Alavi, S.M.A. and Safaei, M.R. and Mahian, O. and Goodarzi, M. and Yarmand, H. and Dahari, M. and Wongwises, S. (2015) A hybrid finiteelement/finitedifference scheme for solving the 3D energy equation in transient nonisothermal fluid flow over a staggered tube bank. Numerical Heat Transfer Part BFundamentals, 68 (2). pp. 169183. ISSN 10407790, DOI https://doi.org/10.1080/10407790.2015.1012440.

PDF (A Hybrid FiniteElement/FiniteDifference Scheme for Solving the 3D Energy Equation in Transient Nonisothermal Fluid Flow over a Staggered Tube Bank)
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Abstract
This article presents a hybrid finiteelement/finitedifference approach. The approach solves the 3D unsteady energy equation in nonisothermal fluid flow over a staggered tube bank with five tubes in the flow direction. The investigation used Reynolds numbers of 100 and 300, Prandtl number of 0.7, and pitchtodiameter ratio of 1.5. An equilateral triangle (ET) tube pattern is considered for the staggered tube bank. The proposed hybrid method employs a 2D TaylorGalerkin finiteelement method, and the energy equation perpendicular to the tube axis is discretized. On the other hand, the finitedifference technique discretizes the derivatives toward the tube axis. Weighting the 3D, transient, convectiondiffusion equation for a cube verifies the numerical results. The L2 norm of the error between numerical and exact solutions is also presented for three different hybrid meshes. A grid independence study for the energy equation preceded the final mesh. The outcome is found to be in acceptable concurrence with those from the previous studies. After the temperature field is attained, the local Nusselt number is computed for the tubes in the bundle at different times. The isotherms are also obtained at different times until a steadystate solution is reached. The numerical results converge to the exact results through refining the mesh. The implemented hybrid scheme requires less computation time compared with the conventional 3D finiteelement method, requiring less program coding.
Item Type:  Article 

Funders:  High Impact Research Grant UM.C/HIR/MOHE/ENG/23 , UMRG Grant RP012C13AET , Thailand Research Fund IRG5780005 
Additional Information:  ISI Document Delivery No.: CJ1QT Times Cited: 0 Cited Reference Count: 36 Cited References: Afgan I., 2007, THESIS U MANCHESTER Alavi M. A., 2009, COMPUTATIONAL METHOD, VXIV ALAVI SMA, 2010, ASME 2010 10 BIENN C, P171, DOI 10.1115/ESDA201025015 Arefmanesh A, 2008, INT J NUMER METHOD H, V18, P50, DOI 10.1108/09615530810839741 Bao Y, 2010, COMPUT FLUIDS, V39, P882, DOI 10.1016/j.compfluid.2010.01.002 Chaabane R, 2011, J QUANT SPECTROSC RA, V112, P2013, DOI 10.1016/j.jqsrt.2011.04.002 Dai WZ, 2000, NUMER HEAT TR AAPPL, V38, P573 Fan JF, 2012, NUMER HEAT TR AAPPL, V62, P271, DOI 10.1080/10407782.2012.666931 Floan BW, 2012, NUMER HEAT TR AAPPL, V62, P81, DOI 10.1080/10407790.2012.685125 Gholami AA, 2014, INT COMMUN HEAT MASS, V54, P132, DOI 10.1016/j.icheatmasstransfer.2014.02.016 Goodarzi M, 2014, ABSTR APPL ANAL, DOI 10.1155/2014/762184 He YN, 2008, APPL NUMER MATH, V58, P1503, DOI 10.1016/j.apnum.2007.08.005 Hughes T.J., 2012, FINITE ELEMENT METHO Iacovides H., 2013, INT S TURB SHEAR FLO Iacovides H, 2014, INT J HEAT FLUID FL, V49, P69, DOI 10.1016/j.ijheatfluidflow.2014.05.011 Iacovides H., 2014, INT ASS COMPUTATIONA LAUNDER BE, 1978, J HEAT TRANST ASME, V100, P565 Le Feuvre R. F., 1973, THESIS IMPERIAL COLL Lee DH, 2012, INT COMMUN HEAT MASS, V39, P161, DOI 10.1016/j.icheatmasstransfer.2011.11.009 Lo DC, 2012, INT J HEAT MASS TRAN, V55, P6916, DOI 10.1016/j.ijheatmasstransfer.2012.07.005 Lotfi B, 2014, ENERGY, V73, P233, DOI 10.1016/j.energy.2014.06.016 Nobari MRH, 2013, INT J NONLIN MECH, V57, P90, DOI 10.1016/j.ijnonlinmec.2013.06.014 Ortiz FJG, 2011, APPL THERM ENG, V31, P3463, DOI 10.1016/j.applthermaleng.2011.07.001 Ozgoren M, 2013, INT J MULTIPHAS FLOW, V53, P54, DOI 10.1016/j.ijmultiphaseflow.2013.02.001 Pierre C, 2014, J COMPUT PHYS, V268, P84, DOI 10.1016/j.jcp.2014.02.037 Pongsoi P, 2014, INT J HEAT MASS TRAN, V79, P417, DOI 10.1016/j.ijheatmasstransfer.2014.07.072 Safaei MR, 2014, NUMER HEAT TR AAPPL, V66, P1321, DOI 10.1080/10407782.2014.916101 Sigrist JF, 2008, COMPUT METHOD APPL M, V197, P1080, DOI 10.1016/j.cma.2007.10.010 Tahseen TA, 2014, INT COMMUN HEAT MASS, V50, P85, DOI 10.1016/j.icheatmasstransfer.2013.11.007 TEZDUYAR TE, 1991, J ENG MECHASCE, V117, P854, DOI 10.1061/(ASCE)07339399(1991)117:4(854) Wang BL, 2012, FINITE ELEM ANAL DES, V50, P201, DOI 10.1016/j.finel.2011.09.010 Wang YQ, 2000, NUMER HEAT TR AAPPL, V38, P819 Wu XM, 2014, NUMER HEAT TR AAPPL, V65, P357, DOI 10.1080/10407782.2013.831673 Yataghene M, 2013, COMPUT FLUIDS, V71, P380, DOI 10.1016/j.compfluid.2012.10.026 Yusuf R, 2011, CHEM ENG SCI, V66, P1550, DOI 10.1016/j.ces.2010.12.015 Zhu DS, 2013, NUMER HEAT TR AAPPL, V63, P396, DOI 10.1080/10407782.2013.733270 Alavi, Seyyed Mahmood Aboulhasan Safaei, Mohammad Reza Mahian, Omid Goodarzi, Marjan Yarmand, Hooman Dahari, Mahidzal Wongwises, Somchai Engineering, Faculty /I79352015 Engineering, Faculty /0000000248487052 High Impact Research Grant UM.C/HIR/MOHE/ENG/23; UMRG Grant RP012C13AET; Faculty of Engineering, University of Malaya, Malaysia; "Research Chair Grant" National Science and Technology Development Agency (NSTDA); Thailand Research Fund IRG5780005; National Research University Project The authors gratefully acknowledge High Impact Research Grant UM.C/HIR/MOHE/ENG/23, UMRG Grant RP012C13AET, and the Faculty of Engineering, University of Malaya, Malaysia, for support in conducting this research work. The seventh author would like to thank the "Research Chair Grant" National Science and Technology Development Agency (NSTDA), the Thailand Research Fund (IRG5780005), and the National Research University Project for their support. 0 TAYLOR & FRANCIS INC PHILADELPHIA NUMER HEAT TR BFUND 
Uncontrolled Keywords:  Heattransfer characteristics, transfer enhancement, vortex generators, pressuredrop, exchangers, conduction, surface, bundle, model, air, 
Subjects:  T Technology > T Technology (General) T Technology > TJ Mechanical engineering and machinery 
Divisions:  Faculty of Engineering 
Depositing User:  Mr Jenal S 
Date Deposited:  04 Apr 2016 01:14 
Last Modified:  04 Apr 2016 01:14 
URI:  http://eprints.um.edu.my/id/eprint/15730 
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