RBF simulation of natural convection in a nanofluid-filled cavity

Bengisen Pekmen Geridonmez; Bengisen Pekmen Geridonmez

doi:10.3934/Math.2016.3.195

AIMS Mathematics

2016, Volume 1, Issue 3: 195-207. doi: 10.3934/Math.2016.3.195

Previous Article Next Article

Research article

RBF simulation of natural convection in a nanofluid-filled cavity

Bengisen Pekmen Geridonmez ^,

Basic Sciences Unit, TED University, Ankara, Turkey

Received: 31 July 2016 Accepted: 26 August 2016 Published: 30 August 2016

In this study, natural convection in a cavity filled with a nanofluid is solved numerically utilizing a radial basis function pseudo spectral (RBF-PS) approach in the space domain and a differential quadrature method (DQM) in the time domain. The governing dimensionless equations are solved in terms of stream function, temperature and vorticity. In the cavity, thermally insulated top and bottom walls are maintained while the left and right walls are at constant temperatures. Numerical solutions present the average Nusselt number variation as well as streamlines, isotherms and vorticity contours. The non-dimensional problem parameters, Rayleigh number $Ra$, solid volume fraction $\chi$ and aspect ratio $AR$ are varied as $10^3\leq Ra \leq 10^6,\, 0 \leq \chi \leq 0.2$ and $AR=0.25,\, 0.5,\,1,\, 2,\, 4$, respectively. It is found that the fluid velocity and the heat transfer are enhanced in presence of nanoparticles, and the convective heat transfer is reduced in a rectangular cavity.
- radial basis functions,
- multiquadrics,
- differential quadrature method,
- nanofluid,
- naturalconvection
Citation: Bengisen Pekmen Geridonmez. RBF simulation of natural convection in a nanofluid-filled cavity[J]. AIMS Mathematics, 2016, 1(3): 195-207. doi: 10.3934/Math.2016.3.195

Related Papers:

Abstract

In this study, natural convection in a cavity filled with a nanofluid is solved numerically utilizing a radial basis function pseudo spectral (RBF-PS) approach in the space domain and a differential quadrature method (DQM) in the time domain. The governing dimensionless equations are solved in terms of stream function, temperature and vorticity. In the cavity, thermally insulated top and bottom walls are maintained while the left and right walls are at constant temperatures. Numerical solutions present the average Nusselt number variation as well as streamlines, isotherms and vorticity contours. The non-dimensional problem parameters, Rayleigh number $Ra$, solid volume fraction $\chi$ and aspect ratio $AR$ are varied as $10^3\leq Ra \leq 10^6,\, 0 \leq \chi \leq 0.2$ and $AR=0.25,\, 0.5,\,1,\, 2,\, 4$, respectively. It is found that the fluid velocity and the heat transfer are enhanced in presence of nanoparticles, and the convective heat transfer is reduced in a rectangular cavity.

References

[1]	H. R Ashorynejad, A. A. Mohamad, and M. Sheikholeslami,Magnetic field e ects on naturalconvection flow of a nanofluid in a horizontal cylindrical annulus using Lattice Boltzmann method ,Int. J. Therm. Sci., 64 (2013), 240-250.
[2]	H. C. Brinkman, The viscosity of concentrated suspensions and solutions, J. Chem. Phys., 3 (1952),571-581.
[3]	G. de vahl Davis, Natural convection of air in a square cavity : A bench mark numerical solution,Int. J. Numer. Meth. Fl., 3 (1983), 249-264.
[4]	G. Fasshauer, Meshfree Approximation Methods with Matlab, World Scientific Publications, Sin-gapore, 2007.
[5]	E. Fattahi, M. Farhadi, K. Sedighi, and H. Nemati, Lattice Boltzmann simulation of natural con-vection heat transfer in nanofluids, Int. J. Therm. Sci., 52 (2012), 137-144.
[6]	B. Ghasemi, S. M. Aminossadati, and A. Raisi, Magnetic field e ect on natural convection in ananofluid-filled square enclosure, Int. J. Therm. Sci., 50 (2011), 1748-1756.
[7]	S. Gumgum and M. Tezer-Sezgin, DRBEM solution of natural convection flow of nanofluids with a heat source, Eng. Ana. Bound., 34 (2010), 727-737.
[8]	M. Jahanshahi, S. E. Hosseinizadeh, M. Alipanah, A. Dehghani, and G. R. Vakilinejad, Numerical simulation of free convection based on experimental measured conductivity in a square cavity using Water/SiO2 nanofluid, Int. Comm. Heat Mass, 37 (2010), 687-694.
[9]	R. Y. Jou and S. C. Tzeng, Numerical research of nature convective heat transfer enchancement filled with nanofluids in rectangular enclosures, Int. J. Heat Mass Tran., 33 (2006), 727-736.
[10]	K. Khanafer, K. Vafai, and M. Lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, Int. J. Heat Mass Tran., 46 (2003), 3639-3653.
[11]	W. R. Madych and S. A. Nelson, Bounds on multivariate polynomials and exponential errorestimates for multiquadric interpolation, J. Approx. Theory, 70 (1992), 94-114.
[12]	A. H. Mahmoudi, I. Pop, M. Shahi, and F. Talebi, MHD natural convection and entropy generation in a trapezoidal enclosure using Cu-water nanofluid, Comput. Fluids, 72 (2013), 46-62.
[13]	J. C. Maxwell-Garnett, Colors in metal glasses and in metallic films, Phil. Trans R. Soc. A, 203(1904), 385-420.
[14]	C. A. Michelli, Interpolation of scattered data: Distance matrices and conditionally positivedefinite functions, Constr. Approx., 2 (1986), 11-22.
[15]	M. Muthtamilselvan, P. Kandaswamy, and J. Lee, Heat transfer enhancement of copper-waternanofluids in a lid-driven enclosure, Commun. Nonlinear Sci. Numer. Simulat.,15 (2010), 1501-1510.
[16]	J. Serna, F. J. S. Velasco, and A. S. Meca, Application of network simulation method to viscousflow: The nanofluid heated lid cavity under pulsating flow, Comput. Fluids, 91 (2014), 10-20.
[17]	M. Shahi, A. H. Mahmoudi, and A. H. Raouf, Entropy generation due to natural convection coolingof nanofluid, Int. Comm. Heat Mass, 38 (2011), 972-983.
[18]	C. Shu, Di erential quadrature and its application in engineering, Springer-Verlag, 2000.
[19]	R. K. Tiwari and M. K. Das, Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilising nanofluids, Int. J. Heat Mass Tran., 50 (2007), 2002-2018

Reader Comments

Your name:*

Email:*
© 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)