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Fully HOC Scheme for Mixed Convection Flow in a Lid-Driven Cavity Filled with a Nanofluid

Published online by Cambridge University Press:  03 June 2015

Dingfang Li ,
Xiaofeng Wang  and
Hui Feng
Dingfang Li*
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China
Xiaofeng Wang*
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, Henan, China
Hui Feng*
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China
*
Email: dfli@whu.edu.cn
*Corresponding author.Email: wangxiaofeng1166@163.com
Email: hfeng.math@whu.edu.cn
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Abstract

A fully higher-order compact (HOC) finite difference scheme on the 9-point two-dimensional (2D) stencil is formulated for solving the steady-state laminar mixed convection flow in a lid-driven inclined square enclosure filled with water-Al2O3 nanofluid. Two cases are considered depending on the direction of temperature gradient imposed (Case I, top and bottom; Case II, left and right). The developed equations are given in terms of the stream function-vorticity formulation and are non-dimensionalized and then solved numerically by a fourth-order accurate compact finite difference method. Unlike other compact solution procedure in literature for this physical configuration, the present method is fully compact and fully higher-order accurate. The fluid flow, heat transfer and heat transport characteristics were illustrated by streamlines, isotherms and averaged Nusselt number. Comparisons with previously published work are performed and found to be in excellent agreement. A parametric study is conducted and a set of graphical results is presented and discussed to elucidate that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by inclination of the enclosure at moderate and large Richardson numbers.

Keywords

35K5765N0676T20HOC difference schemepseudo-time derivativemixed convectionADI method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 1 , February 2013 , pp. 55 - 77
Copyright
Copyright © Global-Science Press 2013

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