An Inverse Method for Controlling the Temperature Distribution and Identification of the Conductivity of Thick Cylindrical Shells

Abstract

The paper presents an inverse method for control of temperature distribution in thick cylindrical shells. Since the thickness is large enough, three-dimensional heat diffusion equations must be considered. To control the temperature distribution, the heat fluxes at the boundary surfaces of the cylindrical shell are assigned values such that the desired temperature distribution, which satisfies the steady state heat conduction equation, will be achieved. Furthermore, a Lyapunov-based method for identification of the conductivity of the cylinder is presented, and the estimated conductivity is updated such that it converges to the exact value. The numerical results are obtained by the finite element method (FEM), which include the heat flux at the surfaces of the cylinder. These results are shown to be in excellent agreement with the analytical solution.