Transient Hyperbolic Heat Conduction in a Functionally Graded Hollow Cylinder

2010 ◽  
Vol 24 (2) ◽  
pp. 325-330 ◽  
Author(s):  
M. H. Babaei ◽  
Zengtao Chen
Keyword(s):  
Heat Conduction ◽  
Hollow Cylinder ◽  
Functionally Graded ◽  
Hyperbolic Heat Conduction

General Solution for Equation of Transient Heat Conduction in Functionally Graded Material Hollow Cylinder With Piezoelectric Internal and External Layers

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
M. Jabbari ◽  
M. A. Kiani
Keyword(s):  
Heat Conduction ◽  
Hollow Cylinder ◽  
Functionally Graded Material ◽  
Separation Of Variables ◽  
Transient Heat Conduction ◽  
Two Dimensions ◽  
Functionally Graded ◽  
Power Functions ◽  
Generalized Bessel Function ◽  
Graded Material

In this paper, the exact solution of the equation of transient heat conduction in two dimensions for a hollow cylinder made of functionally graded material (FGM) and piezoelectric layers is developed. Temperature distribution, as function of radial and circumferential directions and time, is analytically obtained for different layers, using the method of separation of variables and generalized Bessel function. The FGM properties are assumed to depend on the variable r, and they are expressed as power functions of r.

A New Approach to Thermal Analysis of a Multilayered Cylindrical Structure With Imperfect Bonds and Internal Heat Source

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
M. Bakhtiari ◽  
K. Daneshjou ◽  
R. Alibakhshi
Keyword(s):  
Thermal Analysis ◽  
Heat Conduction ◽  
Heat Source ◽  
State Space ◽  
Hollow Cylinder ◽  
Internal Heat ◽  
Functionally Graded ◽  
State Space Method ◽  
Augmented State ◽  
Space Method

In the present research, a new and straightforward mathematical model, named augmented state-space method, is introduced to solve the heat conduction equation for a multilayered orthotropic hollow cylinder with bonding imperfection in the presence of heat source. Since such problems including heat source are inherently inhomogeneous and complex, augmented state-space method converts these inhomogeneous equations into homogeneous ones. The transient solution will be achieved by present method based on laminate approximation theory in the Laplace domain, and then the solutions obtained are retrieved into the time domain by applying the numerical Laplace transform inversion. All material properties can be considered to vary continuously within the cylinder along the radial direction with arbitrary grading pattern. Based on the proposed method, the solution of heat conduction problem can be also obtained for general boundary conditions which may be included various combinations of arbitrary temperature, flux, or convection. Due to lack of any data on the transient thermal analysis corresponding to problems with imperfect bonds in the cylindrical coordinate system (r,θ), comparison is carried out with the available results for the three-layer semi-circular annular region with perfect bonds in the literature. Finally, the influence of orthotropy and interface imperfection on the distribution of the temperature field for three-layer hollow cylinder, in which the second layer is made of orthotropic functionally graded material (FGM), will be visualized.

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.

DUAL PHASE LAG HEAT CONDUCTION IN FUNCTIONALLY GRADED HOLLOW SPHERES

2014 ◽  
Vol 06 (01) ◽  
pp. 1450002 ◽  
Author(s):  
A. H. AKBARZADEH ◽  
Z. T. CHEN
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Hollow Spheres ◽  
Functionally Graded ◽  
Inversion Method ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Spherically Symmetric ◽  
Dual Phase ◽  
Phase Lags

In the present work, the dual phase lag heat conduction in functionally graded hollow spheres is investigated under spherically symmetric and axisymmetric thermal loading. The heat conduction equation is given based on the dual phase lag theory to consider the details of energy transport in the material in comparison with the non-Fourier hyperbolic heat conduction. All the material properties of the sphere are taken to vary continuously along the radial direction following a power-law with arbitrary non-homogeneity indices except the phase lags which are assumed to be constant for simplicity. The specified spherically symmetric and axisymmetric boundary conditions of the sphere lead to a 1D and 2D heat conduction problem, respectively. Employing the Laplace transform to eliminate the time dependency of the problem, analytical solutions are obtained for the temperature and heat flux. The final results in the time domain are obtained by a numerical Laplace inversion method. The speed of thermal wave in the functionally graded sphere based on the dual phase lag is compared with that of the hyperbolic heat conduction. Furthermore, the numerical results are shown to clarify the effects of phase lags and non-homogeneity indices on the thermal response. The current results are verified with those reported in the literature.

Analysis of One-Dimensional Hyperbolic Heat Conduction in a Functionally Graded Thin Plate

2011 ◽  
Author(s):  
Mohammad Reza Raveshi ◽  
Shayan Amiri ◽  
Ali Keshavarz
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Functionally Graded ◽  
Dimensionless Temperature ◽  
Hyperbolic Heat Conduction ◽  
Temperature Peak ◽  
Trial Solution ◽  
One Dimensional ◽  
Graded Material ◽  
The Time Domain

This paper presents the analytical solution of one-dimensional non-Fourier heat conduction problem for a finite plate made of functionally graded material. To investigate the influence of material properties variation, exponential space-dependant functions of thermal conductivity and specific heat capacity are considered. The problem is solved analytically in the Laplace domain, and the final results in the time domain are obtained using numerical inversion of the Laplace transform. The trial solution method with collocation optimizing criterion has been applied to solve the hyperbolic heat conduction equation based on polynomial shape function approximation. Due to the reflection and interaction of the thermal waves, the temperature peak happens on the insulated wall of the FGM plate, so the major aim of this paper is to find the amount of temperature peak and the time at which it happens. It has been shown that the dimensionless temperature peak and its happening time increase along with an increase in the dimensionless relaxation time. The results are validated by comparison with the results from an exact available solution solved at special case which shows a close agreement.

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