TY - JOUR
T1 - The method of images in thermoelasticity with an application to wafer heating
AU - Veldman, Daniel W.M.
AU - Fey, Rob H.B.
AU - Zwart, Hans
AU - van de Wal, Marc M.J.
AU - van den Boom, Joris D.B.J.
AU - Nijmeijer, Henk
N1 - Funding Information:
This work has been financially supported by the Impuls II research program of the High Tech System Center (HTSC) at the Eindhoven University of Technology.
Publisher Copyright:
© 2021 The Author(s). Published with license by Taylor & Francis Group, LLC.
PY - 2021/8/3
Y1 - 2021/8/3
N2 - The well-known method of images relates the solution of the heat equation on (Formula presented.) (typically n = 2 or n = 3) to the solution of the heat equation on certain spatial subdomains Ω of (Formula presented.) By reformulating the method of images in terms of a convolution kernel, two novel extensions are obtained in this paper. First, the method of images is extended from thermal problems to thermoelastic problems, that is, it is demonstrated how the heat-induced deformations on (Formula presented.) can be related to the heat-induced deformations on certain subdomains Ω of (Formula presented.) Secondly, an explicit expression for the convolution kernel for the disk is obtained. This enables the application of the method of images to circular domains to which it could not be applied before. The two obtained extensions lead to a computationally efficient simulation method for repetitive heat loads on a disk. In a representative simulation example of wafer heating, the proposed method is more than ten times faster than a conventional Finite Element approach.
AB - The well-known method of images relates the solution of the heat equation on (Formula presented.) (typically n = 2 or n = 3) to the solution of the heat equation on certain spatial subdomains Ω of (Formula presented.) By reformulating the method of images in terms of a convolution kernel, two novel extensions are obtained in this paper. First, the method of images is extended from thermal problems to thermoelastic problems, that is, it is demonstrated how the heat-induced deformations on (Formula presented.) can be related to the heat-induced deformations on certain subdomains Ω of (Formula presented.) Secondly, an explicit expression for the convolution kernel for the disk is obtained. This enables the application of the method of images to circular domains to which it could not be applied before. The two obtained extensions lead to a computationally efficient simulation method for repetitive heat loads on a disk. In a representative simulation example of wafer heating, the proposed method is more than ten times faster than a conventional Finite Element approach.
KW - Analytical solutions
KW - Boundary conditions
KW - Disk
KW - Repetitive heat sources
KW - Thermal loading
UR - http://www.scopus.com/inward/record.url?scp=85109879287&partnerID=8YFLogxK
U2 - 10.1080/01495739.2021.1936321
DO - 10.1080/01495739.2021.1936321
M3 - Article
AN - SCOPUS:85109879287
SN - 0149-5739
VL - 44
SP - 970
EP - 1010
JO - Journal of Thermal Stresses
JF - Journal of Thermal Stresses
IS - 8
ER -