In a counter-flow heat exchanger, water is heated at the rate of $$1.5kg/s$$ from $$\,40{}^ \circ C\,$$ to $$\,80{}^ \circ C\,$$ by an oil entering at $$\,120{}^ \circ C\,$$ and leaving at $$\,60{}^ \circ C\,$$. The specific heats of water and oil are $$4.2kJ/kgK$$ and $$2kJ/kgK,$$ respectively. The overall heat transfer coefficient is $$400\,W/{m^2}K.$$ The required heat transfer surface are (in $${m^2}$$) is

Consider a parallel-flow heat exchanger with area $${A_p}$$ and a counter-flow heat exchanger with area $${A_c}.$$ In both the heat exchangers, the hot stream flowing at $$1$$ $$kg/s$$ cools from $$80{}^ \circ C$$ to $$50{}^ \circ C$$. For the cold stream in both the heat exchangers, the flow rate and the inlet temperature are $$2$$ $$kg/s$$ and $$10{}^ \circ C$$, respectively. The hot and cold streams in both the heat exchangers are of the same fluid. Also, both the heat exchangers have the same overall heat transfer coefficient. The ratio $${A_c}/{A_p}$$ is ______________

A balanced counter-flow heat exchanger has a surface area of $$20\,\,{m^2}$$ and overall heat transfer coefficient of $$20$$ $$W/{m^2}$$-$$K$$. Air $$\left( {{C_p} = 1000J/kg - K} \right)$$ entering at $$0.4$$ $$kg/s$$ and $$280$$ $$K$$ is to preheated by the air leaving the system at $$0.4$$ $$kg/s$$ and $$300$$ $$K.$$ The outlet temperature (in $$K$$) of the preheated air is