The products of combustion from a burner are routed to an industrial application through a thin-walled metallic duct of diameter
Di=1 m and length L=100 m. The gas enters the duct at atmospheric pressure and a mean temperature and velocity of Tm,i=1600 K and Um,i=10 m/s, respectively. It must exit the duct at a temperature that is no less than Tm,o=1400 K. What is the minimum thickness of an alumina-silica insulation (Kins=0.125 W/m*K) needed to meet the outlet requirement under worst case conditions for which the duct is exposed to ambient air at T[infinity]=250 K and a cross-flow velocity of V=15 m/s? The properties of the gas may be approximated as those of air, and as a first estimate, the effect of the insulation thickness on the convection coefficient and the thermal resistance associated with the cross flow may be neglected.
1 answer:
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Answer:
V1=5<u>ft3</u>
<u>V2=2ft3</u>
n=1.377
Explanation:
PART A:
the volume of each state is obtained by multiplying the mass by the specific volume in each state
V=volume
v=especific volume
m=mass
V=mv
state 1
V1=m.v1
V1=4lb*1.25ft3/lb=5<u>ft3</u>
state 2
V2=m.v2
V2=4lb*0.5ft3/lb= <u> 2ft3</u>
PART B:
since the PV ^ n is constant we can equal the equations of state 1 and state 2
P1V1^n=P2V2^n
P1/P2=(V2/V1)^n
ln(P1/P2)=n . ln (V2/V1)
n=ln(P1/P2)/ ln (V2/V1)
n=ln(15/53)/ ln (2/5)
n=1.377
