The finite velocity of propagation of thermal perturbations in media with constant thermal conductivity

1976 ◽  
Vol 16 (5) ◽  
pp. 141-149 ◽  
Author(s):  
L.K. Martinson
Keyword(s):  
Thermal Conductivity ◽  
Finite Velocity ◽  
Constant Thermal Conductivity ◽  
Velocity Of Propagation ◽  
Thermal Perturbations

scholarly journals A NOTE ON THE CONSTANT THERMAL CONDUCTIVITY HYPOTHESIS AND ITS CONSEQUENCE FOR CONDUCTION HEAT TRANSFER PROBLEMS

2014 ◽  
Vol 13 (2) ◽  
pp. 48
Author(s):  
R. M. S. Gama
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
High Temperature ◽  
Heat Generation ◽  
Strong Dependence ◽  
Temperature Gradients ◽  
Conduction Heat Transfer ◽  
Kirchhoff Transformation ◽  
Constant Thermal Conductivity ◽  
Transfer Problems

This work discuss the usual constant conductivity assumption and its consequences when a given material presents a strong dependence between the temperature and the thermal conductivity. The discussion is carried out considering a sphere of silicon with a given heat generation concentrated in a vicinity of its centre, giving rise to high temperature gradients. This particular case is enough to show that the constant thermal conductivity hypothesis may give rise to very large errors and must be avoided. In order to surpass the mathematical complexity, the Kirchhoff transformation is used for constructing the solution of the problem. In addition, an equation correlating thermal conductivity and the temperature is proposed.

Thermodynamic Extremum Principles for Nonequilibrium Stationary State in Heat Conduction

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Yangyu Guo ◽  
Ziyan Wang ◽  
Moran Wang
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Stationary State ◽  
Transient Heat Conduction ◽  
Clear Understanding ◽  
Minimum Entropy ◽  
Dissipation Potential ◽  
Nonequilibrium Stationary State ◽  
Minimum Entropy Production ◽  
Constant Thermal Conductivity

Minimum entropy production principle (MEPP) is an important variational principle for the evolution of systems to nonequilibrium stationary state. However, its restricted validity in the domain of Onsager's linear theory requires an inverse temperature square-dependent thermal conductivity for heat conduction problems. A previous derivative principle of MEPP still limits to constant thermal conductivity case. Therefore, the present work aims to generalize the MEPP to remove these nonphysical limitations. A new dissipation potential is proposed, the minimum of which thus corresponds to the stationary state with no restriction on thermal conductivity. We give both rigorous theoretical verification of the new extremum principle and systematic numerical demonstration through 1D transient heat conduction with different kinds of temperature dependence of the thermal conductivity. The results show that the new principle remains always valid while MEPP and its derivative principle fail beyond their scopes of validity. The present work promotes a clear understanding of the existing thermodynamic extremum principles and proposes a new one for stationary state in nonlinear heat transport.

scholarly journals Nonlinear thermal conductivity in gases

2016 ◽  
Vol 57 ◽  
Author(s):  
Arvydas Juozapas Janavičius ◽  
Sigita Turskienė
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Nonlinear Equation ◽  
Diffusion Processes ◽  
Finite Velocity ◽  
Practical Applications ◽  
Different Temperatures ◽  
Gas Molecules ◽  
Diffusivity Equation ◽  
Nonlinear Thermal Conductivity

The nonlinear diffusion equation corresponds to the diffusion processes which can occur with a finite velocity. A.J. Janavičius proposed nonlinear equation which describes more exactly the diffusion of impurities in Si crystals in many interesting practical applications. The heat transfer in gases is also based on diffusion of gas molecules from hot regions to the coldest ones with a finite velocity by random Brownian motions. In this case the heat transfer can be considered using similar nonlinear thermal diffusivity equation. The approximate analytical solution of this nonlinear equation can be used for the experimental analysis of thermal conductivity coefficients using temperature profiles dependence on different temperatures and pressures in gases.  

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