Thermal instability of a viscoelastic fluid in a fluid-porous system with a plane Poiseuille flow

doi:10.1007/s10483-020-2663-7

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (11): 1631-1650.doi: https://doi.org/10.1007/s10483-020-2663-7

Thermal instability of a viscoelastic fluid in a fluid-porous system with a plane Poiseuille flow

Chen YIN¹, Chunwu WANG¹, Shaowei WANG²

1. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2. Department of Engineering Mechanics, School of Civil Engineering, Shandong University, Jinan 250061, China

收稿日期:2020-06-09 修回日期:2020-07-19 发布日期:2020-10-24
通讯作者: Chen YIN E-mail:yinchen@nuaa.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11702135, 11271188, and 11672164), the Natural Science Foundation of Jiangsu Province of China (No. BK20170775), the China Postdoctoral Science Foundation (No. 2016M601798), and the Jiangsu Planned Project for Postdoctoral Research Funds of China (No. 1601169B)

Thermal instability of a viscoelastic fluid in a fluid-porous system with a plane Poiseuille flow

Chen YIN¹, Chunwu WANG¹, Shaowei WANG²

1. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2. Department of Engineering Mechanics, School of Civil Engineering, Shandong University, Jinan 250061, China

Received:2020-06-09 Revised:2020-07-19 Published:2020-10-24
Contact: Chen YIN E-mail:yinchen@nuaa.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11702135, 11271188, and 11672164), the Natural Science Foundation of Jiangsu Province of China (No. BK20170775), the China Postdoctoral Science Foundation (No. 2016M601798), and the Jiangsu Planned Project for Postdoctoral Research Funds of China (No. 1601169B)

摘要/Abstract

摘要： The thermal convection of a Jeffreys fluid subjected to a plane Poiseuille flow in a fluid-porous system composed of a fluid layer and a porous layer is studied in the paper. A linear stability analysis and a Chebyshev τ-QZ algorithm are employed to solve the thermal mixed convection. Unlike the case in a single layer, the neutral curves of the two-layer system may be bi-modal in the proper depth ratio of the two layers. We find that the longitudinal rolls (LRs) only depend on the depth ratio. With the existence of the shear flow, the effects of the depth ratio, the Reynolds number, the Prandtl number, the stress relaxation, and strain retardation times on the transverse rolls (TRs) are also studied. Additionally, the thermal instability of the viscoelastic fluid is found to be more unstable than that of the Newtonian fluid in a two-layer system. In contrast to the case for Newtonian fluids, the TRs rather than the LRs may be the preferred mode for the viscoelastic fluids in some cases.

关键词: viscoelastic fluid, thermal convection, Poiseuille flow, fluid-porous system

Abstract: The thermal convection of a Jeffreys fluid subjected to a plane Poiseuille flow in a fluid-porous system composed of a fluid layer and a porous layer is studied in the paper. A linear stability analysis and a Chebyshev τ-QZ algorithm are employed to solve the thermal mixed convection. Unlike the case in a single layer, the neutral curves of the two-layer system may be bi-modal in the proper depth ratio of the two layers. We find that the longitudinal rolls (LRs) only depend on the depth ratio. With the existence of the shear flow, the effects of the depth ratio, the Reynolds number, the Prandtl number, the stress relaxation, and strain retardation times on the transverse rolls (TRs) are also studied. Additionally, the thermal instability of the viscoelastic fluid is found to be more unstable than that of the Newtonian fluid in a two-layer system. In contrast to the case for Newtonian fluids, the TRs rather than the LRs may be the preferred mode for the viscoelastic fluids in some cases.

Key words: viscoelastic fluid, thermal convection, Poiseuille flow, fluid-porous system

中图分类号:

Chen YIN, Chunwu WANG, Shaowei WANG. Thermal instability of a viscoelastic fluid in a fluid-porous system with a plane Poiseuille flow[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(11): 1631-1650.

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Thermal instability of a viscoelastic fluid in a fluid-porous system with a plane Poiseuille flow

Thermal instability of a viscoelastic fluid in a fluid-porous system with a plane Poiseuille flow

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