Problem

Hot combustion gases of a furnace are flowing through a concrete chimney (k= 1.4 W/m·K) of...

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 20cm × 40 cm, and the thickness of the wall is 10 cm. The average temperature of the hot gases in the chimney is Ti = 280°C, and the average convection heal transfer coefficient inside the chimney is is hi75 W/m2∙K. The chimney is losing heat from its outer surface to the ambient air at To = 15°C by convection with a heat transfer coefficient of h0 = 18 W/m2·K and to the sky by radiation. The emissivity of the outer surface of the wall is e = 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, and (c) evaluate the rate of heat loss for a 1-m-long section of the chimney.