Multi-dimensional dual-phase-lag heat conduction in cylindrical coordinates: Analytical and numerical solutions

Abstract This work investigates the temperature distribution for the case of cylindrical geometry subjected to heat flux boundary condition on one of the bases and constant temperature on other boundary conditions considering dual-phase-lag (DPL) model of heat conduction. Two types of heat flux were considered: a continuously operating and exponential pulsed. Both exact analytical and numerical solutions were applied. For the analytical one, the separation of variables analytical method together with Duhamel’s theorem was employed. However, implicit finite difference method was used for the numerical technique. The DPL model of heat conduction renders the hyperbolic nature for heat transport, which is based on one correction made to the Cattaneo–Vernotte model of heat transfer. After comparing the results from both methods and confirmation regarding the validation of analytical solution, the effects of temperature gradient lags on the temperature distribution were analyzed.

[1]  M. K. Moallemi,et al.  Experimental evidence of hyperbolic heat conduction in processed meat , 1995 .

[2]  J. Ghazanfarian,et al.  Effect of boundary phonon scattering on Dual-Phase-Lag model to simulate micro- and nano-scale heat conduction , 2009 .

[3]  Zahra Shomali,et al.  Investigation of dual-phase-lag heat conduction model in a nanoscale metal-oxide-semiconductor field-effect transistor , 2012 .

[4]  Jung-Chang Wang,et al.  Analysis of thermal damage to laser irradiated tissue based on the dual-phase-lag model , 2014 .

[5]  Da Yu Tzou,et al.  Macro- to Microscale Heat Transfer: The Lagging Behavior , 2014 .

[6]  R. Shirmohammadi.  Thermal Response of Microparticles Due to Laser Pulse Heating , 2011 .

[7]  Arunn Narasimhan,et al.  Non-Fourier bio heat transfer modelling of thermal damage during retinal laser irradiation , 2013 .

[8]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[9]  W. Kaminski.  Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure , 1990 .

[10]  H. S. Carslow,et al.  Conduction of Heat in Solids, Second Edition , 1986 .

[11]  Paul J. Antaki.  Effect of dual-phase-lag heat conduction on ignition of a solid , 2000 .

[12]  Han-Taw Chen,et al.  Investigation for the dual phase lag behavior of bio-heat transfer , 2010 .

[13]  G. Espinosa-Paredes,et al.  Fuel rod model based on Non-Fourier heat conduction equation , 2009 .

[14]  Abbas Abbassi,et al.  Investigation of 2D Transient Heat Transfer under the Effect of Dual-Phase-Lag Model in a Nanoscale Geometry , 2012 .

[15]  P. Antaki.  Importance of nonFourier heat conduction in solid-phase reactions , 1998 .

[16]  M. M. Tung,et al.  Modeling the heating of biological tissue based on the hyperbolic heat transfer equation , 2008, Math. Comput. Model..

[17]  Seyfolah Saedodin,et al.  Analytical and Numerical Solutions of Hyperbolic Heat Conduction in Cylindrical Coordinates , 2011 .

[18]  D. Tang,et al.  Numerical analysis of two-dimensional lagging thermal behavior under short-pulse-laser heating on surface , 2006 .

[19]  Da Yu Tzou,et al.  The generalized lagging response in small-scale and high-rate heating , 1995 .

[20]  Paul J. Antaki.  Solution for non-Fourier dual phase lag heat conduction in a semiinfinite slab with surface heat flux , 1998 .

[21]  Dual-phase lag behavior of a gas-saturated porous-medium heated by a short-pulsed laser , 2014 .