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.

Hot water flows with a velocity of $$0.1$$ $$m/s$$ in a $$100mm$$ long, $$0.1m$$ diameter pipe. Heat lost from the pipe outer wall is uniform and equal to $$420$$ $$W/{m^2}$$. If the inlet water temperature is $${80^ \circ }C,$$ calculate the water temp at the exit. Neglect effect of pipe wall thickness. $${C_p}$$ (water) $$=4.2$$ $$kJ/kg$$-$$K$$ and density of water $$=1000$$ $$kg/\,{m^3}.$$

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.