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Research Papers

# Mixed Convection in an Inclined Nanofluid Filled-Cavity Saturated With a Partially Layered Porous Medium

[+] Author and Article Information
Abdelraheem M. Aly

Department of Mathematics,
Faculty of Science,
King Khalid University,
P. O. Box 3236,
Abha, Saudi Arabia;
Department of Mathematics,
Faculty of Science,
South Valley University,
P. O. Box 83523,
Qena, Egypt
e-mails: ababdallah@kku.edu.sa;
abdelreheam.abdallah@sci.svu.edu.eg

Z. A. S. Raizah

Department of Mathematics,
Faculty of Science,
King Khalid University,
P. O. Box 3236,
Abha, Saudi Arabia

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received September 1, 2018; final manuscript received December 10, 2018; published online March 25, 2019. Assoc. Editor: Aaron P. Wemhoff.

J. Thermal Sci. Eng. Appl 11(4), 041002 (Mar 25, 2019) (9 pages) Paper No: TSEA-18-1430; doi: 10.1115/1.4042352 History: Received September 01, 2018; Revised December 10, 2018

## Abstract

The contribution of the current study is to investigate the mixed convection in an inclined nanofluid filled cavity saturated with a partially layered non-Darcy porous medium. Moreover, due to the advantage of the particle-based methods, we presented the improved version of an incompressible smoothed particle hydrodynamics (ISPH) method. The current ISPH method was improved in boundary conditions treatment using renormalization kernel function. In the current investigation, we assumed that the inclined cavity is filled with a Cu-water nanofluid. The upper half of the cavity is saturated with a non-Darcy porous medium. Here, one domain approach is used for coupling the nanofluid and the porous medium layer. The cooled top wall of the cavity is carrying a tangential unit velocity and the bottom wall is heated. The other two wall sides are adiabatic at zero velocity. Here, we investigated the effects of the Richardson parameter $Ri0.0001–100$, Darcy parameter Da $10−5–10−2$, an inclination angle $α0–90deg$ and a various solid volume fraction $ϕ0–0.05$ on the heat transfer of a Cu-water nanofluid. The obtained results showed that the average Nusselt number decreases as the Richardson number increases. An addition of 1–5% Cu nanoparticles slightly increased the overall heat transfer rate.

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## Figures

Fig. 1

Initial schematic diagram for the inclined nanofluid-filled cavity partially filled with the porous medium

Fig. 2

Flowchart of the current ISPH method

Fig. 3

Comparison of the horizontal and vertical velocity profiles at X=0.5 for the present ISPH method and benchmark results according to Ghia et al. [42] at Re=100, Re=400, and Re=1000

Fig. 4

Streamlines and isothermal contours under the effects of the Richardson parameter at the inclination angle α=0deg,Darcy parameter Da=10−4 and solid volume fraction ϕ=0.01

Fig. 5

Streamlines and isothermal contours under the effects of the Darcy parameter Da=10−2, 10−4 and 10−5 at the Richardson parameter Ri=1.0, the inclination angle α=0deg, and solid volume fraction ϕ=0.01

Fig. 6

Streamlines and isothermal contours under the effects of the solid volume fraction ϕ=0, 0.01, and 0.05 at the Richardson parameter Ri=1.0, the inclination angle α=45deg, and Darcy parameter Da=10−4

Fig. 7

Streamlines and isothermal contours under the effects of the inclination angle. α = 0 deg, 60 deg and 90 deg at the Richardson parameter Ri = 1.0, Darcy parameter Da = 10−4 and solid volume fraction ϕ = 0.01.

Fig. 8

Temperature profiles at the midsection of the inclined cavity (X = 0.5) under the effects of the Richardson parameter Ri=0.0001, 1, and 100 at α=0deg and Da=10−4

Fig. 9

Average Nusselt number along the Richardson parameter under the effects of the inclination angle α=0deg, 30deg, and 60deg at Darcy parameter Da=10−4

Fig. 10

Average Nusselt number along the Richardson parameter under the effects of the Darcy parameter at two different values of the inclination angle α=30deg and 60deg

Fig. 11

Average Nusselt number under the effects of the solid volume fraction ϕ at inclination angle α=45deg, Richardson parameter Ri=1 and Darcy parameter Da=10−4

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