A tubular furnace must be designed so that it can treat materials at an inner surface temperature of 1200°C yet have its outer surface be at a temperature no more than 45°C. The inner layer of the...

A tubular furnace must be designed so that it can treat materials at an inner surface temperature of 1200°C yet have its outer surface be at a temperature no more than 45°C. The inner layer of the furnace is made of a ceramic with thermal conductivity of 0.5 W/mK. Around that we have a layer of high temperature insulation with a thermal conductivity of 0.038 W/mK. Finally, the outer surface is stainless steel with a thermal conductivity of 15 W/mK. The external environment is held at 20°C and air movement about the furnace gives a heat transfer coefficient of 10 W/m2K. We can buy materials in any thickness we want but, the inner radius must be 3 cm and the outer radius no more than 35 cm:

a. Design a furnace that meets the requirements.

b. If the insulation can take a temperature of no more than 1125°C, how thin a wall can be used to meet the requirements?

c. Given the constraints above and in part (b), what wall will yield minimum heat flow?