Two fluids, $$A$$ and $$B$$ exchange heat in a counter-current heat exchanger. Fluid $$A$$ enters at $${420^ \circ }C$$ and has a mass flow rate of $$1$$ $$kg/s.$$ Fluid $$B$$ enters at $${20^ \circ }C$$ and also has a mass flow rate of $$1$$ $$kg/s,$$ Effectiveness of heat exchanger is $$75\% $$. Determine the heat transfer rate and exit temperature of fluid $$B.$$ (Specific heat of fluid $$A$$ is $$1$$ $$kJ/kg$$ $$K$$ and that of fluid $$B$$ is $$4$$ $$kJ/kgK$$).

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 $$=1000$$ $$kg/\,{m^3}.$$

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 $${C_p} = 4.2\,\,kJ/kg\,\,K$$