Discontinuity waves in temperature and diffusion models

Ciarletta, Michele; Straughan, Brian; Tibullo, Vincenzo

Abstract

We analyse shock wave behaviour in a hyperbolic diffusion system with a general forcing term which is qualitatively not dissimilar to a logistic growth term. The amplitude behaviour is interesting and depends critically on a parameter in the forcing term. We also develop a fully nonlinear acceleration wave analysis for a hyperbolic theory of diffusion coupled to temperature evolution. We consider a rigid body and we show that for three-dimensional waves there is a fast wave and a slow wave. The amplitude equation is derived exactly for a one-dimensional (plane) wave and the amplitude is found for a wave moving into a region of constant temperature and solute concentration. This analysis is generalized to allow for forcing terms of Selkov–Schnakenberg, or Al Ghoul-Eu cubic reaction type. We briefly consider a nonlinear acceleration wave in a heat conduction theory with two solutes present, resulting in a model with equations for temperature and each of two solute concentrations. Here it is shown that three waves may propagate.

Citation

Ciarletta, M., Straughan, B., & Tibullo, V. (2024). Discontinuity waves in temperature and diffusion models. Mechanics Research Communications, 137, Article 104274. https://doi.org/10.1016/j.mechrescom.2024.104274

• Journal Article Type: Article
• Acceptance Date: Apr 5, 2024
• Online Publication Date: Apr 10, 2024
• Publication Date: 2024-05
• Deposit Date: Apr 26, 2024
• Publicly Available Date: Apr 26, 2024
• Journal: Mechanics Research Communications
• Print ISSN: 0093-6413
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 137
• Article Number: 104274
• DOI: https://doi.org/10.1016/j.mechrescom.2024.104274
• Public URL: https://durham-repository.worktribe.com/output/2383490