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

In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to

Customers arrive at a ticket counter at a rate of $$50$$ per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is $$1$$ $$min.$$ Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in $$min$$ is