Hot combustion gases of a furnace are flowing through a concrete chimney (k = 1.4 W/m · K) of rectangular cross section. The flow section of the chimney is 20 cm × 40 cm, and the thickness of the wall is 10 cm. The average temperature of the hot gases in the chimney is T_i = 280°C, and the average convection heat transfer coefficient inside the chimney is h_i = 75 W/m² · K. The chimney is losing heat from its outer surface to the ambient air at T_o = 15°C by convection with a heat transfer coefficient of h_o = 18 W/m² · K and to the sky by radiation. The emissivity of the outer surface of the wall is ε = 0.9, and the effective sky temperature is estimated to be 250 K.

Using the finite difference method with Δx = Δy = 10 cm and taking full advantage of symmetry,

(a) Obtain the finite difference formulation of this problem for steady two-dimensional heat transfer,

(b) Determine the temperatures at the nodal points of a cross section,

(c) Evaluate the rate of heat loss for a 1-m-long section of the chimney.

Transcribed Image Text:

To ho Chimney kk 10 cm Hot gases T₁, hi E 10 cm 20 cm 10 cm -40 cm- 10 cm