Steady-State Temperatures in an Infinite Medium Split by a Pair of Coplanar Cracks

1988 ◽  
Vol 110 (2) ◽  
pp. 283-289 ◽  
Author(s):  
Shangchow Chang
Keyword(s):  
Steady State ◽  
Integral Transform ◽  
Continuation Method ◽  
Infinite Medium ◽  
Analytical Continuation ◽  
Crack Plane ◽  
Solution Methods ◽  
Steady State Heat ◽  
Integral Transform Technique ◽  
Coplanar Cracks

This article presents a study on the steady-state heat conduction in an infinite medium containing two coplanar cracks. Using an integral transform technique, formal temperature solutions have first been worked out for both the fundamental symmetric and antisymmetric cases. The explicit and exact expressions for temperatures are then developed via both the conventional inversion transform approach and an analytical continuation method proposed in this paper. Numerical results prepared from analytic and numerical methods are presented in graphic form for temperatures on the horizontal crack plane and on a plane slant to the cracks. The relative merit of various possible solution methods is also discussed.

scholarly journals SEMI-ANALYTICAL SOLUTION OF THE HEAT CONDUCTION IN A PLATE WITH HEAT GENERATION

2017 ◽  
Vol 16 (1) ◽  
pp. 58
Author(s):  
L. C. da Silva ◽  
D. J. N. M. Chalhub ◽  
A. L. O. Calil ◽  
R. S. de Moura
Keyword(s):  
Heat Conduction ◽  
Heat Generation ◽  
Truncation Error ◽  
Integral Transform ◽  
Solution Process ◽  
High Concentration ◽  
Classical Integral ◽  
Steady State Heat ◽  
Central Finite Difference ◽  
Integral Transform Technique

In the present work, a formulation for the solution of the two-dimensional steady state heat conduction with heat generation is presented. The classical integral transform technique (CITT) is used to solve the problem in a semi- analytical manner. CITT deals with expansions of the sought solution in terms of infinite orthogonal basis of eigenfunctions, keeping the solution process always within a continuous domain. For the particular problem, the resulting system is composed of a set of uncoupled differential equations which can be solved analytically. However, a truncation error is involved since the infinite series must be truncated to obtain numerical results. For comparison and validation purposes, the second order central finite difference method (FDM) is also implemented. The convergence analysis showed that CITT has a greater performance having no difficulties to obtain accurate results with very few terms in the solution summation. The FDM had convergence troubles specially for the positions near the center and for high concentration of heat generation in the center of the plate.

scholarly journals A pair of arbitrarily-oriented coplanar cracks in an anisotropic elastic slab

1991 ◽  
Vol 32 (3) ◽  
pp. 284-295 ◽  
Author(s):  
W. T. Ang
Keyword(s):  
Integral Equations ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Finite Part ◽  
Fourier Integral Transform ◽  
Anisotropic Elastic ◽  
Elastic Slab ◽  
Integral Transform Technique ◽  
Coplanar Cracks

AbstractThe problem of an anisotropic elastic slab containing two arbitrarily-oriented coplanar cracks in its interior is considered. Using a Fourier integral transform technique, we reduce the problem to a system of simultaneous finite-part singular integral equations which can be solved numerically. Once the integral equations are solved, relevant quantities such as the crack energy can be readily computed. Numerical results for specific examples are obtained.

Steady-State Temperature Field in a Separator System Featuring Active Thermal Protection with Anisotropic Properties

2020 ◽  
pp. 4-19
Author(s):  
A.V. Attetkov ◽  
P.A. Vlasov ◽  
I.K. Volkov
Keyword(s):  
Temperature Field ◽  
Steady State ◽  
Heat Exchange ◽  
Integral Transform ◽  
Thermal Protection ◽  
Local Heating ◽  
Steady State Temperature ◽  
The Media ◽  
Steady State Heat ◽  
Flow Power

We stated and solved the problem of determining the steady-state temperature field of a system simulated by a wall separating two different media. One of the wall surfaces has a thermally active layer that functions according to the feedback principle and features an anisotropic coating subjected to local heating while undergoing heat exchange with the environment. We show that the sought-after temperature field is an additive composition of two independent components, the first of which is exclusively a function of the heat exchange intensity between the separated media and the boundary surfaces of the system under consideration, and the second is a function of the heat flow power density affecting the separator system for the temperatures of the media separated being zero. We used integral transform methods in an analytically closed form to find solutions to respective steady-state heat conductivity problems. The results obtained confirm the existence of a previously found temperature field "drift" effect in an anisotropic material displaying general anisotropy of its properties.

Steady State Heat Conduction Modeling by the Generalized Finite Element Method

2018 ◽  
Author(s):  
Humberto Alves da Silveira Monteiro ◽  
Guilherme Garcia Botelho ◽  
Roque Luiz da Silva Pitangueira ◽  
Rodrigo Peixoto ◽  
FELICIO BARROS
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Steady State ◽  
Generalized Finite Element Method ◽  
State Heat ◽  
Steady State Heat ◽  
Generalized Finite Element ◽  
Element Method

An Investigation of the Effect of interrupted fin arrangements on the Thermal Performance of a Heat Sink under a Free Convection Condition

2019 ◽  
Vol 7 (1) ◽  
pp. 43-53
Author(s):  
Abbas Jassem Jubear ◽  
Ali Hameed Abd
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Natural Convection ◽  
Thermal Performance ◽  
Heat Sink ◽  
Numerical Study ◽  
Ansys Fluent ◽  
Fluent Software ◽  
Steady State Heat ◽  
Steady State Heat Transfer

The heat sink with vertically rectangular interrupted fins was investigated numerically in a natural convection field, with steady-state heat transfer. A numerical study has been conducted using ANSYS Fluent software (R16.1) in order to develop a 3-D numerical model.  The dimensions of the fins are (305 mm length, 100 mm width, 17 mm height, and 9.5 mm space between fins. The number of fins used on the surface is eight. In this study, the heat input was used as follows: 20, 40, 60, 80, 100, and 120 watts. This study focused on interrupted rectangular fins with a different arrangement and angle of the fins. Results show that the addition of interruption in fins in various arrangements will improve the thermal performance of the heat sink, and through the results, a better interruption rate as an equation can be obtained.

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