A dual-phase-lag (DPL) transient non-Fourier heat transfer analysis of functional graded cylindrical material under axial heat flux

Abstract

A dynamic thermal conduction problem needs a mathematical formulation and solution consisting of cylindrical coordinates of materials for the application of nuclear reactor and/or laser therapeutic when subjected to higher heat fluxes. In this study, dual-phase-lag (DPL) transient non-Fourier heat conduction in a functional graded cylindrical material is analytically solved under axial heat flux condition. Functional Graded Material (FGM) properties are based by exponential low. Governing equations on the model are expressed in 2D cylindrical coordinates and solved by using the separation of variable method. An effect of the heterogeneity coefficient of the material using Fourier method, Cattaneo–Vernote model and the dual phase lag is analyzed. An influence of non-dimensional temperature changes to the Fourier number in the pure and functional material is analyzed. Results showed that DPL model requires less time to meet the steady temperature compared with single-phase-lag (SPL) model. In the FGMs, each model and method tends to have a constant temperature based on the amount of heterogeneity coefficient, and it can be concluded that one of the factors determining the amount of stable temperature is the properties of the material. The current results provide a straightforward multivariate analytical solution of the non-Fourier conduction equation in a finite cylinder, for cylinders with any boundary conditions and, for cylinders with functional graded materials. It was found that negligible issues with the critical points being presented when compared to the Laplace operator method.