A thin metal plate is exposed to solar radiation. The air and the surroundings are at $${30^ \circ }C\,.$$ The heat transfer coefficient by free convection from the upper surface of the plate is $$17.4$$ $$\,W/{m^2}K$$. The plate has an absorptivity of $$0.9$$ at solar wavelength and an emissivity of $$0.1$$ at the long wavelength. Neglecting any heat loss from the lower surface, determine the incident solar radiation intensity in $$kW/{m^2}$$ , if the measured equilibrium temperature of the plate is $${50^ \circ }C\,.$$ Stefan Boltzmannn constant is $$5.67 \times {10^{ - 8}}\,\,W/{m^2}{K^4}$$

Air enters a counter-flow heat exchanger at $${7^ \circ }C$$ and leaves at $${40^ \circ }C$$. Water enters at $${30^ \circ }C$$ and leaves at $${50^ \circ }C$$. The $$LMTD$$ in deg $$C$$ is

A company places orders for supply of two items $$A$$ and $$B.$$ The order cost for each of the items is Rs.$$300$$ /order. The inventory carrying cost is $$18\% $$ of the unit price per year per unit. The unit prices of the items are Rs.$$40$$ and Rs.$$50$$ respectively. The annual demands are $$10,000$$ and $$20,000$$ respectively.

(a) Find the economic order quantities and the minimum total cost
(b) A supplier is willing to give a $$1\% $$ discount on price, if both the items are ordered from him and if the order quantities for each item are $$1000$$ units or more. Is it profitable to avail the discount?

Given below are the data for a project network.
(a) Draw the network for the above project capturing the precedence relationships.
(b) Find the critical path and its duration.