Question

Incorrect Question 19 0/8 pts Methane (CH4) at 298 K, 1 atm enters a furnace operating at steady state and burns completely with 220% of theoretical air entering at 400 K, 1 atm. The products of combustion exit at 500 K, 1 atm. The flow rate of the methane is 1.2 kg/min. Kinetic and potential energy effects are negligible and air can be modeled as 21% O2 and 79% N2 on a molar basis. Determine the rate of heat transfer for a control volume enclosing the reacting gases, in kW (use sign convention). There is a +/- 5% tolerance. 858.3516

Answer 1

47 Products ti Tp= 500k 400k, latmi 220 °. heo | 8cv air h CHY. Il 998k, datm -----

Engineering Model. i) 3.76 moles of Nz accompany each - oxygen in the air. 2) Ne is inert rii) The control volume is at steady state. Waveo and Kinetic and potential energy effects are negligible. V De ideal gas model is used for all streams. The balanced chemical equation for complete combustion of methane with the theoretical amount of air is given by CH4 + 2(02+ 3.76 N2) → coz + 2H20 + 7.52 N,.

for combustion of fuel with 220% of theoretical air CHy + (2-2)2 (02+3.76 Ne) → a CO2 + 6H2O + COLtd Nz | CH4 + 3-76 N2) ► aco, + 6H2O + C 02 +0 N2 Applying conservation of mass to carbon, hydrogen, oxygen and nitrogen respectively, 1 = a. H : 4 = 26 → b=2. . (4.4)(2) = 2a+b+ 20 T 8.8 = 2(1) + 2+2c > 8.8= 4+20 → 4.8=20 => c= 9.4 N (4.4)(3-76) (2) = 2d. → do 16.544 a=1, b = 2, CE 2.4 and do 16.544. he balanced chemical equation for complete combustion of the fuel with 220% of theoretical air i's CH4 + 4.4(02+ 3.76N2) → Coq + 2 H20(9)+ 2.404 + 16:54405

Now, the energy rate balance reduces to give ne ► ocv = (hcos) + 2 (7 the le+ 2.4(702) + 16.5v4 (5 na) - (Tou) – 4.4(702) - 16.544(Fr.) Ocv . [ het ho goo - T 299 )co, + 2[Ff+ hoo - Th298 Juzole) +2.4 [667 Fosco - 728]o+ 16-504[ Bgm Tosco hage] Na - [The Iann - 44 [ Bati nyoo- hagslos - 16-544 [ hyoo - h299 INZ

Nov = [-393,510 + (14,628 - 9,3८५)] + २ [- 241, 820 + (16,828 -9, 9०५)] Me + ३.५ [ 14, +10 - 8, 632] + 16.5५५ [14,581- 8,669] - [~१५, 850] - ५.५ L , +II - 8, 6 82] - 16. 5 ५५ [ 11, 6५० - 8, 669] __ ने Ecv -385 2.56 - 469792 + 14611. 2. + 91808.128 / no ++५850 - 13327.6 ~ 49152. 224

- -730258.496 kJ/kmol fuel. Now, evo riex (-730258-496) kJ/kmol fuel. m2 ss flow rate of methane, mies 1.2 kg i min (2) ugls = 0.02 kgls. = reX MF. So where me is the mass of methane. is 0.02 kg/s = A * 16.04 kg/kmol. 2 ne 0.001247 kmolls · so, cv = (0.001247 umorys) (-730258-496) k5/kmol. -910.55 kW. = -910,55 kJ/s = control volume Hence rate of beat transfer for a enclosing the reacting Jases, fev = [-910.55 kn - 910.55 kW