A Simple Model for Transient Heat Conduction in an Infinite Cylinder With Convective Boundary Conditions

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Messaoud Guellal ◽  
Hamou Sadat ◽  
Christian Prax
Keyword(s):  
Heat Conduction ◽  
Simple Model ◽  
Perturbation Method ◽  
Explicit Solution ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Infinite Cylinder ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
One Dimensional

A perturbation method is used to solve an unsteady one-dimensional heat conduction problem in a cylinder. A simple second order explicit solution is obtained. It is shown that this solution is accurate even for high values of the Biot number in a region surrounding the center of the cylinder.

scholarly journals ANALYTICAL SOLUTION OF A 2D TRANSIENT HEAT CONDUCTION PROBLEM USING GREEN´S FUNCTIONS

2020 ◽  
Vol 19 (1) ◽  
pp. 66
Author(s):  
J. R. F. Oliveira ◽  
J. A. dos Santos Jr. ◽  
J. G. do Nascimento ◽  
S. S. Ribeiro ◽  
G. C. Oliveira ◽  
...  
Keyword(s):  
Temperature Field ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Heat Fluxes ◽  
Two Dimensional ◽  
One Dimensional ◽  
Transient Heat Conduction Problem

Through the present work the authors determined the analytical solution of a transient two-dimensional heat conduction problem using Green’s Functions (GF). This method is very useful for solving cases where heat conduction is transient and whose boundary conditions vary with time. Boundary conditions of the problem in question, with rectangular geometry, are of the prescribed temperature type - prescribed flow in the direction x and prescribed flow - prescribed flow in the direction y, implying in the corresponding GF given by GX21Y22. The initial temperature of the space domain is assumed to be different from the prescribed temperature occurring at one of the boundaries along x. The temperature field solution of the two-dimensional problem was determined. The intrinsic verification of this solution was made by comparing the solution of a 1D problem. This was to consider the incident heat fluxes at y = 0 and y = 2b tending to zero, thus making the problem one-dimensional, with corresponding GF given by GX21. When comparing the results obtained in both cases, for a time of t = 1 s, it was seen that the temperature field of both was very similar, which validates the solution obtained for the 2D problem.

Investigation of the one-dimensional transient heat conduction problem of a coated high strength steel plate

2019 ◽  
Vol 24 (11) ◽  
pp. 3472-3484 ◽  
Author(s):  
Yang Yang ◽  
Hong-Liang Dai ◽  
Chao Ye ◽  
Wei-Li Xu ◽  
Ai-Hui Luo
Keyword(s):  
Heat Conduction ◽  
High Strength Steel ◽  
Heat Conduction Problem ◽  
Thermal Relaxation ◽  
High Strength ◽  
Transient Heat Conduction ◽  
One Dimensional ◽  
Temperature Increment ◽  
Transient Heat Conduction Problem ◽  
The One

In this paper, the one-dimensional transient heat conduction problem is investigated of a coated high strength steel (HSS) plate which is composed of two coating layers and a HSS layer. As the coating is extremely thin, non-Fourier heat conduction is applied to this part, while the steel part is analyzed by Fourier conduction. Then the temperature increment equations are obtained, which can be calculated by the Newmark method. The effects of thermal relaxation time, temperature boundary conditions, and coating parameters on temperature increment distribution of the coated HSS plate are also presented. Thus, the one-dimensional transient heat conduction problem of a coated HSS plate can be solved, which contributes to practical application and engineering design.

scholarly journals ANALITYCAL SOLUTION OF THE ONE DIMENSIONAL NONLINEAR TRANSIENT HEAT CONDUCTION PROBLEM USING GREEN’S FUNCTIONS

2021 ◽  
Vol 20 (2) ◽  
pp. 55
Author(s):  
S. S. Ribeiro ◽  
G. C. Oliveira ◽  
J. R. F. Oliveira ◽  
G. Guimarães
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Green's Functions ◽  
Green’S Functions ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
One Dimensional ◽  
Transient Heat Conduction Problem ◽  
Kirchhoff Transformation ◽  
Nonlinear Transient

Analytical solutions showed to be an important and strong tool for understand thermal problems using mathematic tools. In this work we propose an approach about one dimensional analytical solution for a nonlinear transient heat conduction problem, were used mathematical elements such as Kirchhoff transformation, Green’s functions and the combination of them.  The combination of this two methods showed that was possible to determinate an analytical solution for the nonlinear thermal problem, and showed a good approximation when compared with results from numerical methods.

Efficient Solution Processes for Finite Element Analysis of Transient Heat Conduction

1971 ◽  
Vol 93 (3) ◽  
pp. 257-263 ◽  
Author(s):  
R. H. Gallagher ◽  
R. H. Mallett
Keyword(s):  
Heat Conduction ◽  
Degrees Of Freedom ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Element Analysis ◽  
One Dimensional ◽  
Solution Processes ◽  
Transient Heat Conduction Problem ◽  
Matrix Differential ◽  
State Relations

Systematic procedures are presented for reducing the order of a matrix differential equation governing transient heat conduction in solids. Two principal aspects of this development are a condensation of the set of gridpoint temperature degrees of freedom using steady-state relations and the introduction of generalized (modal) temperature degrees of freedom to achieve a further reduction. These processes are illustrated in an elementary one-dimensional transient heat conduction problem.

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