Use of 3D-transient analytical solution based on Green’s function to reduce computational time in inverse heat conduction problems

Abstract

a b s t r a c tInverse problems can be found in many areas of science and engineering and can be applied in different ways. Two examples can be cited: thermal properties estimation or heat flux function estimation in some engineering thermal process. Different techniques for the solution of inverse heat conduction problem (IHCP) can be found in literature. However, any inverse or optimization technique has a basic and common characteristic: the need to solve the direct problem solution several times. This characteristic is the cause of the great computational time consumed. In heat conduction problem, the time consumed is, usually, due to the use of numerical solutions of multidimensional models with refined mesh. In this case, if analytical solutions are available the computational time can be reduced drastically. This study presents the development and application of a 3D-transient analytical solution based on Green's function. The inverse problem is due to the thermal properties estimation of conductors. The method is based on experimental determination of thermal conductivity and diffusivity using partially heated surface method without heat flux transducer. Originally developed to use numerical solution, this technique can, using analytical solution, estimate thermal properties faster and with better accuracy.

Solution of the inverse heat conduction problem with Neumann boundary condition by using the homotopy perturbation method

“…There is only few works presenting such an approach [14][15][16][17]. The homotopy perturbation method presented in the paper is an example of the analytical method used for solving the inverse heat conduction problem.…”

A heat-flux based “building block” approach for solving heat conduction problems

“…These differences, in fact, require very accurate values of the temperature, in particular when the space and time intervals chosen for approximating the surface heat flux are very small. However, the computational time is greatly reduced by using analytical solutions [15].…”

Analytical solutions to hyperbolic heat conductive models using Green's function method

“…Majumdar and Xia (2007) analyzed the laser heating of materials using Green's function method. In addition, Green's function was also applied in inverse transient heat conduction problems (Fernandes et al, 2010).…”