Sains Malaysiana 46(5)(2017): 803–815

http://dx.doi.org/10.17576/jsm-2017-4605-15

 

Darcian Natural Convection in an Inclined Trapezoidal Cavity Partly Filled with a Porous Layer and Partly with a Nanofluid Layer

(Perolakan Semula Jadi Darcian dalam Rongga Trapezium Condong yang Sebahagiannya Dipenuhi

dengan Lapisan Berliang dan Sebahagiannya dengan Lapisan Nanobendalir)

 

A.I. ALSABERY¹, A.J. CHAMKHA^2,3, H. SALEH¹, I. HASHIM¹* & B. CHANANE⁴

 

¹School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

 

²Department of Mechanical Engineering, Prince Mohammad Bin Fahd University

P.O. Box 1664, Al Khobar 31952, Saudi Arabia

 

³Prince Sultan Endowment for Energy and Environment, Prince Mohammad Bin Fahd University

Al-Khobar 31952, Saudi Arabia

 

⁴Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran-31261, Saudi Arabia

 

Received: 22 February 2016/Accepted: 1 November 2016

 

ABSTRACT

The problem of Darcian natural convection in a trapezoidal cavity partly filled with porous layer and partly with nanofluid layer is studied numerically using finite difference method. The left slopping wall is maintained at a constant hot temperature and the right slopping wall is maintained at a constant cold temperature, while the horizontal walls are adiabatic. Water-based nanofluids with Ag or Cu or TiO2 nanoparticles are chosen for the investigation. The governing parameters of this study are the Rayleigh number (104 ≤ Ra ≤ 107), Darcy number (10–5 ≤ Da ≤ 10–3), nanoparticle volume fraction (0 ≤ φ ≤ 0.2), porous layer thickness (0.3 ≤ S ≤ 0,7), the side wall inclination angle (0° ≤ ϕ ≤ 21.8°) and the inclination angle of the cavity (0° ≤ ϖ ≤ 90°). Explanation for the influence of various above-mentioned parameters on streamlines, isotherms and overall heat transfer is provided on the basis of thermal conductivities of nanoparticles, water and porous medium. It is shown that convection increases remarkably by the addition of silver-water nanofluid and the heat transfer rate is affected by the inclination angle of the cavity variation. The results have possible applications in heat-removal and heat-storage fluid-saturated porous systems.

 

Keywords: Darcy model; nanofluid; natural convection; partially filled; porous media

 

 

ABSTRAK

Masalah perolakan semula jadi Darcian dalam rongga trapezium yang sebahagiannya dipenuhi dengan lapisan berliang dan sebahagiannya dengan lapisan nanobendalir dikaji secara berangka menggunakan kaedah perbezaan terhingga. Dinding cerun sebelah kiri dikekalkan pada suhu panas tetap yang berterusan dan dinding cerun kanan dikekalkan pada suhu sejuk berterusan, manakala dinding mendatar secara adiabatik. Nanobendalir berasaskan air dengan zarah nano Ag atau Cu atau TiO telah dipilih untuk kajian. Parameter penentu kajian ini adalah nombor Rayleigh (104 ≤ Ra ≤ 107), nombor Darcy (10–5 ≤ Da ≤ 10–3), pecahan isi padu zarah nano (0 ≤ φ ≤ 0.2), ketebalan lapisan berliang (0.3 ≤ S ≤ 0,7), sebelah dinding sudut condong (0° ≤ ϕ ≤ 21.8°) dan sudut condong berongga (0° ≤ ϖ ≤ 90°). Penjelasan untuk pengaruh pelbagai parameter yang tersebut ke atas garis strim, isoterma dan pemindahan haba keseluruhan juga disediakan berdasarkan terma kekonduksian zarah nano, air dan medium berliang. Ia menunjukkan bahawa perolakan meningkat secara luar biasa dengan penambahan bendalir nano air-perak dan kadar pemindahan haba dipengaruhi oleh sudut condong variasi berongga. Keputusan ini mempunyai potensi pengaplikasian dalam sistem pemindahan haba dan penyimpanan haba cecair-tepu berliang.

 

Kata kunci: Nanobendalir; media berliang; model Darcy; perolakan semula jadi; sebahagiannya diisi

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*Corresponding author; email: ishak_h@ukm.edu.my