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Research Papers: Micro/Nanoscale Heat Transfer

# Combined Effects of Thermophoresis, Brownian Motion, and Nanofluid Variable Properties on CuO-Water Nanofluid Natural Convection in a Partially Heated Square Cavity

[+] Author and Article Information
M. S. Astanina

Laboratory on Convective Heat
and Mass Transfer,
Tomsk State University,
Tomsk 634050, Russia

Department of Mechanical Engineering,
Khalifa University,
Abu Dhabi 127788, United Arab Emirates

M. A. Sheremet

Laboratory on Convective Heat
and Mass Transfer,
Tomsk State University,
Tomsk 634050, Russia
e-mail: Michael-sher@yandex.ru

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 20, 2017; final manuscript received January 14, 2018; published online April 11, 2018. Assoc. Editor: Antonio Barletta.

J. Heat Transfer 140(8), 082401 (Apr 11, 2018) (12 pages) Paper No: HT-17-1422; doi: 10.1115/1.4039217 History: Received July 20, 2017; Revised January 14, 2018

## Abstract

Numerical investigation of natural convective heat transfer and fluid flow in a differentially heated square cavity filled with a CuO-water nanofluid having variable properties is performed. Governing partial differential equations formulated in nondimensional stream function, vorticity, temperature, and nanoparticles volume fraction are solved by the second-order accurate finite difference method and taking into account the Brownian diffusion and thermophoresis. The effects of Rayleigh number (Ra = 104–106), initial nanoparticles volume fraction (C0 = 0–0.09), location of the heater (Δ = 0.0–0.9), and dimensionless time (τ = 0–300) on flow patterns, isotherms, and concentration fields as well as the local and average Nusselt numbers at the heater surface are studied. The isoconcentrations reveal that for most of the cavity domain the nanoparticle concentration is around the initial average concentration of nanoparticles except for a very limited variation in a region close to the cavity walls that experiences minor deviation from the initial concentration. It was found that the flow strength within the cavity (i.e., $ψmaxRa⋅Pr$) is inversely proportional to the heater location Δ and is directly proportional to the Rayleigh number. Also, it was found that the best location of the heater, from a heat transfer perspective, is placing it entirely at the left wall of the cavity where a maximum average Nusselt number is registered. This study revealed that for all heater locations there is always an adverse impact of nanoparticles on the heat transfer and the worst case is registered for the Δ = 0 and the least deterioration is noticed for Δ = 0.9.

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## Figures

Fig. 1

Physical model and coordinate system

Fig. 2

Comparison of streamlines ψ and isotherms θ at Ra = 3.5 × 104: numerical results of Hyun and Lee [41]—(a), present study—(b)

Fig. 3

Comparison of streamlines ψ and isotherms θ at Ra = 3.5 × 105: numerical results of Hyun and Lee [41]—(a), present study—(b)

Fig. 4

Profiles of vertical velocity (a) and temperature (b) along middle cross section y = 0.5 versus the mesh parameters

Fig. 5

Streamlines ψ, isotherms θ and isoconcentrations ϕ for C0 = 0.03, Δ = 0.5, τ = 300: Ra = 104—(a), Ra = 105—(b), and Ra = 106—(c)

Fig. 6

Variations of the average total Nusselt number at heater (a) and maximum absolute value of stream function (b) versus the Rayleigh number and dimensionless time for C0 = 0.03, Δ = 0.5

Fig. 7

Streamlines ψ, isotherms θ and isoconcentrations ϕ for Ra = 105, C0 = 0.03, τ = 300: Δ = 0.0—(a), Δ = 0.25—(b), Δ = 0.75—(c), and Δ = 0.9—(d)

Fig. 8

Variations of the maximum absolute value of stream function (a) and average total Nusselt number at heater (b) versus the heater location and Rayleigh number for C0 = 0.03, τ = 300

Fig. 9

Profiles of local Nusselt numbers along the heater versus the heater location for C0 = 0.03, τ = 300: Ra = 104—(a), Ra = 105—(b), and Ra = 106—(c)

Fig. 10

Streamlines ψ, isotherms θ and isoconcentrations ϕ for Ra = 105, Δ = 0.5, τ = 300: C0 = 0.0—(a), C0 = 0.05—(b), and C0 = 0.09—(c)

Fig. 11

Variations of the maximum absolute value of stream function versus initial nanoparticles volume fraction and heater location and for Ra = 105, τ = 300

Fig. 12

Variations of the average total Nusselt number at heater (a) and normalized average total Nusselt number at heater (b) versus initial nanoparticles volume fraction and heater location for Ra = 105, τ = 300

Fig. 13

Variations of the average total Nusselt number at heater (a) and normalized average total Nusselt number at heater (b) versus initial nanoparticles volume fraction and Rayleigh number for Δ = 0.5, τ = 300

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