Find a (steady state) temperature distribution in a partially submerged pipe shown.
0.5
-20°
3
6
+10°
5
water
Temperature of air = -20°, fluid (inside) = + 15°.
Temperature in soil: Changes from +2° at the bottom of the pipe to the air temperature at
the surface, as a linear function of the radial angle.
Pocket of water, at 0º as shown
When using Fourier series in angular coordinate $\theta$, retain the number of terms that
provides reasonable accuracy. Comment on: how this number changes with the radial
coordinate.
Plot lines of equal temperature.
Sketch zones where temperature gradients are highest (in these zones, mechanical
stresses, caused by temperature gradients, will be the highest)