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Research Papers: Natural and Mixed Convection

Numerical Solutions of Natural Convection Flow of a Dusty Nanofluid About a Vertical Wavy Truncated Cone

[+] Author and Article Information
Sadia Siddiqa

Head, Department of Mathematics,
COMSATS Institute of Information Technology,
Kamra Road,
Attock 43600, Pakistan
e-mail: saadiasiddiqa@gmail.com

Naheed Begum

Institute of Applied Mathematics (LSIII),
TU Dortmund,
Vogelpothsweg 87,
Dortmund D-44221, Germany

M. A. Hossain

UGC Professor
Department of Mathematics,
University of Dhaka,
Dhaka 1000, Bangladesh

Rama Subba Reddy Gorla

Department of Mechanical & Civil Engineering,
Purdue University Northwest,
Westville, IN 46391
e-mail: rgorla@pnw.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 13, 2016; final manuscript received August 20, 2016; published online November 8, 2016. Assoc. Editor: Dr. Antonio Barletta.

J. Heat Transfer 139(2), 022503 (Nov 08, 2016) (11 pages) Paper No: HT-16-1378; doi: 10.1115/1.4034815 History: Received June 13, 2016; Revised August 20, 2016

This paper reports the numerical results for the natural convection flow of a two-phase dusty nanofluid along a vertical wavy frustum of a cone. The general governing equations are transformed into parabolic partial differential equations, which are then solved numerically with the help of implicit finite difference method. Comprehensive flow formations of carrier and dusty phases are given with the aim to predict the behavior of heat and mass transport across the heated wavy frustum of a cone. The effectiveness of utilizing the nanofluids to control skin friction and heat and mass transport is analyzed. The results clearly show that the shape of the waviness changes when nanofluid is considered. It is shown that the modified diffusivity ratio parameter, NA, extensively promotes rate of mass transfer near the vicinity of the cone, whereas heat transfer rate reduces.

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Figures

Grahic Jump Location
Fig. 2

Rate of heat transfer for a=0.0,0.25,0.5, while Dρ=0.0, Pr=6.7, αd=0.0, Nr = 0.0, NA=NB=0.0, ω=10 deg, and X0=1.0

Grahic Jump Location
Fig. 3

(a) τw, (b) Qw, and (c) Mw for a=(0.0,0.1,0.3), while ω=π/7, Pr=7.0, γ=0.1, αd=0.01, Dρ=10.0, Ec = 1.0, NA=1.0, NB=1.0, Ln = 10.0, Nr = 0.05, and X0=1.0

Grahic Jump Location
Fig. 4

(a) τw, (b) Qw, and (c) Mw for ω=(0.0,π/7,π/6), while a = 0.2, Pr=7.0, γ=0.1, αd=0.01, Dρ=10.0, Ec = 1.0, NA=1.0, NB=1.0, Ln = 10.0, Nr = 0.05, and X0=1.0

Grahic Jump Location
Fig. 5

(a) τw, (b) Qw, and (c) Mw for Dρ=0.0,10.0, while ω=π/7, a = 0.3, Pr=7.0, γ=0.1, αd=0.01, Ec = 2.0, NA=1.0, NB=1.0, Ln = 10.0, Nr = 0.05, and X0=1.0

Grahic Jump Location
Fig. 6

(a) τw, (b) Qw, and (c) Mw for NA=(0.0,5.0,10.0), while ω=π/7, a = 0.2, Pr=7.0, γ=0.1, αd=0.01, Dρ=10.0, Ec = 1.0, NB=1.0, Ln = 10.0, Nr = 0.05, and X0=1.0

Grahic Jump Location
Fig. 7

(a) τw, (b) Qw, and (c) Mw for NB=(0.0,1.0,5.0), while ω=π/7, a = 0.3, Pr=7.0, γ=0.1, αd=0.01, Dρ=10.0, Ec = 1.0, NA=1.0, Ln = 10.0, Nr = 0.05, and X0=1.0

Grahic Jump Location
Fig. 8

(a) τw, (b) Qw, and (c) Mw for Nr=(0.0,0.1,0.2), while ω=π/7, a = 0.2, Pr=7.0, γ=0.1, αd=0.01, Dρ=10.0, Ec = 0.1, NA=1.0, NB=1.0, Ln = 10.0, Nr = 0.05, and X0=1.0

Grahic Jump Location
Fig. 9

(a) Streamlines and (b) isotherms for Dρ=(0.0,10.0), while ω=π/7, a = 0.3, Pr=7.0, γ=0.1, αd=0.01, Ec = 1.0, NA=1.0, NB=1.0, Ln = 10.0, Nr = 0.05, and X0=1.0

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