# Temperature problem in fluids mechanics

1. Feb 8, 2012

### PythagoreLove

1. The problem statement, all variables and given/known data
Assume the temperature of the exhaust in an exhaust pipe can be approximated by
T=T0(1+ae-bx)[1+c cos($\omega$t)]
T0=100oC,
a=3,
b=0.03m-1,
c=0.05,
$\omega$=100 rad/s.

If the exhaust speed is a constant 3 m/s, determine the time rate of change of temperature of the fluid particle at x=0 and x=4 m when t=0.

2. Relevant equations
We know the equation of the temperature in function of the time and the position
T=T0(1+ae-bx)[1+c cos($\omega$t)]

3. The attempt at a solution
We know that the time rate of change of temperature of the fluid particle is dT/dt

$\frac{dT}{dt}$=T0(1+ae-bx)[-c $\omega$ sin($\omega$t)]

When t=0, dT/dt=0... unfortunately that isn't the answer, since I don't use the exhaust speed (and have no idea how I could use it).

Thank you
PytLove

2. Feb 9, 2012

### LawrenceC

What if you treated x and t as a variables....

3. Feb 9, 2012

### PythagoreLove

Seems like a wonderful idea and totally worked, that problem was so different from the others I've done in fluid mechanics... I have no idea that I needed to use x(t) in my dT/dt.

Thank you Lawrence

PytLove