Modelling and simulation of radiative heat transfer in non-grey absorbing and emitting media under phase change

Moutahir, Fatima-Ezzahrae; Belhamadia, Youssef; Seaid, Mohammed; El-Amrani, Mofdi

Abstract

A class of mathematical models are proposed for modelling and numerical simulation of coupled radiative and conductive heat transfer in non-grey absorbing and emitting media under phase change. Progress in this area of mathematical modelling would contribute to a sustainable future manufacturing involving high temperature and phase change. Accurately predicting phase-change interface is the crucial step for these applications in non-grey semi-transparent media. In the present study, the conduction and radiation effects are analyzed by a set of nonlinear partial differential equations and a linear integral equation, respectively. The proposed model forms a system of nonlinear integro-differential equations and it accounts for both thermal radiation and phase change in the design. For non-grey media, the spectrum is divided into a sequence of finite intervals of frequency bands with averaged absorption coefficients resulting in coupled systems to be solved for each frequency band. The coupled equations are approximated using a second-order method in both time and space. Using discrete ordinates for the angular discretization of the integral equation for the radiation effects, a Newton-type algorithm is used to deal with the nonlinear systems. Numerical results are presented for several test problems in both grey and non-grey media, and comparisons to simulations without radiation are also shown in this study. The findings here could be used to understand effects of thermal radiation in non-grey absorbing and emitting media under phase change.

Citation

Moutahir, F.-E., Belhamadia, Y., Seaid, M., & El-Amrani, M. (2024). Modelling and simulation of radiative heat transfer in non-grey absorbing and emitting media under phase change. Computers and Mathematics with Applications, 176, 432-446. https://doi.org/10.1016/j.camwa.2024.11.005

• Journal Article Type: Article
• Acceptance Date: Nov 4, 2024
• Online Publication Date: Nov 11, 2024
• Publication Date: Dec 15, 2024
• Deposit Date: Nov 15, 2024
• Publicly Available Date: Nov 20, 2024
• Journal: Computers & Mathematics with Applications
• Print ISSN: 0898-1221
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 176
• Pages: 432-446
• DOI: https://doi.org/10.1016/j.camwa.2024.11.005
• Public URL: https://durham-repository.worktribe.com/output/3095681