In a concentric counter flow heat exchanger, water flows through the inner tube at $${25^ \circ }C$$ and leaves at $${42^ \circ }C$$. The engine oil enters at $${100^ \circ }C$$ and flows in the annular flow passage. The exit temperature of the engine oil is $${50^ \circ }C.$$ Mass flow rate of water and the engine oil are $$1.5kg/s$$ and $$1$$ $$kg/s,$$ respectively. The specific heat of water and oil are $$4178$$ $$J/kg.K$$ and $$2130$$ $$J/kg.K,$$ respectively. The effectiveness of this heat exchanger is _________.

Water (specific heat, $${c_p} = 4.18\,\,kJ/kgK$$ ) enters a pipe at a rate of $$0.01$$ $$kg/s$$ and temperature of $${20^ \circ }C.$$ The pipe, of diameter $$50$$ $$mm$$ and length $$3$$ $$m,$$ is subjected to a wall heat flux $${q_w}$$ in $$W/{m^2}:$$

If $${q_w}$$ $$=2500x,$$ where $$x$$ is $$m$$ and in the direction of flow ($$x=0$$ at the inlet), the bulk mean temperature of the water leaving the pipe in $$^ \circ C$$ is

Water (specific heat, $${c_p} = 4.18\,\,kJ/kgK$$ ) enters a pipe at a rate of $$0.01$$ $$kg/s$$ and temperature of $${20^ \circ }C.$$ The pipe, of diameter $$50$$ $$mm$$ and length $$3$$ $$m,$$ is subjected to a wall heat flux $${q_w}$$ in $$W/{m^2}:$$

If $${q_w}$$ $$=5000$$ and the convection heat transfer coefficient at the pipe outlet is $$1000$$ $$W/{m^2}K,$$ the temperature in $$^ \circ C$$ at the inner surface of the pipe at the outlet is

Water $$\left( {{C_p} = 4.18\,kJ/kg.K} \right)$$ at $${80^ \circ }C$$ enters a counter flow heat exchanger with a mass flow rate of $$0.5kg/s.$$ Air $$\left( {{C_p} = 1\,kJ/kg.\,K} \right)$$ enters at $${80^ \circ }C$$ with a mass flow rate $$2.09$$ $$kg/s.$$ If the effectiveness of the heat exchanger is $$0.8,$$ the $$LMTD$$ (in $$^ \circ C$$) is