Three-dimensional Green’s functions for transient heat conduction problems in anisotropic bimaterial
•Transient heat conduction problems in general anisotropic media are solved.•Three-dimensional Green’s functions in bimaterial are derived for the first time.•Solutions can be reduced to simple cases of material properties or structures.•Numerical results show the effects of interface and the proper...
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| Published in | International journal of heat and mass transfer Vol. 146; p. 118805 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
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01.01.2020
Elsevier BV |
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| Abstract | •Transient heat conduction problems in general anisotropic media are solved.•Three-dimensional Green’s functions in bimaterial are derived for the first time.•Solutions can be reduced to simple cases of material properties or structures.•Numerical results show the effects of interface and the properties of anisotropy.
In this paper, three-dimensional Green’s functions for transient heat conduction problems in general anisotropic bimaterial are obtained based on two-dimensional Fourier transform and Laplace transform, and are separated as a sum of a full-space Green’s function and a complementary part. We can get the bimaterial Green's functions in the transformed domain by boundary conditions, and then in the physical domain by the inverse Fourier and Laplace transform. Although the present paper aims to develop Green's function in anisotropic bimaterial, the derived solutions can be reduced to simple cases, such as in isotropic or orthotropic materials, and in half-space or full-space. Moreover, this method can be extended to derivation of new Green’s functions in multi-layer materials. Numerical examples are presented to verify the validity and applicability of present solutions. When the source is constant and time extends to infinity, the present transient solution approaches the steady one. Besides, the anisotropic solution indicates high correlation with the properties of material. |
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| AbstractList | •Transient heat conduction problems in general anisotropic media are solved.•Three-dimensional Green’s functions in bimaterial are derived for the first time.•Solutions can be reduced to simple cases of material properties or structures.•Numerical results show the effects of interface and the properties of anisotropy.
In this paper, three-dimensional Green’s functions for transient heat conduction problems in general anisotropic bimaterial are obtained based on two-dimensional Fourier transform and Laplace transform, and are separated as a sum of a full-space Green’s function and a complementary part. We can get the bimaterial Green's functions in the transformed domain by boundary conditions, and then in the physical domain by the inverse Fourier and Laplace transform. Although the present paper aims to develop Green's function in anisotropic bimaterial, the derived solutions can be reduced to simple cases, such as in isotropic or orthotropic materials, and in half-space or full-space. Moreover, this method can be extended to derivation of new Green’s functions in multi-layer materials. Numerical examples are presented to verify the validity and applicability of present solutions. When the source is constant and time extends to infinity, the present transient solution approaches the steady one. Besides, the anisotropic solution indicates high correlation with the properties of material. In this paper, three-dimensional Green's functions for transient heat conduction problems in general anisotropic bimaterial are obtained based on two-dimensional Fourier transform and Laplace transform, and are separated as a sum of a full-space Green's function and a complementary part. We can get the bimaterial Green's functions in the transformed domain by boundary conditions, and then in the physical domain by the inverse Fourier and Laplace transform. Although the present paper aims to develop Green's function in anisotropic bimaterial, the derived solutions can be reduced to simple cases, such as in isotropic or orthotropic materials, and in half-space or full-space. Moreover, this method can be extended to derivation of new Green's functions in multi-layer materials. Numerical examples are presented to verify the validity and applicability of present solutions. When the source is constant and time extends to infinity, the present transient solution approaches the steady one. Besides, the anisotropic solution indicates high correlation with the properties of material. |
| ArticleNumber | 118805 |
| Author | Zhou, Jiakuan Han, Xueli |
| Author_xml | – sequence: 1 givenname: Jiakuan surname: Zhou fullname: Zhou, Jiakuan email: jiakuan_zhou@qq.com – sequence: 2 givenname: Xueli surname: Han fullname: Han, Xueli |
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| Snippet | •Transient heat conduction problems in general anisotropic media are solved.•Three-dimensional Green’s functions in bimaterial are derived for the first... In this paper, three-dimensional Green's functions for transient heat conduction problems in general anisotropic bimaterial are obtained based on... |
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| StartPage | 118805 |
| SubjectTerms | Anisotropic bimaterial Anisotropy Boundary conditions Conduction heating Conductive heat transfer Fourier and Laplace transform Fourier transforms Green's functions Green’s function Half spaces Laplace transforms Multilayers Transient heat conduction |
| Title | Three-dimensional Green’s functions for transient heat conduction problems in anisotropic bimaterial |
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