Water $$\left( {{C_p} = 4.18\,kJ/kg.K} \right)$$ at $${80^ \circ }C$$ enters a counter flow heat exchanger with a mass flow rate of $$0.5kg/s.$$ Air $$\left( {{C_p} = 1\,kJ/kg.\,K} \right)$$ enters at $${80^ \circ }C$$ with a mass flow rate $$2.09$$ $$kg/s.$$ If the effectiveness of the heat exchanger is $$0.8,$$ the $$LMTD$$ (in $$^ \circ C$$) is

Cold water flowing at $$0.1$$ $$kg/s$$ is heated from $${20^ \circ }C$$ to $${70^ \circ }C$$ in a counter-flow type heat exchanger by a hot water stream flowing at $$0.1$$ $$kg/s$$ and entering at $${90^ \circ }C$$. The specific heat of water is $$4200$$ $$J$$($$kg$$ $$K$$) and density is $$1000$$ $$kg/{m^3}.$$ If the overall heat transfer coefficient $$U$$ for the heat exchanger is $$2000$$ $$W/\,\,\left( {{m^2}\,\,K} \right),$$ the required heat exchange area (in $${{m^2}}$$) is

An industrial gas $$\left( {{C_p} = 1kJ/kgK} \right)$$ enters a parallel flow heat exchanger at $${250^ \circ }C$$ with a flow rate of $$2$$ $$kg/s$$ to heat a water stream.
The water stream $$\left( {{C_p} = 4kJ/kgK} \right)$$ enters the heat exchanger at $${50^ \circ }C$$ with a flow rate of $$1kg/s.$$ The heat exchanger has an effectiveness of $$0.75.$$ The gas stream exit temperature will be