchanger where the inlet hot fluid contacts the inlet cold fluid, the log-mean temperature difference is:

\[\Delta T_{l m, c o-f l o w}=\left[\frac{\left(T_{h i}-T_{c i}\right)-\left(T_{h o}-T_{c o}\right)}{\ln \left(\frac{T_{h i}-T_{c i}}{T_{h o}-T_{c o}}\right)}\right]\]