Saturated steam at $${100^ \circ }C$$ condenses on the outside of a tube. Cold fluid enters the tube at $${20^ \circ }C$$ and exits at $${50^ \circ }C.$$ The value of the Log Mean Temperature Difference $$(LMTD)$$ is _________ $$^ \circ C.$$

For a heat exchanger, $$\Delta {T_{\max }}$$ is the maximum temperature difference and $$\Delta {T_{\min }}$$ is the minimum temperature difference between the two fluids. $$LMTD$$ is the log mean temperature difference. $${C_{\min }}$$ and $${C_{\max }}$$ are the minimum and the maximum heat capacity rates. The maximum possible heat transfer $$\left( {{Q_{\max }}} \right)$$ between the two fluids is

Saturated vapor is condensed to saturated liquid in a condenser. The heat capacity ratio is $${c_r} = {{{c_{\min }}} \over {{c_{\max }}}}.$$ The effectiveness $$(s)$$ of the condenser is.

In a heat exchanger, it is observed that $$\Delta {T_1} = \Delta {T_2},$$ where $$\Delta {T_1}$$ is the temperature difference between the two single phase fluid streams at one end and $$\Delta {T_2}$$ is the temperature difference at the other end. This heat exchanger is