Identification of the heat conduction coefficients of a functionally graded ‎material with inverse application of the boundary elements method and using ‎imperialist competitive algorithm

Identification of the thermal conductivity of a functionally graded material (FGM) is considered as an inverse heat conduction problem. ýIn this investigation, the measurements of the temperatures on the portion of the 2D body where heat flux is specified as the boundary ýcondition and/or the heat flux on the portion of the boundary where temperature is specified as the boundary condition are used as ýadditional data needed to identify the thermal conductivity of the FGM domain in an inverse procedure. The thermal conductivity is ýapproximated as a quadratic function of only one direction, and therefore three constant coefficients should be estimated simultaneously.ýþ þThe solution of the direct heat conduction problem forþ þFGM domain is obtained using the boundary elements method (BEM).ýþ þThe ýimperialist competitive algorithm (ICA) which is an evolutionary and meta-heuristic global optimization is used to identify the constants ýin the thermal conductivity function of the quadratic FGM. An inverse computer code is developed which employs the boundary ýtemperature and heat flux measurements data obtained by solving the direct boundary elements code with known thermal conductivity. ýTo show the feasibility and effectiveness of the developed inverse code, a number of example problems are solved and results are ýverified.ý