Consider two large parallel plates, one at $${T_1} = {727^ \circ }C$$ with emissivity $${\varepsilon _1} = 0.8$$ and the other at $${T_2} = {227^ \circ }C\,$$ with emissivity $${\varepsilon _2} = 0.4.$$ An aluminium radiation shield with an emissivity, $${\varepsilon _s} = 0.05$$ on both sides is placed between the plates. Calculate the percentage reduction in heat transfer rate between the two plates as a result of the shield.
Use $$\sigma = 5.67 \times {10^{ - 8}}W/\left( {{m^2}{K^4}} \right)$$

A counter flow heat exchanger is to heat air entering at $${400^ \circ }C$$ with a flow rate of $$6$$ $$kg/s$$ by the exhaust gas entering at $${800^ \circ }C$$ with a flow rate of $$4$$ $$kg/s$$. The overall heat transfer coefficient is $${100^ \circ }C$$ $$W/\left( {{m^2}K} \right)$$ and the outlet temperature of the air is $${551.5^ \circ }C.$$ Specific heat at constant pressure for both air and the exhaust gas can be taken as $$1100$$ $$J/(kgK).$$ Calculate the heat transfer area needed and the number of transfer units.

If the demand for an item is doubled and the ordering cost halved, the economic order quantity

Consider the following data for a product:
Demand $$=1000$$ units/year
Order cost $$=$$ Rs.$$40$$/order
Holding cost $$ = 10\% $$ of the unit cost / unit-year
Unit cost $$=$$ Rs.$$500$$

(a) What is the economic order quantity?
(b) Under the $$EOQ$$ what is the number of annual orders?
(c) With a policy of ordering every month what would be the total annual cost as a percentage of the cost at $$EOQ$$?