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.

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.

Application of numerical procedure for thermal diagnostics of the delamination of strengthening material at concrete construction

2019 ◽  
Vol 30 (5) ◽  
pp. 2655-2668 ◽  
Author(s):  
Wojciech Piotr Adamczyk ◽  
Marcin Gorski ◽  
Ziemowit Ostrowski ◽  
Ryszard Bialecki ◽  
Grzegorz Kruczek ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Thermal Resistance ◽  
Quantitative Assessment ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Decision Variable ◽  
Assessment Procedure ◽  
Ir Camera ◽  
Content Type ◽  
Transient Heat Conduction Problem

Purpose Large structural objects, primarily concrete bridges, can be reinforced by gluing to their stretched surface tapes of fiber-reinforced polymer (FRP). The condition for this technology to work requires the quality of the bonding of FRP and the concrete to be perfect. Possible defects may arise in the phase of construction but also as a result of long-term fatigue loads. These defects having different forms of voids and discontinuities in the bonding layer are difficult to detect by optical inspection. This paper aims to describe the development of a rapid and nondestructive method for quantitative assessment of the debonding between materials. Design/methodology/approach The applied technique belongs to the wide class of active infrared (IR) thermography, the principle of which is to heat (or cool) the investigated object, and determine the properties of interest from the recorded, by an IR camera, temperature field. The methodology implemented in this work is to uniformly heat for a few seconds, using a set of halogen lamps, the FRP surface attached to the concrete. The parameter of interest is the thermal resistance of the layer separating the polymer tape and the concrete. The presence of voids and debonding will result in large values of this resistance. Its value is retrieved by solving an inverse transient heat conduction problem. This is accomplished by minimizing, in the sense of least squares, the difference between the recorded and simulated temperatures. The latter is defined as a solution of a 1D transient heat conduction problem with the already mentioned thermal resistance treated as the only decision variable. Findings A general method has been developed, which detects debonding of the FRP tapes from the concrete. The method is rapid and nondestructive. Owing to a special selection of the compared dimensionless measured and simulated temperatures, the method is not sensitive to the surface quality (roughness and emissivity). Measurements and calculation may be executed within seconds. The efficiency of the technique has been shown at a sample, where the defects have been artificially introduced in a controlled manner. Originality/value A quantitative assessment procedure which can be used to determine the extent of the debonding has been developed. The procedure uses inverse technique whose result is the unknown thermal resistance between the member and the FRP strip.

Conservation laws and associated Lie point symmetries admitted by the transient heat conduction problem for heat transfer in straight fins

Open Physics ◽  
2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Partner Ndlovu ◽  
Rasselo Moitsheki
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Conduction ◽  
Conservation Laws ◽  
Linear Function ◽  
Power Law ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Lie Point Symmetries ◽  
Transient Heat Conduction Problem

AbstractSome new conservation laws for the transient heat conduction problem for heat transfer in a straight fin are constructed. The thermal conductivity is given by a power law in one case and by a linear function of temperature in the other. Conservation laws are derived using the direct method when thermal conductivity is given by the power law and the multiplier method when thermal conductivity is given as a linear function of temperature. The heat transfer coefficient is assumed to be given by the power law function of temperature. Furthermore, we determine the Lie point symmetries associated with the conserved vectors for the model with power law thermal conductivity.

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