A study of a multidimensional transient heat conduction problem with a moving heat source Part 1: Analytical solution

1991 ◽  
Vol 9 (1) ◽  
pp. 35-40 ◽  
Author(s):  
T.W. Abou-Arab ◽  
M.A. Al-Nimr
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Moving Heat Source ◽  
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.

An Analytical Solution to Transient Heat Conduction in a Composite Region With a Cylindrical Heat Source

1995 ◽  
Vol 117 (3) ◽  
pp. 242-248 ◽  
Author(s):  
Yian Gu ◽  
D. L. O’Neal
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Heat Pumps ◽  
Orthogonal Expansion ◽  
Transient Heat Conduction Problem ◽  
Cylindrical Source ◽  
Thermal Diffusivities ◽  
Composite Region

An approximate analytical solution to the transient heat-conduction problem in a large composite region with an internal cylindrical source is presented. The generalized orthogonal expansion technique is utilized in deriving the solution. Such problems are encountered in the design or simulation of the ground-coupled heat exchangers used in ground-coupled heat pumps. Solutions are presented for the nondimensional temperature as a function of the ratios of the thermal conductivities and thermal diffusivities of the two materials in the layers. To verify the correctness of the solution, comparisons are made between the two-layer composite solution and the classical homogeneous cylindrical source solution and a finite difference solution.

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.

Sign in / Sign up

Export Citation Format

Share Document