Numerical approximation of solution of an inverse heat conduction problem based on Legendre polynomials

In this paper, we consider an inverse heat conduction problem (IHCP). The given heat conduction equation, the boundary condition, and the initial condition are presented in a dimensionless form. A set of temperature measurements at a single sensor location inside the heat conduction body is required. Using a linear transformation, the ill-posed IHCP becomes a Cauchy problem. This problem will be solved by applying Legendre polynomials. Results show that an excellent estimation can be obtained within a couple of minutes CPU time at pentium IV-2.4 GHz PC.