Application of the Reverberation-Ray Matrix to the Non-Fourier Heat Conduction in Functionally Graded Materials

2016 ◽  
Vol 71 (2) ◽  
pp. 113-119
Author(s):  
Feng-xi Zhou
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Materials ◽  
Thermal Response ◽  
Functionally Graded ◽  
Conduction Model ◽  
Graded Materials ◽  
Material Inhomogeneity ◽  
Power Law Function ◽  
Fourier Heat Conduction ◽  
And Diffusion

AbstractThe method of the reverberation-ray matrix has been developed and successfully applied to analyse the wave propagation in a multibranched framed structure or in a layered medium. However, the method is confined to the case of mechanical loads applied at the medium until now. This paper aims to extend the formulation of the reverberation-ray matrix to cases of thermal propagation and diffusion. The thermal response in functionally graded materials (FGM) with the non-Fourier heat conduction model is analysed. In the present work, it is assumed that the material properties of an FG plate vary only in the thickness direction by following the power law function. The effect of non-Fourier and material inhomogeneity in the plate subjected to a periodic thermal disturbance is investigated. The present approach is validated by comparing it with the solutions obtained by other methods.

scholarly journals Study on Transient Thermal Response for Functionally Graded Materials Based on Peridynamic Theory

2019 ◽  
Vol 37 (5) ◽  
pp. 903-908
Author(s):  
Fei Wang ◽  
Yu'e Ma ◽  
Yanning Guo ◽  
Wei Huang
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Materials ◽  
Thermal Response ◽  
Functionally Graded ◽  
Temperature Fields ◽  
Distribution Area ◽  
Conduction Time ◽  
Time Step ◽  
Graded Materials ◽  
Temperature Load

The transient heat conduction formula of functionally graded materials (FGMs) is presented based on peridynamics (PD). The simplified micro-heat conductivity model for FGMs is proposed and the numerical discretization and the peridynamic numerical formation are also illustrated. A FORTRAN program is coded to implement calculations. The accuracy of the program is verified by comparing the FEM and analytical results with PD solution. The FGM rectangle plate composed by titanium alloy coating zirconium oxide is performed to calculate temperature fields. The effects of material gradient, porosity and temperature load on thermal response are studied. It is shown that the ceramic proportion of FGMs is increased with an increasing material shape parameter and the thermal shielding performance of FGMs is also improved. The effect of the porosity on thermal response is more and more significant with the increasing time step. The increasing temperature load only affects the temperature response of FGM ceramic area. The thickness of temperature distribution area is increased with the increasing of heat conduction time.

TRANSIENT HEAT CONDUCTION IN FUNCTIONALLY GRADED MATERIALS

2007 ◽  
Vol 04 (04) ◽  
pp. 603-619 ◽  
Author(s):  
S. M. HAMZA-CHERIF ◽  
A. HOUMAT ◽  
A. HADJOUI
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Functionally Graded Materials ◽  
Degrees Of Freedom ◽  
Functionally Graded ◽  
P Element ◽  
Transient Temperature ◽  
Test Problems ◽  
Shape Functions ◽  
Graded Materials

The h-p version of the finite element method (FEM) is considered to determine the transient temperature distribution in functionally graded materials (FGM). The h-p version may be regarded as the marriage of conventional h-version and p-version. The graded Fourier p-element is used to set up the two-dimensional heat conduction equations. The temperature is formulated in terms of linear shape functions used generally in FEM plus a variable number of trigonometric shape functions representing the internal degrees of freedom (DOF). In the graded Fourier p-element, the function of the thermal conductivity is computed exactly within the conductance matrix and thus overcomes the computational errors caused by the space discretization introduced by the FEM. Explicit and easily programmed trigonometric enriched capacitance, conductance matrices and heat load vectors are derived for plates and cylinders by using symbolic computation. The convergence properties of the h-p version proposed and the results of the numbers of test problems are in good agreement with the analytical solutions. Also, the effect of the non-homogeneity of the FGM on the temperature distribution is considered.

scholarly journals Non-Fourier Heat Conduction of a Functionally Graded Cylinder Containing a Cylindrical Crack

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Jiawei Fu ◽  
Keqiang Hu ◽  
Linfang Qian ◽  
Zengtao Chen
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Intensity Factor ◽  
Functionally Graded ◽  
Conduction Model ◽  
Heat Conduction Model ◽  
Flux Intensity ◽  
Cylindrical Crack ◽  
Heat Flux Intensity ◽  
Fourier Heat Conduction

The present work investigates the problem of a cylindrical crack in a functionally graded cylinder under thermal impact by using the non-Fourier heat conduction model. The theoretical derivation is performed by methods of Fourier integral transform, Laplace transform, and Cauchy singular integral equation. The concept of heat flux intensity factor is introduced to investigate the heat concentration degree around the crack tip quantitatively. The temperature field and the heat flux intensity factor in the time domain are obtained by transforming the corresponding quantities from the Laplace domain numerically. The effects of heat conduction model, functionally graded parameter, and thermal resistance of crack on the temperature distribution and heat flux intensity factor are studied. This work is beneficial for the thermal design of functionally graded cylinder containing a cylindrical crack.

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