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Research Papers: Porous Media

Natural Convection in a Wavy Porous Cavity With Sinusoidal Temperature Distributions on Both Side Walls Filled With a Nanofluid: Buongiorno's Mathematical Model

[+] Author and Article Information
M. A. Sheremet

Department of Theoretical Mechanics,
Faculty of Mechanics and Mathematics,
Tomsk State University,
Tomsk 634050, Russia
Institute of Power Engineering,
Tomsk Polytechnic University,
Tomsk 634050, Russia
e-mail: michael-sher@yandex.ru

I. Pop

Department of Applied Mathematics,
Babeş-Bolyai University,
CP 253, Cluj-Napoca 400082, Romania
e-mail: popm.ioan@yahoo.co.uk

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 3, 2014; final manuscript received January 28, 2015; published online March 24, 2015. Assoc. Editor: Terry Simon.

J. Heat Transfer 137(7), 072601 (Jul 01, 2015) (8 pages) Paper No: HT-14-1436; doi: 10.1115/1.4029816 History: Received July 03, 2014; Revised January 28, 2015; Online March 24, 2015

A numerical study of the natural convection flow in a porous cavity with wavy bottom and top walls having sinusoidal temperature distributions on vertical walls filled with a nanofluid is numerically investigated. The mathematical model has been formulated in dimensionless stream function and temperature taking into account the Darcy–Boussinesq approximation and the Buongiorno's nanofluid model. The boundary-value problem has been solved numerically on the basis of a second-order accurate finite difference method. Efforts have been focused on the effects of five types of influential factors such as the Rayleigh (Ra = 10–300) and Lewis (Le = 1–1000) numbers, the buoyancy-ratio parameter (Nr = 0.1–0.4), the Brownian motion parameter (Nb = 0.1–0.4), and the thermophoresis parameter (Nt = 0.1–0.4) on the fluid flow and heat transfer characteristics. It has been found that the average Nusselt and Sherwood numbers are increasing functions of the Rayleigh number, buoyancy- ratio parameter, and thermophoresis parameter, and decreasing functions of the Lewis number and Brownian motion parameter.

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Figures

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Fig. 1

Physical model and coordinate system

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Fig. 2

Streamlines ψ, isotherms θ, and isoconcentrations ϕ for Le = 100, Nr = Nb = Nt = 0.1: Ra = 10 − a, Ra = 100 − b, Ra = 300 − c

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Fig. 3

Variation of the average Nusselt number at left vertical wall with the Rayleigh number and dimensionless time for Le = 100, Nr = Nb = Nt = 0.1

Grahic Jump Location
Fig. 4

Streamlines ψ, isotherms θ, and isoconcentrations ϕ for Ra = 100, Nr = Nb = Nt = 0.1: Le = 1 − a, Le = 1000 − b

Grahic Jump Location
Fig. 5

Variation of the average Nusselt number at left vertical wall with the Lewis number and dimensionless time for Ra = 100, Nr = Nb = Nt = 0.1

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