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

A company uses $$2555$$ units of an item annually. Delivery lead time is $$8$$ days. The recorder point (in number of units) to achieve optimum inventory is

The expected time $$\left( {{t_e}} \right)$$ of a $$PERT$$ activity in terms of optimistic time $$\left( {{t_0}} \right)$$, pessimistic $$\left( {{t_p}} \right)$$ and most likely time $$\left( {{t_L}} \right)$$ is given by

Consider the following network

The optimistic time, most likely time and pessimistic time of all the activities are given in the table below :

The critical path duration of the network (in days) is