Application of optimal control theory in pipe insulation

Optimum insulation thickness of a pipe subjected to convective heat transfer that minimizes the heat loss is studied using the control theory approach and steepest descent method. As a constraint to the problem, the amount of insulation material is assumed to be fixed. A circular pipe through which fluid is transported from one end to the other is considered. Variations of the bulk temperature of the fluid as well as the temperatures of the outer surface of the insulation are evaluated. It is shown that obtaining an optimal thickness variation of insulation that minimizes the heat losses to the ambient using control theory can be done in a systematic manner. The method can be extended easily to more complex and nonlinear problems.