TY - JOUR
T1 - Three-dimensional Green's functions for transient heat conduction problems in anisotropic bimaterial
AU - Zhou, Jiakuan
AU - Han, Xueli
N1 - Publisher Copyright:
© 2019 Elsevier Ltd
PY - 2020/1
Y1 - 2020/1
N2 - 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.
AB - 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.
KW - Anisotropic bimaterial
KW - Fourier and Laplace transform
KW - Green's function
KW - Transient heat conduction
UR - http://www.scopus.com/inward/record.url?scp=85073246959&partnerID=8YFLogxK
U2 - 10.1016/j.ijheatmasstransfer.2019.118805
DO - 10.1016/j.ijheatmasstransfer.2019.118805
M3 - Article
AN - SCOPUS:85073246959
SN - 0017-9310
VL - 146
JO - International Journal of Heat and Mass Transfer
JF - International Journal of Heat and Mass Transfer
M1 - 118805
ER -