In Section 11.8 we discussed the ability to use a heat exchanger simultaneously as a chemical reactor. In that example, we were running an exothermic reaction. Suppose we were interested in running an endothermic, first-order, decomposition reaction instead.

a. On which side of the heat exchanger should we run the reaction and why?

b. Repeating the analysis of Section 11.8 along with its restrictions, show that the design equation for the exchanger becomes:

\[q=U P_{d} L\left\{\frac{\left(T_{h i}-T_{c o}\right)-\left(T_{h o}-T_{c i}-\Delta T_{R}\right)}{\ln \left[\frac{T_{h i}-T_{c o}}{T_{h o}-T_{c i}-\Delta T_{R}}\right]}\right\}\]