Assume the temperature of the exhaust in an exhaust pipe can be approximated by

trainart1

trainart1

Answered question

2021-11-10

Assume the temperature of the exhaust in an exhaust pipe can be approximated by
T=T0(1+aebx)[1+ccos(ωt)]
where T0=100rm{C},a=3,b=0.03rm{m}1,c=0.05,  and  ω=100rads. If the exhaust speed is a constant 3 m/s, determine the time rate of change of temperature of the fluid particles at x = 0 and x = 4 m when t = 0.

Answer & Explanation

Alrew1959

Alrew1959

Beginner2021-11-11Added 16 answers

Step 1
In order to find solution will analyze the equation of material derivative
DTDt=Tt+uTx+vTy+wTz
Where is:
T=T0(1+aebx)[1+ccos(ωt)]
T0=100C
a=31m
b=0.031m
c=0.05
V=3ms
p=100rads
v=0
w=0
Now we can find he time rate of change of temperature.
DTDt=Tt+uTx
Tt=t(T0(1+aebx)[1+ccos(wt)])
Tt=T0(1+aebx)t[1+ccos(wt)]
Tt=T0cwsin(wt)(1+aebx)
uTx=3xT0(1+aebx)[1+ccos(wt)]
uTx=3(1+ccos(wt))xT0(1+aebx)
uTx=3

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