1. The problem statement, all variables and given/known data 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? 2. Relevant equations q/A = k dT/dx A = 2*(pi)*r*L, Assume L is 1 ft. 3. 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 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution
I may be able to help a bit..I had a question simmilar to this, but I've handed it in. I made and used a spreadsheet to solve it, not calculus. With all of your given information, you can solve for the temperature of the fluid inside the pipe. (Is the thermal conductivity of the pipe neglected?) Knowing the fluid temperature and the surface temperature, with the k value for each composite could you not solve for the thickness required to limit the temp. to 300?