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Methane gas (CH4) at 25oC, 1 atm, and a volumetric flow rate of 27m3/h enters a furnace operating at steady-state. The methane burns completely with 140% of theoretical air that enters at 127oC, 1 atm. Products of combustion exit at 427oC, 1 atm. Determine:
(a) the volumetric flow rate of the air, in m3/h.
(b) the rate of heat transfer from the furnace, in kJ/h.

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Answer:

a)  [tex]r_a=37.8m^3/h[/tex]

b)[tex]Q=2.8Kw[/tex]

Explanation:

Temperature of CH_4[tex]t=25C[/tex]

CH_4Flow rate of [tex]r=27m3/h[/tex]

Air Percentage [tex]=140\%=1.4[/tex]

Temperature of air [tex]t_a=127=>400K[/tex]

Temperature at exit[tex]t_e=427C=>700k[/tex]

Generally the equation for Air's flow Rate is mathematically given by

 [tex]r_a=air\%*r[/tex]

 [tex]r_a=1.4*27[/tex]

 [tex]r_a=37.8m^3/h[/tex]

Generally the equation for Ideal Gas is mathematically given by

 [tex]PV=mRT[/tex]

 [tex]m=\frac{PV}{RT}[/tex]

 [tex]m=\frac{1.01*10^5*37.8}{0.287*10^3*400}[/tex]

 [tex]m=33.35kg[/tex]

Therefore

The rate of heat transfer from the furnace, in kJ/h is

 [tex]Q=mC_p(T_e-T_a)[/tex]

 [tex]Q=33.35*1.005*(700-400)[/tex]

 [tex]Q=2.8Kw[/tex]

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