Maintaining uniform surface temperature along pipes by insulation

An analytical solution is obtained for the insulation thickness variation over a pipe to maintain a uniform outer surface temperature. A high temperature fluid is considered to be flowing through the pipe. The amount of the insulation material is assumed to be limited. Heat transfer from the outer surface of the pipe is through convection and radiation. The solution of the insulation thickness is found to be independent from the outer surface convective and radiative heat transfer coefficients. In addition, the solution is found to be very close to linear variation which is very easy to implement in practice.