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Research Papers: Micro/Nanoscale Heat Transfer

# Unsteady Finite Amplitude Convection of Water–Copper Nanoliquid in High-Porosity Enclosures

[+] Author and Article Information
P. G. Siddheshwar

Professor
Department of Mathematics,
Bangalore University,
Bangalore 560056, India
e-mail: mathdrpgs@gmail.com

K. M. Lakshmi

Department of Mathematics,
Bangalore University,
Bangalore 560056, India
e-mail: lakshmikmmaths@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 6, 2018; final manuscript received February 15, 2019; published online April 17, 2019. Assoc. Editor: Evelyn Wang.

J. Heat Transfer 141(6), 062405 (Apr 17, 2019) (11 pages) Paper No: HT-18-1206; doi: 10.1115/1.4043165 History: Received April 06, 2018; Revised February 15, 2019

## Abstract

Unicellular Rayleigh–Bénard convection of water–copper nanoliquid confined in a high-porosity enclosure is studied analytically. The modified-Buongiorno–Brinkman two-phase model is used for nanoliquid description to include the effects of Brownian motion, thermophoresis, porous medium friction, and thermophysical properties. Free–free and rigid–rigid boundaries are considered for investigation of onset of convection and heat transport. Boundary effects on onset of convection are shown to be classical in nature. Stability boundaries in the $R1*$–R2 plane are drawn to specify the regions in which various instabilities appear. Specifically, subcritical instabilities' region of appearance is highlighted. Square, shallow, and tall porous enclosures are considered for study, and it is found that the maximum heat transport occurs in the case of a tall enclosure and minimum in the case of a shallow enclosure. The analysis also reveals that the addition of a dilute concentration of nanoparticles in a liquid-saturated porous enclosure advances onset and thereby enhances the heat transport irrespective of the type of boundaries. The presence of porous medium serves the purpose of heat storage in the system because of its low thermal conductivity.

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## Figures

Fig. 1

Schematic representation of nanoliquid-saturated high-porosity enclosures: (a) h < b (Shallow), (b) h = b (Square), and (c) h > b (Tall)

Fig. 2

Stability diagrams for water–copper saturated porous medium in shallow and tall enclosures

Fig. 3

Stability diagrams for water–copper nanoliquid and water–copper nanoliquid-saturated porous medium

Fig. 4

Plot of Nusselt number, Nu, versus τ* for different values of A, α, Λ, and σ2: (a) α = 0.06, Λ = 1.2, σ2 = 10, (b) α = 0.06, Λ = 1.2, σ2 = 10, (c) A = 1, Λ = 1.2, σ2 = 10, (d) A = 1, Λ = 1.2, σ2 = 10, (e) A = 1, α = 0.06, σ2 = 10, (f) A = 1, α = 0.06, σ2 = 10, (g) A = 1, α = 0.06, Λ = 1.2, and (h) A = 1, α = 0.06, Λ = 1.2

Fig. 5

Plot of linear and nonlinear amplitudes, A0 versus τ* for different values of σ2 and A = 1, α = 0.06, Λ = 1.2

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