Solving Non-Fourier Heat Conduction-Radiation Problem, a Semi-Analytical Approach

Objectives: In this study, the thermal analysis of a thin film exposed to laser heating, was investigated using Cattaneo Vernotte non-Fourier heat conduction model. Methods/Statistical Analysis: Nonfourier equations were derived based on radiative heat loss and also variable thermal conductivity. Then Variational Iteration Method (VIM) and Reduced Differential Transformation Method (RDTM) were used to solve these equations. Findings: VIM is an efficient choice to find an approximate solution of nonlinear non-Fourier heat conduction and its accuracy is higher than RDTM. Considering the thermal conductivity vary with temperature creates a significant difference in the temperature profiles, which shows the importance of nonlinear analysis of the problem. In certain values of relaxation time, temperature variations take place and out of that certain domain, variations of relaxation time doesn’t effect on temperature at all. Application/Improvements: There is a remarkable difference between the Fourier and non-Fourier solutions of heat conduction equations that demonstrate the importance of non-Fourier analysis of this type of equations.