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.

A one shell pass, one tube-pass heat exchanger, has counter flow configuration between the shell side and tube side fluids. The total number of tubes within the heat exchanger is $$10$$ and the tube dimensions are $$ID=10$$ $$mm,$$ $$OD=12$$ $$mm$$ and length $$=1m.$$ saturated dry steam enters the shell side at a flow rate of $$2$$ $$kg/s$$ and the temp of $${100^ \circ }C.$$ In the tube side, cold water enters at a flow rate of $$10$$ $$kg/s$$ with an inlet temp of $${25^ \circ }C.$$ The $$OHTC$$ based on the outer surface area of the tubes is $$50$$ $$W/{m^2}K.$$ The specific heat of water is $$4.18$$ $$kJ/kg$$-$$K$$ and the latent heat of steam is $$2500$$ $$kJ/kg.$$ What is the condition of the steam at the exit.

A double pipe counter flow heat exchanger is to be designed to cool $$12000$$ $$kg/hr$$ of an oil of specific heat $$1.95$$ $$kJ/kgK$$ from $$\,85{}^ \circ C$$ to $$\,55{}^ \circ C$$ by water entering the heat exchanger at $$\,30{}^ \circ C$$ and leaving at $$\,45{}^ \circ C$$. If the $$OHTC$$ of heat exchanger is $$400$$ $$\,W/{m^2}K.\,$$ Calculate the $$LMTD$$ and the surface area of the heat exchanger

A shell and tube heat exchanger is to be designed for heating pressurized water by means of hot gasses which get cooled the data are as follows
Temp of water at the inlet $$ = \,80{}^ \circ C$$
Temp of the water at the outlet $$ = \,140{}^ \circ C$$
Temp of hot gasses at the inlet $$ = \,340{}^ \circ C$$
Temp of hot gasses at the outlet $$ = \,180{}^ \circ C$$
Mass flow rate of water $$=12$$ $$kg/s,$$ Specific heat of water $$=4.2kJ/kgK$$
$$OHTC=30$$ $$W/{m^2}K$$,
Correction factor for $$LMTD$$ based on counter flow conditions $$=0.9$$
Calculate the tube surface area required in the heat exchanger and the effectiveness of the heat exchanger.