An autonomous system for thermal convection of viscoelastic fluids in a porous layer using a thermal nonequilibrium model

doi:10.1007/s11708-010-0017-x

Front Energ Power Eng Chin

2010, Vol. 4

Issue (4) : 507-516 https://doi.org/10.1007/s11708-010-0017-x

RESEARCH ARTICLE

An autonomous system for thermal convection of viscoelastic fluids in a porous layer using a thermal nonequilibrium model

Qi WEI(

), Xiaohui ZHANG

School of Physics Science and Technology, Soochow University, Suzhou 215006, China

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Abstract

Thermal convection of viscoelastic fluids saturating a horizontal porous layer heated from below is analyzed using a thermal nonequilibrium model to take account of the interphase heat transfer between the fluid and the solid. The viscoelastic character of the flow is considered by a modified Darcy’s law. An autonomous system with five differential equations is deduced by applying the truncated Galerkin expansion to the momentum and heat transfer equations. The effects of interphase heat transfer H on the thermal convection of viscoelastic fluids in a porous medium are analyzed and discussed. The results show that the weak interphase heat transfer tends to stabilize the steady convection.

Keywords thermal convection porous media viscoelastic fluid thermal nonequilibrium model

Corresponding Author(s): WEI Qi,Email:weiqi@suda.edu.cn

Issue Date: 05 December 2010

Cite this article:

Qi WEI,Xiaohui ZHANG. An autonomous system for thermal convection of viscoelastic fluids in a porous layer using a thermal nonequilibrium model[J]. Front Energ Power Eng Chin, 2010, 4(4): 507-516.

URL:

https://academic.hep.com.cn/fie/EN/10.1007/s11708-010-0017-x
https://academic.hep.com.cn/fie/EN/Y2010/V4/I4/507

Fig.1 Time history of and phase portraits at , =0.05
(a) Time history of ; (b) phase portrait of -; (c) phase portrait of -; (d) phase portrait of -

Fig.2 Time history of and phase portraits at =5, =0.05
(a) Time history of ; (b) phase portrait of -; (c) phase portrait of -; (d) phase portrait of -

Fig.3 Time history of and phase portraits at = 40, = 0.05
(a) Time history of ; (b) phase portrait of -; (c) phase portrait of -; (d) phase portrait of -

Fig.4 Time history of and phase portraits at =2, =0.01
(a) Time history of; (b) phase portrait of -; (c) phase portrait of -; (d) phase portrait of -

Fig.5 Time history of and phase portraits at =5, =0.01
(a) Time history of ; (b) phase portrait of -; (c) phase portrait of -; (d) phase portrait of -

Fig.6 Time history of and phase portraits at =40, =0.01
(a) Time history of ; (b) phase portrait of -; (c) phase portrait of -; (d) phase portrait of -

Fig.7 Time history of and phase portraits at , =5
(a) Time history of ; (b) phase portrait of -; (c) phase portrait of -; (d) phase portrait of -

Fig.8 Time history of and phase portraits at = 5, = 5
(a) Time history of ; (b) phase portrait of -; (c) phase portrait of -; (d) phase portrait of -

Fig.9 Time history of and phase portraits at = 40, = 5
(a) Time history of ; (b) phase portrait of -; (c) phase portrait of -; (d) phase portrait of -

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