Question

Flue gas from a methane combustor is at 1400 K and 1 bar pressure for stoichiometric combustion with air. Estimate the radiant heat transfer to the walls of a 0.50-m square duct maintained at 700 K. Assume the walls are black. Repeat the calculation for an excess air ratio of 2.

Answer 1

Here, it is given that the walls are black. Hence, we assume ? to be unity (1). Hence we apply the formula for black body heat transfer which is-

q=?A(T₁⁴-T₂⁴)

Now we calculate the area A as:

A=0.5*0.5=0.25 m²

?=5.67*10^-8W/m ²K⁴

T₁=1400 K and T₂=700K

Hence by putting the values in the formula, we calculate q as:

q=5.67*10^-8*0.25*(1400⁴-700⁴)

q=51051.2625 W=51051.3 W

Now, in the case when excess air ratio is 2 we have the same flue gas and along with it the same amount of air is also present. Hence, the total mass of the flue gas becomes twice the initial case but the total heat content of the gases is the same as the heat produced is from the same methane combustor and the amount of methane is not changing. Therefore, we get that the temperature of the new system will be half that of the earlier system. Hence the new temperature will be 1400/2=700 K.

Since there is no difference in temperature between the wall and the gas the radiant heat transfer for the new case is equal to zero.