A hot fluid at $${200^ \circ }C$$ enters a heat exchanger at a mass flow rate of $${10^4}\,\,kg/hr.$$ Its specific heat is $$2000$$ $$J/kg$$-$$K.$$ It is to be cooled by another fluid entering at $${25^ \circ }C$$ with a mass flow rate $$2500$$ $$kg/hr$$ and specific heat $$400$$ $$J/kg$$-$$K$$. The overall heat transfer coefficient based on outside area of $$20\,\,{m^2}$$ is $$250\,\,\,W/{m^2}K.$$ Find the exit temperature of the hot fluid when the fluids are in parallel flow.

In a certain double pipe heat exchanger hot water flows at a rate of $$50,000$$ $$kg/h$$ and gets cooled from $${95^ \circ }C$$ to $${65^ \circ }C$$. At the same time $$50,000$$ $$kg/h$$ of cooling water at $${30^ \circ }C$$ enters the heat exchanger. The flow conditions are such that the overall heat transfer coefficient remains constant at $$2270$$ $$W/{m^2}K$$. Calculate the heat transfer area required, assuming the two streams are in parallel flow, and for both the streams $${C_p} = 4.2\,\,kJ/kg\,\,K$$

A counter flow heat exchanger is to heat air entering at $${400^ \circ }C$$ with a flow rate of $$6$$ $$kg/s$$ by the exhaust gas entering at $${800^ \circ }C$$ with a flow rate of $$4$$ $$kg/s$$. The overall heat transfer coefficient is $${100^ \circ }C$$ $$W/\left( {{m^2}K} \right)$$ and the outlet temperature of the air is $${551.5^ \circ }C.$$ Specific heat at constant pressure for both air and the exhaust gas can be taken as $$1100$$ $$J/(kgK).$$ Calculate the heat transfer area needed and the number of transfer units.

Two streams of fluid of unit constant specific heats and unit mass flow rate exchange thermal energy in an adiabatic heat exchanger. The inlet temps of hot and cold streams are $${300^ \circ }C$$ and $${30^ \circ }C$$ respectively. Calculate the $$LMTD$$ and effectiveness of the heat exchanger if the hot fluid is cooled to zero entropy condition.