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 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.

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.

Steady State Heat Transfer Within a Nanoscale Spatial Domain

2012 ◽  
Vol 134 (7) ◽  
Author(s):  
Kirill V. Poletkin ◽  
Vladimir Kulish
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Transfer Coefficient ◽  
Spatial Domain ◽  
Thermal Waves ◽  
Steady State Heat ◽  
Steady State Heat Transfer ◽  
The Heat Transfer Coefficient

In this paper, we study the steady state heat transfer process within a spatial domain of the transporting medium whose length is of the same order as the distance traveled by thermal waves. In this study, the thermal conductivity is defined as a function of a spatial variable. This is achieved by analyzing an effective thermal diffusivity that is used to match the transient temperature behavior in the case of heat wave propagation by the result obtained from the Fourier theory. Then, combining the defined size-dependent thermal conductivity with Fourier’s law allows us to study the behavior of the heat flux at nanoscale and predict that a decrease of the size of the transporting medium leads to an increase of the heat transfer coefficient which reaches its finite maximal value, contrary to the infinite value predicted by the classical theory. The upper limit value of the heat transfer coefficient is proportional to the ratio of the bulk value of the thermal conductivity to the characteristic length of thermal waves in the transporting medium.

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