A heat recovery device involves transferring energy from hot flue gases passing counter currently through an annular region to pressurized water flowing through the inner tube of the annulus. The inner tube has inner and outer diameters of 24 and 30 mm, respectively, and is connected by eight struts to an insulated outer tube of 60 mm diameter. Each strut is 3 mm thick and is integrally fabricated with the inner tube from carbon steel (k = 50 W/m K). Consider the situation for which water and flue gases enter the device at 300 K and 800 K, respectively. The flue gases may be assumed to have properties of air. The mass flow rate of water is 0.2 kg/s. The mass flow rate of flue gases at 1.0 kg/s. If the desired outlet temperature of the pressurized water is 350 K, determine:

i)  The outlet temperature of flue gases

ii)  The heat transfer coefficient at the water side

iii) The heat transfer coefficient at the air side

iv) The overall heat transfer coefficient based on the inside perimeter (U_i)

v)  The required length of this heat recovery device

Hints:   1)  The struts can be treated as rectangular fins with an adiabatic tip.

            2)  Assume a uniform heat transfer coefficient on the flue gas-side (h_o).