Similarity solutions for the flow and heat transfer over a nonlinear stretching/shrinking sheet in a nanofluid

Nor Azian Aini Mat, Norihan Md Arifin, Roslinda Mohd. Nazar, Fudziah Ismail

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, a similarity solutions for the flow and heat transfer over a nonlinear stretching/shrinking sheet in a nanofluid is considered. The governing equations are first transformed into a system of non-dimensional via the non-dimensional variables, and then into non-similar ordinary differential equations before they are solved numerically using the shooting method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction (0≤≤0.2), the value of velocity ratio parameter ε and the constant exponent m. Three different types of nanoparticles, namely Cu, Al 2O 3 and TiO 2 are considered by using water-based fluid with Prandtl number Pr = 6.2. It was found that the skin friction and Nusselt number have greater values for Cu than for Al 2O 3 and TiO 2. The skin friction coefficient and local Nusselt number increase as the nanoparticle volume fraction and constant exponent m increase. The result also indicate that dual solution exist for a shrinking sheet (ε c ≤ ε ≤-1) for m > 1/3.

Original languageEnglish
Title of host publicationAIP Conference Proceedings
Pages165-172
Number of pages8
Volume1450
DOIs
Publication statusPublished - 2012
Event5th International Conference on Research and Education in Mathematics, ICREM5 - Bandung
Duration: 22 Oct 201124 Oct 2011

Other

Other5th International Conference on Research and Education in Mathematics, ICREM5
CityBandung
Period22/10/1124/10/11

Fingerprint

skin friction
Nusselt number
heat transfer
nanoparticles
coefficient of friction
exponents
Prandtl number
temperature profiles
differential equations
velocity distribution
fluids
water

Keywords

  • Nanofluid
  • Nonlinear stretching/shrinking sheet
  • Similarity solutions

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Mat, N. A. A., Arifin, N. M., Mohd. Nazar, R., & Ismail, F. (2012). Similarity solutions for the flow and heat transfer over a nonlinear stretching/shrinking sheet in a nanofluid. In AIP Conference Proceedings (Vol. 1450, pp. 165-172) https://doi.org/10.1063/1.4724135

Similarity solutions for the flow and heat transfer over a nonlinear stretching/shrinking sheet in a nanofluid. / Mat, Nor Azian Aini; Arifin, Norihan Md; Mohd. Nazar, Roslinda; Ismail, Fudziah.

AIP Conference Proceedings. Vol. 1450 2012. p. 165-172.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Mat, NAA, Arifin, NM, Mohd. Nazar, R & Ismail, F 2012, Similarity solutions for the flow and heat transfer over a nonlinear stretching/shrinking sheet in a nanofluid. in AIP Conference Proceedings. vol. 1450, pp. 165-172, 5th International Conference on Research and Education in Mathematics, ICREM5, Bandung, 22/10/11. https://doi.org/10.1063/1.4724135
Mat, Nor Azian Aini ; Arifin, Norihan Md ; Mohd. Nazar, Roslinda ; Ismail, Fudziah. / Similarity solutions for the flow and heat transfer over a nonlinear stretching/shrinking sheet in a nanofluid. AIP Conference Proceedings. Vol. 1450 2012. pp. 165-172
@inproceedings{5c028a4a24094d48b84652782ad19636,
title = "Similarity solutions for the flow and heat transfer over a nonlinear stretching/shrinking sheet in a nanofluid",
abstract = "In this paper, a similarity solutions for the flow and heat transfer over a nonlinear stretching/shrinking sheet in a nanofluid is considered. The governing equations are first transformed into a system of non-dimensional via the non-dimensional variables, and then into non-similar ordinary differential equations before they are solved numerically using the shooting method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction (0≤≤0.2), the value of velocity ratio parameter ε and the constant exponent m. Three different types of nanoparticles, namely Cu, Al 2O 3 and TiO 2 are considered by using water-based fluid with Prandtl number Pr = 6.2. It was found that the skin friction and Nusselt number have greater values for Cu than for Al 2O 3 and TiO 2. The skin friction coefficient and local Nusselt number increase as the nanoparticle volume fraction and constant exponent m increase. The result also indicate that dual solution exist for a shrinking sheet (ε c ≤ ε ≤-1) for m > 1/3.",
keywords = "Nanofluid, Nonlinear stretching/shrinking sheet, Similarity solutions",
author = "Mat, {Nor Azian Aini} and Arifin, {Norihan Md} and {Mohd. Nazar}, Roslinda and Fudziah Ismail",
year = "2012",
doi = "10.1063/1.4724135",
language = "English",
isbn = "9780735410497",
volume = "1450",
pages = "165--172",
booktitle = "AIP Conference Proceedings",

}

TY - GEN

T1 - Similarity solutions for the flow and heat transfer over a nonlinear stretching/shrinking sheet in a nanofluid

AU - Mat, Nor Azian Aini

AU - Arifin, Norihan Md

AU - Mohd. Nazar, Roslinda

AU - Ismail, Fudziah

PY - 2012

Y1 - 2012

N2 - In this paper, a similarity solutions for the flow and heat transfer over a nonlinear stretching/shrinking sheet in a nanofluid is considered. The governing equations are first transformed into a system of non-dimensional via the non-dimensional variables, and then into non-similar ordinary differential equations before they are solved numerically using the shooting method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction (0≤≤0.2), the value of velocity ratio parameter ε and the constant exponent m. Three different types of nanoparticles, namely Cu, Al 2O 3 and TiO 2 are considered by using water-based fluid with Prandtl number Pr = 6.2. It was found that the skin friction and Nusselt number have greater values for Cu than for Al 2O 3 and TiO 2. The skin friction coefficient and local Nusselt number increase as the nanoparticle volume fraction and constant exponent m increase. The result also indicate that dual solution exist for a shrinking sheet (ε c ≤ ε ≤-1) for m > 1/3.

AB - In this paper, a similarity solutions for the flow and heat transfer over a nonlinear stretching/shrinking sheet in a nanofluid is considered. The governing equations are first transformed into a system of non-dimensional via the non-dimensional variables, and then into non-similar ordinary differential equations before they are solved numerically using the shooting method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction (0≤≤0.2), the value of velocity ratio parameter ε and the constant exponent m. Three different types of nanoparticles, namely Cu, Al 2O 3 and TiO 2 are considered by using water-based fluid with Prandtl number Pr = 6.2. It was found that the skin friction and Nusselt number have greater values for Cu than for Al 2O 3 and TiO 2. The skin friction coefficient and local Nusselt number increase as the nanoparticle volume fraction and constant exponent m increase. The result also indicate that dual solution exist for a shrinking sheet (ε c ≤ ε ≤-1) for m > 1/3.

KW - Nanofluid

KW - Nonlinear stretching/shrinking sheet

KW - Similarity solutions

UR - http://www.scopus.com/inward/record.url?scp=84861925960&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861925960&partnerID=8YFLogxK

U2 - 10.1063/1.4724135

DO - 10.1063/1.4724135

M3 - Conference contribution

AN - SCOPUS:84861925960

SN - 9780735410497

VL - 1450

SP - 165

EP - 172

BT - AIP Conference Proceedings

ER -