Question

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.

Answer 1

a)
`r_a=37.8m^3/h`

b)
`Q=2.8Kw`

Step-by-step explanation:

Temperature of CH_4
`t=25C`

CH_4Flow rate of
`r=27m3/h`

Air Percentage
`=140\%=1.4`

Temperature of air
`t_a=127=>400K`

Temperature at exit
`t_e=427C=>700k`

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

`r_a=air\%*r`

`r_a=1.4*27`

`r_a=37.8m^3/h`

Generally the equation for Ideal Gas is mathematically given by

`PV=mRT`

`m=(PV)/(RT)`

`m=(1.01*10^5*37.8)/(0.287*10^3*400)`

`m=33.35kg`

Therefore

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

`Q=mC_p(T_e-T_a)`

`Q=33.35*1.005*(700-400)`

`Q=2.8Kw`