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# Effect of Local Thermal Nonequilibrium on the Stability of Natural Convection in an Oldroyd-B Fluid Saturated Vertical Porous Layer

[+] Author and Article Information
B. M. Shankar

Department of Mathematics,
PES University,
Bangalore 560 085, India
e-mail: bmshankar@pes.edu

I. S. Shivakumara

Department of Mathematics,
Bangalore University,
Bangalore 560 056, India

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 1, 2016; final manuscript received November 4, 2016; published online January 18, 2017. Assoc. Editor: Dr. Antonio Barletta.

J. Heat Transfer 139(4), 044503 (Jan 18, 2017) (10 pages) Paper No: HT-16-1345; doi: 10.1115/1.4035199 History: Received June 01, 2016; Revised November 04, 2016

## Abstract

The effect of local thermal nonequilibrium (LTNE) on the stability of natural convection in a vertical porous slab saturated by an Oldroyd-B fluid is investigated. The vertical walls of the slab are impermeable and maintained at constant but different temperatures. A two-field model that represents the fluid and solid phase temperature fields separately is used for heat transport equation. The resulting stability eigenvalue problem is solved numerically using Chebyshev collocation method as the energy stability analysis becomes ineffective in deciding the stability of the system. Despite the basic state remains the same for Newtonian and viscoelastic fluids, it is observed that the base flow is unstable for viscoelastic fluids and this result is qualitatively different from Newtonian fluids. The results for Maxwell fluid are delineated as a particular case from the present study. It is found that the viscoelasticity has both stabilizing and destabilizing influence on the flow. Increase in the value of interphase heat transfer coefficient $Ht$, strain retardation parameter $Λ2$ and diffusivity ratio $α$ portray stabilizing influence on the system while increasing stress relaxation parameter $Λ1$ and porosity-modified conductivity ratio $γ$ exhibit an opposite trend.

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## Figures

Fig. 1

Physical configuration

Fig. 2

Neutral stability curves

Fig. 3

Variation of (a) RD c, (b) ac, and (c) cc with Ht for various values of  Λ1 when Λ2=0.1,γ=0.5, and α=1

Fig. 4

Variation of (a) RD c, (b) ac, and (c) cc with Ht for various values of Λ2 when Λ1=0.5,γ=0.5, and α=1

Fig. 5

Variation of (a) RD c, (b) ac, and (c) cc with Ht for various values of  γ when Λ1=0.3,Λ2=0.1, and α=1

Fig. 6

Variation of (a) RD c, (b) ac, and (c) cc with Λ1 for various values of Ht and Λ2 when γ=0.5, α=1

Fig. 7

Variation of (a) RD c, (b) ac, and (c) cc with Λ1 for various values of α and Λ2 when Ht=20, γ=0.5

Fig. 8

Variation of (a) RD c, (b) ac, and (c) cc with Λ1 for various values of γ and Λ2 when Ht=20, α=1

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