A 4-in.-OD pipe is used to transport liquid metals and will have an outside surface temperature of 1400 F under operating conditions. Insulation 6-in. thick and having a thermal conductivity expressed as k = 0.08(1-0.0003T) where k is in [Btu/hr*ft*F] and T is in [F], is applied to the outside surface of the pipe.
(a)What thickness of insulation would be required for the outside insulation temperature to be no higher than 300 F.
(b) What heat-flow rate will occur under these conditions?
q/A = k dT/dx
A = 2*(pi)*r*L, Assume L is 1 ft.
The Attempt at a Solution
q/A dr = k dT
Integrate on both sides
q/2*(pi)( ln(r-pipe)-ln(r-insulation)) = 0.08(T-0.00015T^2)(evaluate from 1400 to 300)
Is this a Trick question? Do I assume that the insulation thickness is 6-in? Or is there a trick that I am missing?
I would like to have help on this by Wednesday November 25th by 4PM PST. Thanks