Thermal Performance of a Convective Functionally Graded Fin Using Fractional Non-Fourier Heat Conduction

2021 ◽  
pp. 1-10
Author(s):  
Xue-Yang Zhang ◽  
Xian-Fang Li
Keyword(s):  
Heat Conduction ◽  
Thermal Performance ◽  
Functionally Graded ◽  
Fourier Heat Conduction

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.

Transient Heat Conduction in Functionally Graded Hollow Cylinders and Spheres

2012 ◽  
Author(s):  
A. H. Akbarzadeh ◽  
Z. T. Chen
Keyword(s):  
Heat Conduction ◽  
Transient Heat Conduction ◽  
Functionally Graded ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Conduction Theory ◽  
Hollow Cylinders ◽  
Fourier Heat Conduction ◽  
Cylinders And Spheres

In the present work, transient heat conduction in functionally graded (FG) hollow cylinders and spheres is investigated based on the non-Fourier heat conduction theories. Since the heat transmission has been observed to propagate at a finite speed for applications with very low temperature, short-pulse thermal-heating, and micro temporal and spatial scales, dual phase lag (DPL) and hyperbolic heat conduction theories are considered in current study instead of the conventional Fourier heat conduction theory. Except the phase lags which are assumed to be constant, all the other material properties of the hollow cylinders and spheres are taken to change continuously along the radial direction according to a power-law formulation with different non-homogeneity indices. The heat conduction equations are written based on the dual phase lag theory which includes the hyperbolic heat conduction theory as well. These equations are applied for axisymmetric hollow cylinders of infinite lengths and spherically symmetric hollow spheres. Using the Laplace transform and Bessel functions, the analytical solutions for temperature and heat flux are obtained in the Laplace domain. The solutions are then converted into the time domain by employing the fast Laplace inversion technique. The exact expression is obtained for the speed of thermal wave in FG cylinders and spheres based on the DPL and hyperbolic heat conduction theories. Finally, the current results are verified with those reported in the literature based on the hyperbolic heat conduction theory.

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.

Thermopiezoelectric Response of a One-Dimensional Functionally Graded Piezoelectric Medium to a Moving Heat Source - A Review

2012 ◽  
Vol 151 ◽  
pp. 396-400 ◽  
Author(s):  
Zeng Tao Chen ◽  
Hamid Akbarzadeh ◽  
Hossein Babaei
Keyword(s):  
Heat Conduction ◽  
Heat Source ◽  
Smart Materials ◽  
Thermal Gradient ◽  
Functionally Graded ◽  
Moving Heat Source ◽  
One Dimensional ◽  
Smart Materials And Structures ◽  
Conduction Theory ◽  
Fourier Heat Conduction

The multi-physics of piezoelectric materials under different environmental conditions has been an active research subject for a few decades. Particularly, the thermoelastic behaviour of smart materials and structures is of great importance to their reliability in different applications. Traditionally, the Fourier heat conduction theory was introduced in dealing with the thermoelastic reactions of smart materials and structures. This may lead to reasonable analyses and useful guidelines in design of smart structures, especially when no severe thermal gradient is involved. However, when a severe thermal gradient is indeed involved in the service environment of a smart structure, the analysing results based on the Fourier heat conduction theory is unrealistic and usually rendered useless. Non-Fourier heat conduction theories have been introduced in the thermoelastic analysis of smart materials and structures in recent years and resulted in reasonable results. In this paper, we review the recent results of a thermopiezoelectric problem of a one-dimensional (1-D), finite length, functionally graded medium excited by a moving heat source using both the Fourier and Non-Fourier heat conduction theories. Numerical examples are displayed to illustrate the effects of non-homogeneity index, length and thermal relaxation time on the results.

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