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 $$\left( {{C_p} = 4.18\,kJ/kg.K} \right)$$ 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

In a parallel flow heat exchanger operating under steady state, the heat capacity rates (product of specific heat at constant pressure and mass flow rate) of the hot and cold fluid are equal. The hot fluid, flowing at $$1kg/sec$$ with $$sp.$$ heat $$= 4kJ/kgK,$$ enters the heat exchanger at $${102^ \circ }C$$ while the cold fluid has an inlet temperature of $${15^ \circ }C$$. The overall heat transfer coefficient for the heat exchanger is estimated to be $$1\,\,kW/{m^2}K$$ and the corresponding heat transfer surface area is $$5{m^2}$$. Neglect heat transfer between the heat exchanger and the ambient.

The heat exchanger is characterized by the following relation $$2\varepsilon = 1 - Exp\left( { - 2NTU} \right).$$ The exit temp (in $$^ \circ C$$) for the cold fluid is

The $$LMTD$$ of a counter flow heat exchanger is $${20^ \circ }C$$. The cold fluid enters at $${20^ \circ }C$$ and the hot fluid enters at $${100^ \circ }C$$. Mass flow rate of the cold fluid is twice that of the hot fluid. specific heat at constant pressure of the fluid is twice that of the cold fluid. The exit temperature of the cold fluid is