FINITE-ELEMENT ANALYSIS OF OPTIMAL HEATING OF A SLAB WITH TEMPERATURE-DEPENDENT THERMAL-CONDUCTIVITY

An infinitely long solid slab of temperature dependent thermal conductivity is heated optimally by the ambient temperature. The physical objective of the problem is to increase the temperature level in the slab to a higher level at the end of a fixed period of time, while keeping the necessary ambient temperature level as low as possible. Reformulated as an optimal control problem, the problem is solved numerically by utilizing the finite element method. An approximate perturbation method is also given for linearizing the necessary conditions for optimality. © 1979.