Consider a counter-flow heat exchanger with the inlet temperatures of two fluids (1 and 2) being T_{1, in} = 300 K and T_{2, in} = 350 K. The heat capacity rates of the two fluids are C₁ = 1000 W/K and C₂ = 400 W/K, and the effectiveness of the heat exchanger is 0.5. The actual heat transfer rate is _____ kW.

(Answer in integer)

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.