I am not sure how to approach this problem. If you have a carbon steel pipe that is being heated on one end at a constant temperature of 1500C. Can you figure out how much distance in pipe will it require before it cools to 790C? The thermal conductivity of Carbon steel is 54 W/mk. Another situation is what if there is insulations on top of the carbon steel, what will happen in that situation. I am pretty sure with insulation the length of the pipe will increase to reaches 790C.
Hi fujifilm. The way I've done this in the past is to break up the pipe into short lengths and analyze each short length independently. There's convective heat transfer removing heat from the pipe and thermal conduction along the length. As heat is removed from convection, the pipe gets cooler. But the cooler it gets per unit length, the higher the thermal conduction. So there's an equilibrium between the two you're searching for. Try setting up a spreadsheet where each row does the calculations for a very short section of pipe. Every row will be identical, and will be hinged on the previous row. Hope that makes sense.
I was wondering what do you mean break up the pipe into short length and analyze each short length mean? I was wondering what method did you use as in terms of equations and theory involved.
I am familiar with with heat transfer calculations by conduction and convection. I guess my confusion is to the assumption that should be made. In this problem I understand that the amount of energy transfer through the pipe using conduction is related to this equation where q=-K(dT/dx) and the equation for convection is q=hA(T1-T2). How can i apply these equations to calculate distance between two temperatures?