Solve the below:
Q: Hot flue gases from a combustion furnace flow though a chimney, which is 7 m tall and has a hollow cylindrical cross section with inner diameter di = 30 cm and outer diameter do = 50 cm. The flue gases flow with an average temperature of Tg = 300oC and convective heat transfer coefficient of hg = 75 W/(m2 K). The chimney is made of concrete, which has a thermal conductivity of k = 1.4 W/(m K). It is exposed to outside air that has an average temperature of Tα = 25oC and convective heat transfer coefficient of 15 W/(m2 K). For steady-state conditions, determine the inner and outer wall temperatures, plot the temperature distribution along the thickness of the chimney wall, and determine the rate of heat loss to outside air from the chimney. Solve the problem by numerical analysis using a nodal network with ?r = 2 cm and ?θ = 10o.
GIVEN
Hot flue gas flow in a hollow cylindrical 7 m tall chimney with inner and outer diameters of di = 0.3 m and do = 0.5 m, and thermal conductivity k = 1.4 W/(m K).
Average hot gas temperature Tg = 300oC and heat transfer coefficient hc,g = 75 W/(m2 K).
Outside air average temperature Tα = 25oC and heat transfer coefficient hc,a = 15 W/(m2 K).
ASSUMPTIONS
Steady state conditions, and there is no heat generation in the chimney wall and the conduction along the height of the chimney is negligible.