In this research, natural convection of a non-Newtonian copper-water nanofluid between two infinite parallel vertical flat plates is investigated. The basic partial differential equations are reduced to ordinary differential equations which are solved analytically using the differential transformation method. The results obtained using the differential transformation method and those from a numerical method are in good agreement which demonstrates the ability of the differential transformation method to solve such problems. It is shown that as the nanoparticle volume fraction increases, the momentum boundary layer thickness increases, whereas the thermal boundary layer thickness decreases.
BruceRWNaTY. Natural convection flow of Powell–Eyring fluids between two vertical flat plates. In: ASME winter annual meeting, Pittsburgh, PA, 12–17 November 1967ASME paper 67. New York: ASME.
2.
ShenoyAVMashelkarRA. Thermal convection in non-Newtonian fluids. Adv Heat Transf1982; 15:143–225.
3.
RajagopalKRNaTY. Natural convection flow of a non-Newtonian fluid between two vertical flat plates. Acta Mech1985; 54: 239–246.
4.
KhanWAPopI. Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf2010; 53: 2477–2483.
5.
VajraveluKPrasadKVLeeJ. Convective heat transfer in the flow of viscous Agewater and Cuewater nanofluids over a stretching surface. Int J Thermal Sci2011; 50: 843–851.
6.
YacobNAIshakAPopI. Boundary layer flow past a stretching/shrinking surface beneath an external uniform shear flow with a convective surface boundary condition in a nanofluid. Nanoscale Res Lett2011; 6.
7.
RandRHArmbrusterD. Perturbation methods bifurcation theory and computer algebraic. Appl Math Sci1987.
8.
ZhouK. Differential transformation and its applications for electrical circuits. Wuhan, China: Huazhong University Press, 1986.
9.
ChenCKHoSH. Solving partial differential equations by two-dimensional differential transform method. Appl Math Comput1999; 106: 171–179.
10.
AyazF. Solutions of the systems of differential equations by differential transform method. Appl Math Comput2004; 147: 547–567.
11.
MomaniaSErturkS. Solutions of non-linear oscillators by the modified differential transform method. Comput Math Appl2008; 55: 833–842.
12.
KurulayMBayramM. Approximate analytical solution for the fractional modified KdV by differential transform method. Commun Nonlinear Sci Numer Simulat2010; 15: 1777–1782.
13.
FereidoonADavoudabadiMRYaghoobiH. Application of homotopy perturbation method and differential transformation method to determine displacenent of damped system with nonlinear spring. World Appl Sci J2010; 9: 681–688.
14.
JoneidiAAGanjiDDBabaelahiM. Differential transformation method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity. Int Commun Heat Mass Transf2009; 36: 757–762.
15.
EbaidAE. A reliable aftertreatment for improving the differential transformation method and its application to nonlinear oscillators with fractional nonlinearities. Commun Nonlinear Sci Numer Simulat2011; 16: 528–536.
16.
AlMMNooraniMSM. Application of the differential transformation method for the solution of the hyperchaotic Rossler system. Commun Nonlinear Sci Numer Simul2009; 14: 1509–1514.
17.
EbaidAH. Approximate periodic solutions for the non-linear relativistic harmonic oscillator via differential transformation method. Commun Nonlinear Sci Numer Simulat2010; 15: 1921–1927.
18.
XuanYRoetzelW. Conceptions for heat transfer correlations of nanofluids. Int J Heat Mass Transf2000; 43: 3701–3707.
19.
AminossadatiSMGhasemiB. Natural convection cooling of a localized heat source at the bottom of a nanofluid-filled enclosure. Eur J Mech B, Fluids2009; 28: 630–640.
