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 d_i = 30 cm and outer diameter d_o = 50 cm. The flue gases flow with an average temperature of T_g = 300^oC and convective heat transfer coefficient of h_g = 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 T_α = 25^oC 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 = 10^o.

GIVEN

• Hot flue gas flow in a hollow cylindrical 7 m tall chimney with inner and outer diameters of d_i = 0.3 m and d_o = 0.5 m, and thermal conductivity k = 1.4 W/(m K).
• Average hot gas temperature T_g = 300^oC and heat transfer coefficient h_c,g = 75 W/(m² K).
• Outside air average temperature T_α = 25^oC and heat transfer coefficient h_c,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.