A GENERAL MINIMUM PRINCIPLE FOR STEADY-STATE CONDUCTION HEAT TRANSFER PROBLEMS WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY SUBJECTED TO LINEAR ROBIN BOUNDARY CONDITIONS

2018 ◽  
Vol 49 (5) ◽  
pp. 413-422
Author(s):  
Rogério Martins Saldanha da Gama
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Minimum Principle ◽  
Robin Boundary Conditions ◽  
Temperature Dependent ◽  
Conduction Heat Transfer ◽  
Transfer Problems ◽  
Robin Boundary ◽  
Temperature Dependent Thermal Conductivity

scholarly journals A Linear Approach Suitable for a Class of Steady-State Heat Transfer Problems with Temperature-Dependent Thermal Conductivity

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
R. M. S. Gama ◽  
R. Pazetto
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Robin Boundary Conditions ◽  
Temperature Dependent ◽  
Steady State Heat ◽  
Steady State Heat Transfer ◽  
Transfer Problems ◽  
Robin Boundary ◽  
Temperature Dependent Thermal Conductivity

This work presents an useful tool for constructing the solution of steady-state heat transfer problems, with temperature-dependent thermal conductivity, by means of the solution of Poisson equations. Specifically, it will be presented a procedure for constructing the solution of a nonlinear second-order partial differential equation, subjected to Robin boundary conditions, by means of a sequence whose elements are obtained from the solution of very simple linear partial differential equations, also subjected to Robin boundary conditions. In addition, an a priori upper bound estimate for the solution is presented too. Some examples, involving temperature-dependent thermal conductivity, are presented, illustrating the use of numerical approximations.

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.

scholarly journals STEADY-STATE HEAT TRANSFER IN A PLATE WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY (AN EXACT SOLUTION)

2019 ◽  
Vol 18 (2) ◽  
pp. 85
Author(s):  
A. Miguelis ◽  
R. Pazetto ◽  
R. M. S. Gama
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Transfer Problem ◽  
Internal Heat ◽  
Temperature Dependent ◽  
State Heat ◽  
Kirchhoff Transformation ◽  
Steady State Heat ◽  
Steady State Heat Transfer

This work presents the solution of the steady-state heat transfer problem in a rectangular plate with an internal heat source in a context in which the thermal conductivity depends on the local temperature. This generalization of one of the most classical heat transfer problems is carried out with the aid of the Kirchhoff transformation and employs only well known tools, as the superposition of solutions and the Fourier series. The obtained results illustrate how the usual procedures may be extended for solving more realistic physical problems (since the thermal conductivity of any material is temperature-dependent). A general formula for evaluating the Kirchhoff transformation as well as its inverse is presented too. This work has a strong didactical contribution since such analytical solutions are not found in any classical heat transfer book. In addition, the main idea can be used in a lot of similar problems.

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