Steady-State Conduction With Variable Thermal Conductivity

1962 ◽  
Vol 84 (1) ◽  
pp. 92-93 ◽  
Author(s):  
Robert K. McMordie
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Variable Thermal Conductivity ◽  
Two Dimensional ◽  
The Real ◽  
State Heat ◽  
Steady State Heat ◽  
Steady State Heat Transfer ◽  
Transfer Problems

A method is developed for solving two-dimensional, steady-state heat-transfer problems with thermal conductivity dependent on temperature. The quantity ∫ KdT is employed in the analysis and although this quantity has been known for some time,2, 3 it seems that the real usefulness of this quantity in analysis has not been, in general, recognized.

scholarly journals An isogeometric analysis approach for twodimensional steady state heat transfer problems

2015 ◽  
Vol 18 (2) ◽  
pp. 164-174
Author(s):  
Em Tuan Le ◽  
Khuong Duy Nguyen ◽  
Hoa Cong Vu
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Isogeometric Analysis ◽  
Basis Functions ◽  
High Rate ◽  
Two Dimensional ◽  
State Heat ◽  
Steady State Heat ◽  
Steady State Heat Transfer ◽  
Transfer Problems

The purpose of this article is studied the application of isogeometric analysis (IGA) to two-dimensional steady state heat transfer problems in a heat sink. By using high order basis functions, NURBS basis functions, IGA is a high rate convergence approach in comparison to a traditional Finite Element Method. Moreover, the development of this method decreased the gaps between CAD and mathematical model and increased the continuity of mesh.

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.

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.

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