Real-time solution of heat conduction in a finite slab for inverse analysis

Abstract

Laplace transform is used to solve the problem of heat conduction over a finite slab. The transfer functions relating the temperature and heat flux on the front and back surfaces of the finite slab are developed. Although there are many competing methods for constructing the inverse Laplace transform, we use polynomial approximation of the transfer function. Therefore, transient solutions for given boundary conditions are easily obtained using SIMULINK. This process is much simpler than other numerical solution methods for the heat equation. Most importantly, our method of solution allows us to obtain, in real-time, the front surface temperature and heat flux based on the thermodynamic measurements on the back surface. We also demonstrate the feasibility of reconstructing the front surface temperature when sensor noise is incorporated to the back surface measurements.