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Natural and Mixed Convection

# Fully Developed Mixed Convection in a Vertical Channel Filled by a Nanofluid

[+] Author and Article Information
T. Grosan

Department of Applied Mathematics, Babes-Bolyai University, CP 253, 400082 Cluj-Napoca, Romaniatgrosan@math.ubbcluj.ro

I. Pop

Department of Applied Mathematics, Babes-Bolyai University, CP 253, 400082 Cluj-Napoca, Romaniapopm.ioan@yahoo.co.uk

J. Heat Transfer 134(8), 082501 (May 29, 2012) (5 pages) doi:10.1115/1.4006159 History: Received July 22, 2011; Revised January 06, 2012; Published May 29, 2012; Online May 29, 2012

## Abstract

The steady fully developed mixed convection flow between two vertical parallel plates with asymmetrical thermal and nanoparticle concentration conditions at the walls filled by a nanofluid is studied. The nanofluid model used in this paper takes into account the Brownian diffusion and the thermophoresis effects, and the analysis is based on analytical solutions. Thus, analytical expressions for the fully developed velocity, temperature, and nanoparticle concentration profiles as well as for the Nusselt and Sherwood numbers at the left wall of the channel are given. A numerical solution has been also obtained and compared with the analytical solution, the agreement being very good.

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## Figures

Figure 1

Physical model and coordinate system

Figure 2

Variation of dimensionless velocity when Nr=0, 10,100, 500, 1000 and Nt=Nb=0.5

Figure 3

Variation of dimensionless velocity when Nb=0.025, 1,2.5, 5, Nr=100, and Nt=0.5

Figure 4

Variation of dimensionless velocity when Nt=0, 1,2.5, 5, Nr=100, and Nb=0.5

Figure 5

Variation of dimensionless temperature (full line) and dimensionless concentration (dot line) when Nb=0.025, 0.25,0.5, 0.75, 1 and Nt=0.5

Figure 6

Variation of dimensionless temperature (full line) and dimensionless concentration (dot line) when Nt=0, 0.25, 0.5,0.75, 1 and Nb=0.5

Figure 7

Variation of reduced Nusselt number -θ′(0) (full line) and reduced Sherwood number -φ′(0) (dot line) with respect to Nb when Nt=0.1,  0.3,  0.5

Figure 8

Variation of reduced Nusselt number -θ′(0) (full line) and reduced Sherwood number -φ′(0) (dot line) with respect to Nt when Nb=0.1,  0.3,  0.5

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