20.500.12556/RUL-152741 Fluid flow during phase transition from viscous fluid to viscoelastic solid via variable-order calculus In this paper, we consider a pressure-driven flow of a viscoelastic fluid in a straight rectangular channel undergoing a solidification phase change due to polymerization. We treat the viscoelastic response of the fluid with a model based on the formalism of variable-order calculus; more specifically, we employ a model utilizing a variable-order Caputo-type differential operator. The order parameter present in the model is determined by the extent of polymerization induced by light irradiation. We model this physical quantity with a simple equation of kinetics, where the reaction rate is proportional to the amount of material available for polymerization and optical transmittance. We treat cases when the extent of polymerization is a function of either time alone or both position and time, and solve them using either analytical or semi-analytical methods. Results of our analysis indicate that in both cases, solutions evolve in time according to a variable-order decay law, with the solution in the first case having a hyperbolic cosine-like spatial dependence, while the spatial dependence in the second case conforms to a bell curve-like function. We infer that our treatment is physically sound and may be used to consider problems of more general viscoelastic flows during solidification, with the advantage of requiring fewer experimentally determined parameters. viscous fluid flow phase change variable-order integro-differential operator tok viskoznega fluida fazna sprememba diferencialno-integralski operator variabilnega reda true false true Angleški jezik Slovenski jezik Članek v reviji 2023-12-05 12:27:58 2023-12-05 12:28:04 2025-04-29 14:14:20 0000-00-00 00:00:00 2023 0 0 21 str. iss. 12, art. 123103 Vol. 35 Dec. 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 532:536.42 1070-6631 10.1063/5.0177121 174918659 Istenic,_Brojan_-_Fluid_flow_during_phase_transition.pdf Istenic,_Brojan_-_Fluid_flow_during_phase_transition.pdf 1 A17A10BBE94C68F5A8A1533FCE31B5D1 fb66da011cebed0b2486a16e24a0fc20f5af22d9f007a503cf49659cf23e6372 144961ef-9362-11ee-867f-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=178362 https://pubs.aip.org/aip/pof/article/35/12/123103/2925737/Fluid-flow-during-phase-transition-From-viscous 1 5b5956ce-9361-11ee-867f-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=178361 Fakulteta za strojništvo 0 0 0