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 _________.

A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tube side water at $$19$$ liter/s is heated from $${10^ \circ }C$$ to $${38^ \circ }C$$. Shell side water at $$25$$ liter/s is entering at $${46^ \circ }C$$. Assume constant properties of water; density is $$1000\,kg/{m^3}$$ and specific heat is $$4186$$ $$J/kg.K.$$ The $$LMTD$$ (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 (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