DTM-BF Method for the Flow and Heat Transfer of a Nanofluid Over a Stretching or Shrinking Sheet


(*) Corresponding author


Authors' affiliations


DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)

Abstract


In this paper we investigate the convective heat and mass transfer in nanofluid flow over a stretching sheet analytically. By introducing a suitable transformation, the governing equations are reduced to a couple nonlinear differential equations. The asymptotic analytical solutions are obtained by using differential transform method-basic functions(DTM-BF). Four types of nanofluids, namely Cu-water, Ag-water, Al2O3-water and TiO2-water are studied. The influence of the nanoparticle volume fraction (, the magnetic parameter M and different nanoparticles on the velocity, temperature and concentration are discussed and shown graphically. The analytical results have been shown to be a good agreement with the numerical results obtained by bvp4c and those in the literature
Copyright © 2013 Praise Worthy Prize - All rights reserved.

Keywords


Asymptotic Expansion; Chemical Reaction; Heat and Mass Transfer; Nanofluid Flow; Volume Fraction Influence

Full Text:

PDF


References


L.J. Crane, Flow past a stretching plate, Z. Angrew. Math. Phys. Volume 21, Issue 4, July 1970, pp.645- 647.

M.S. Abel, E. Sanjayanand, M.M. Nandeppanavar, Viscoelastic MHD flow and heat transfer over a stretching sheet with viscous and ohmic dissipations, Communications in Nonlinear Science and Numerical Simulation, Volume 13, Issue 9, November 2008, pp. 1808-1821.
http://dx.doi.org/10.1016/j.cnsns.2007.04.007

Kelson NA, Desseaux A, Effect of surface condition on flow of micropolar fluid driven by a porous stretching sheet. International Journal of Engineering Science,Volume 39,Number 16, November 2001, pp.1881-1897.
http://dx.doi.org/10.1016/s0020-7225(01)00026-x

Desseaux A, Kelson NA. Flow of a micropolar fluid bounded by a stretching sheet. Australian and New Zealand Industrial and Applied Mathematics Journal. Volume 42, August 2000, pp.536- 560.

Bhargava R, Kumar L, Takhar HS. Finite element solution of mixed convection micropolar fluid driven by a porous stretching sheet. International Journal of Engineering Science. Volume 41, Number 18, November 2003, pp.2161-2178.
http://dx.doi.org/10.1016/s0020-7225(03)00209-x

Bhargava R, Sharma S, Takhar HS, Beg OA, Bhargava P. Numerical solutions for micropolar transport phenomena over a nonlinear stretching sheet. Nonlinear Analysis:Modelling and Control.Vol. 12, No. 1, January 2007, pp.45-63.

Nadeem S, Hussain A, Vajravelu K. Effects of heat transfer on the stagnation flow of a third-order fluid over a shrinking sheet. Zeitschrift für Naturforschung, Volume. 65a , January 2010, pp. 969-994.
http://dx.doi.org/10.1515/zna-2010-1109

Prasad KV, Vajravelu K, Datti PS. Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties. International Journal of Non-Linear Mechanics. Volume 45, Issue 3, April 2010, pp.320-330.
http://dx.doi.org/10.1016/j.ijnonlinmec.2009.12.003

Choi, J.A. Eastman. Enhancing thermal conductivity of fluids with nanoparticles, Developments and Applications of Non-Newtonian Flows, FED-vol. 231/MDvol. 66, October 1995, pp.99-105.

H. Masuda, A. Ebata, K. Teramae, N. Hishinuma. Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles, Netsu Bussei Vol.4, No.4, 1993, pp. 227-233.
http://dx.doi.org/10.2963/jjtp.7.227

M.A.A. Hamada, I. Pop, A.I. Md Ismail. Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate, Nonlinear Analysis: Real World Applications, Volume 12, Issue 3, June 2011, pp. 1338-1346.
http://dx.doi.org/10.1016/j.nonrwa.2010.09.014

F.M. Hady, F.S. Ibrahim, S.M. Abdel-Gaied, Mohamed R. Eid. Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet, Nanoscale Research Letters, Volume 7, Issue 1, April 2012, 229.
http://dx.doi.org/10.1186/1556-276x-7-229

Buongiorno J. Convective transport in nanofluids. Journal of Heat Transfer. vol. 128, n. 3, 2006, pp. 240-250.
http://dx.doi.org/10.1115/1.2150834

Eastman, Jeffrey A. Anomalously increased effective thermal conductivities of ethylene-glycol-based nanofluids containing copper nanoparticles. Applied Physics Letters. Volume:78 , Issue: 6, February 2001, pp.718-720.
http://dx.doi.org/10.1063/1.1341218

Kuznetsov AV, Nield DA. Natural convection boundary-layer of a nanofluid past a vertical plate. International Journal of Thermal Sciences. Volume 49, Issue 2, February 2010, pp.243-247.
http://dx.doi.org/10.1016/j.ijthermalsci.2009.07.015

Tzou DY. Thermal instability of nanofluids in natural convection. International Journal of Heat and Mass Transfer.Volume 51, Issues 11–12, June 2008, pp.2967-2979.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2007.09.014

Tzou DY. Instability of nanofluids in natural convection. Journal of Heat Transfer. vol. 130, n. 7, 2008, pp.1-9.
http://dx.doi.org/10.1115/1.2908427

Bachok N, Ishak A, Pop I. Boundary layer flow of nanofluid over a moving surface in a flowing fluid. International Journal of Thermal Sciences, Volume 49, Issue 9, September 2010, pp. 1663-1668.
http://dx.doi.org/10.1016/j.ijthermalsci.2010.01.026

Khan WA, Pop I. Boundary-layer flow of a nanofluid past a stretching sheet. International Journal of Heat and Mass Transfer,Volume 53, Issues 11–12, May 2010, pp. 2477-2483.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.01.032

SU Xiao-hong , ZHENG Lian-cun , JIANG Feng. Approximate analytical solutions and approximate value of skin friction coefficient for boundary layer of power law fluids. Applied Mathematics and Mechanics. vol.29,n.9, November 2008, pp.1215 -1220.
http://dx.doi.org/10.1007/s10483-008-0910-4

SU Xiao-hong, ZHENG Lian-cun. Approximate Solutions to the MHD Falkner-Skan Flow Over a Permeable Wall. Applied Mathematics and Mechanics. vol.32,n.4,April 2011, pp. 383-390.
http://dx.doi.org/10.1007/s10483-011-1425-9

SU Xiao-hong, ZHENG Lian-cun, ZHANG Xin-xin. Nonlinear Singular boundary value problems arising in the boundary layer of fluid flowing on a conveyor belt. Journal of University of Science and Technology Beijing. vol.27,n.6, December 2005, pp.716-719.

SU Xiao-hong, ZHENG Lian-cun, JIANG Feng. Analytical Approximate Solutions and the Approximate Value of Skin Friction Coefficient for the Boundary Layer of Power Law Fluids. Applied Mathematics and Mechanics.Vol. 29, No. 9, September 2008, pp. 1101-1106.
http://dx.doi.org/10.1007/s10483-008-0910-4

SU Xiao-hong, ZHENG Lian-cun. Approximate solutions to MHD Falkner-Skan flow over permeable wall, Journal of Applied Mathematics and Mechanics. Volume 32, Issue 4, April 2011, pp. 401-408.
http://dx.doi.org/10.1007/s10483-011-1425-9

R.K. Tiwari, M.N. Das. Heat tranfer augmentation in a two–sided lid–driven diffrentially heated square cavity utilizing nanofluids, International Journal of Heat and Mass Transfer, Volume 50, Issues 9–10, May 2007, pp. 2002-2018.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2006.09.034

H.C. Brinkman. The viscosity of concentrated suspensions and solution, Journal of Chemical Physics, Volume 20, Issue 4, December 1951, pp.571-581.

J.C. Maxwell Garnett. Colours in metal glasses and in metallic films, Philos. Trans. R. Soc. Lond. A , vol. 203, June 1904, pp. 385- 420.

C-A. Guérin, P. Mallet, A. Sentenac. Effective-medium theory for finite-size aggregates, J. Opt. Soc. Am. Vol. 23, Issue 2, February 2006, pp. 349-358.
http://dx.doi.org/10.1364/josaa.23.000349

P.K. Kameswaran, M. Narayana, P. Sibanda, P.V.S.N. Murthy. Hydromagnetic nanofluid flow due to a stretching or shrinking sheet with viscous dissipation and chemical reaction effects, International Journal of Heat and Mass Transfer, Volume 55, Issues 25–26, December 2012, pp. 7587-7595.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.07.065

M.M. Rashidi, S.A. Mohimanian Pour, N. Laraqi. A semi- analytical solution of micro polar flow in a porous channel with mass injection by using differential transform method, Nonlinear Analysis: Modelling and Control. Vol. 15, No. 3, September 2010, pp. 341-350.


Refbacks

  • There are currently no refbacks.


Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize