An engineer designs an experimental setup for exhaust analysis of some combustio

Question

An engineer designs an experimental setup for exhaust analysis of some combustion by product on a summer day. A thin-walled tube with a diameter of 6 mm and length of 20 m is used to carry the exhaust gas from the combustion chamber to the nearby gas analysis facility. Wind at a temperature of 27 degree C is blowing directly across the tube at a constant velocity of 6 m/s. If the gas enters the tube at 250 degree C and with a flow rate of 0.005 kg/s, calculate the temperature of the exhaust gas when it reaches the facility.

Explanation / Answer

We shall use the analysis of Incropera p 502 for convection cooling of flow thru a pipe

This uses the mean temp difference: DTo/DTi = exp( -UA/m'Cp)   (1)

where U is the overall heat transfer coeff = h, ( assume the thickness of tube is small so k has no contribn)

A = 2*pi* R*L =2*pi* .003*20 m^2=.377 m^2

From relation for Prandtl number Pr= .7 for air at 300K

Nu =hl/k= .664*sqrt(Re) *Pr^(1/3) == 28.1, where Re for the geometry = V*.006/20= 2265.6

estimates Nu =hL/k = 28.1 ==> h = 36.9 W/m^2K taking k for air from tables as 26.3

Cp air is 1.007 KJ/kgK, A = .377m^2, m'=.005 can now calculate the exponential qty. in eqn(1)

get exp( - 26.3 / .005*1007)=.0054

DTo/DTi = (Tinf-To)/(Tinf-Tin) = (To-27)/(250-27) =.0054 ., tO = 27+ 223*.0054=27+1.2=28.2 Deg C

(note the answer depends on the h calculated from Nusselt number and k. we use k for air. if k is used from the tube, results will change)

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