A Thermal Stability Criterion for Heat Conduction in Multilayer Composite Solids

2009 ◽  
Vol 131 (11) ◽  
Author(s):  
Bingen Yang ◽  
Hang Shi
Keyword(s):  
Thermal Stability ◽  
Heat Conduction ◽  
Heat Generation ◽  
Stability Criterion ◽  
Internal Heat ◽  
Computational Effort ◽  
Stability Test ◽  
Multilayer Composite ◽  
Excessive Heat ◽  
Root Locus Analysis

Excessive heat generation within a body can cause unbounded temperature or thermal instability. In this work, a new stability test is established for heat conduction in one-dimensional multilayer composite solids that have internal heat generation at a rate proportional to the interior temperature. In the development, a spatial state formulation in the Laplace transform domain and a root locus analysis yield a stability criterion. This criterion gives an upper bound of heat source for thermal stability and relates the degree of excessive heat production to the number of unstable (positive) eigenvalues. The proposed stability test does not need any information on system eigenvalues, requests minimum computational effort, and is applicable to composites with thermal resistance at layer interfaces and bodies with nonuniformly distributed parameters. The convenience and efficiency of the stability test are demonstrated in three numerical examples.

A Root Locus Method for Stability Analysis of Heat Conduction in Multilayer Composite Solids

2008 ◽  
Author(s):  
Bingen Yang ◽  
Hang Shi
Keyword(s):  
Heat Source ◽  
Characteristic Equation ◽  
Heat Generation ◽  
Stability Criterion ◽  
Internal Heat ◽  
Root Locus ◽  
Excessive Heat ◽  
Locus Method ◽  
Numerical Effort ◽  
Root Locus Analysis

Excessive heat generation within a body can cause unbounded temperature or thermal instability. In this work, a stability criterion is established for one-dimensional composite solids with internal heat generation at a rate proportional to their temperature. In the development, a spatial state formulation is used to derive a characteristic equation for system eigenvalues. A root locus analysis of the characteristic equation yields a stability criterion, by which an upper bound of heat source for thermal stability is obtained, and the gain of heat source is related to the number of unstable (positive) eigenvalues. The proposed stability test requires minimum numerical effort, does not require the information about system eigenvalues, and is applicable to various spatial distributions of heat source.

Numerical investigation of fast precooling of a cylindrical food product based on the hyperbolic heat conduction model

2013 ◽  
Vol 23 (6) ◽  
pp. 960-978 ◽  
Author(s):  
Mohammed Q. Al‐Odat
Keyword(s):  
Heat Conduction ◽  
Heat Generation ◽  
Internal Heat ◽  
Food Product ◽  
Heat Diffusion ◽  
Numerical Code ◽  
Hyperbolic Model ◽  
Hyperbolic Heat Conduction ◽  
Conduction Model ◽  
Content Type

PurposeIn this study, the purpose was to introduce two‐dimensional hyperbolic heat conduction equations in order to simulate the fast precooling process of a cylindrically shaped food product with internal heat generation. A modified model for internal heat generation due to respiration in the food product was proposed to take the effect of relaxation time into account. The obtained governing equations were solved numerically using an efficient finite difference technique. The influence of Biot number and heat generation parameters on thermal characteristics was examined and discussed. The results based on hyperbolic model were compared with the classical parabolic heat diffusion model. The present numerical code was validated via comparison with analytical solution and a good agreement was found.Design/methodology/approachThe obtained governing equations were solved numerically using an efficient finite difference technique.FindingsThe influence of Biot number and heat generation parameters on thermal characteristics was examined and discussed. The results based on hyperbolic model were compared with the classical parabolic heat diffusion model. The present numerical code was validated via comparison with analytical solution and a good agreement was found.Originality/valueTwo‐dimensional analysis of fast precooling of cylindrical food product based on hyperbolic heat conduction model has not been investigated yet.

Simulation of Nanoscale Multidimensional Transient Heat Conduction Problems Using Ballistic-Diffusive Equations and Phonon Boltzmann Equation

2005 ◽  
Vol 127 (3) ◽  
pp. 298-306 ◽  
Author(s):  
Ronggui Yang ◽  
Gang Chen ◽  
Marine Laroche ◽  
Yuan Taur
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Boundary Conditions ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Computational Time ◽  
Discrete Ordinates ◽  
Fourier Law ◽  
Phonon Boltzmann Equation

Heat conduction in micro- and nanoscale and in ultrafast processes may deviate from the predictions of the Fourier law, due to boundary and interface scattering, the ballistic nature of the transport, and the finite relaxation time of heat carriers. The transient ballistic-diffusive heat conduction equations (BDE) were developed as an approximation to the phonon Boltzmann equation (BTE) for nanoscale heat conduction problems. In this paper, we further develop BDE for multidimensional heat conduction, including nanoscale heat source term and different boundary conditions, and compare the simulation results with those obtained from the phonon BTE and the Fourier law. The numerical solution strategies for multidimensional nanoscale heat conduction using BDE are presented. Several two-dimensional cases are simulated and compared to the results of the transient phonon BTE and the Fourier heat conduction theory. The transient BTE is solved using the discrete ordinates method with a two Gauss-Legendre quadratures. Special attention has been paid to the boundary conditions. Compared to the cases without internal heat generation, the difference between the BTE and BDE is larger for the case studied with internal heat generation due to the nature of the ballistic-diffusive approximation, but the results from BDE are still significantly better than those from the Fourier law. Thus we conclude that BDE captures the characteristics of the phonon BTE with much shorter computational time.

scholarly journals Heat conduction in rectangular solids with internal heat generation

2020 ◽  
pp. 235-235
Author(s):  
Zhipeng Duan ◽  
Hao Ma
Keyword(s):  
Heat Conduction ◽  
Heat Generation ◽  
Shape Factor ◽  
Heat Conduction Problem ◽  
Rectangular Cross Section ◽  
Internal Heat ◽  
Engineering Practice ◽  
Constant Wall Temperature ◽  
Temperature Boundary ◽  
Steady State Heat

A representative steady-state heat conduction problem in rectangular solids with uniformly distributed heat generation has been investigated analytically. An analytical solution is provided by solving a nonhomogeneous partial differential equation. A simple and accurate model is proposed to predict the dimensionless shape factor parameter for the first time. The dimensionless shape factor is obtained in the light of the solution of Poisson equation with constant wall temperature boundary conditions. The area-mean temperature is found by integration on the rectangular cross-section. The model is very concise and nice for quick real world approximations, and it provides acceptable accuracy for engineering practice.

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