# IJPAM: Volume 112, No. 1 (2017)

# Title

ROTATING BOUNDARY LAYER FLOW DUE TOA PERMEABLE EXPONENTIALLY SHRINKING

SHEET IN NANOFLUID

# Authors

S.N.A. Salleh, N. Bachok, N.M. ArifinDepartment of Mathematics and Institute for

Mathematical Research

Universiti Putra Malaysia

43400 UPM Serdang, Selangor, MALAYSIA

# Abstract

In this study, the effect of the suction on the boundary layer flow and heat transfer characteristics over an exponentially shrinking surface in a rotating nanofluid is contemplated for three types of nanoparticles namely, copper Cu, titania TiO and alumina AlO. Similarity transformations have been applied to transform the partial differential equations into a system of ordinary differential equations, which are then solved numerically using a shooting method in Maple software. The effects of the rotation , suction and nanoparticle volume fraction parameters on the velocity field, temperature distribution, local skin friction coefficients and local Nusselt number are taken into account. Results obtain in this study are graphically presented and further discussion have been discussed in detail. The dual solutions are found to exist for a certain values of the governing parameters. It is revealed from the study that the presence of the rotation would increase the skin friction coefficients and heat transfer rate at the surface.# History

**Received: **June 28, 2016
**Revised: **October 5, 2016
**Published: **January 26, 2017

# AMS Classification, Key Words

**AMS Subject Classification: **76D10, 76U05, 80A20
**Key Words and Phrases: **exponentially shrinking sheet, nanofluid, rotating flow, suction

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## Bibliography

- 1
- L.J. Crane, Flow past a stretching plate,
*Z Angew Math. Phys.*,**21**, (1970), 645-647,**doi:**10.1007/BF01587695. - 2
- P. Gupta, A. Gupta, Heat and mass transfer on a stretching sheet with suction and blowing,
*The Can. J. of Chem. Eng.*,**55**, No. 6 (1977), 744-746,**doi:**10.1002/cjce.5450550619. - 3
- C.Y. Wang, Stretching a surface in a rotating fluid,
*J. App. Maths. and Phys.*,**39**, (1988), 177-185,**doi:**10.1007/BF00945764. - 4
- V. Rajeswari, G. Nath, Unsteady flow over a stretching surface in a rotating fluid,
*Int. J. of Eng. Sci.*,**30**, No. 6 (1992), 747-756,**doi:**10.1016/0020-7225(92)90104-O. - 5
- R. Nazar, N. Amin, I. Pop, Unsteady boundary layer flow due to a sretching surface in a rotating fluid,
*Mechanics Research Communications*,**31**, (2004), 121-128,**doi:**10.1016/j.mechrescom.2003.09.004. - 6
- H. Takhar, A. Chamkha, G. Nath, Flow and heat transfer on a stretching surface in a rotating fluid with a magnetic field,
*Int. J. of Thermal Sciences*,**42**, (2003), 23-31,**doi:**10.1016/S1290-0729(02)00004-2. - 7
- Z. Abbas, T. Javed, N. Ali, Unsteady MHD flow and heat transfer on a stretching sheet in a rotating fluid,
*J. of the Taiwan Inst. of Chem. Eng.*,**41**, (2010), 644-650,**doi:**10.1016/j.jtice.2010.02.002. - 8
- T. Mahmood, S. Ali, M. Khan, Magnetohydrodynamic flow due to a stretching surface in rotating fluid,
*Journal of Mathematics*,**46**, No. 1 (2014), 39-50. - 9
- S. Nadeem, A. Rehman, R. Mehmood, Boundary layer flow of rotating two phase nanofluid over a stretching surface,
*Heat Transfer Asian Research*,**45**, (2016), 285-298,**doi:**10.1002/htj.21167. - 10
- S.U.S Choi, Enhancing thermal conductivity of fluids with nanoparticles,
*ASME Publication*,**66**, (1995), 99-101. - 11
- M. Mustafa, T. Hayat, I. Pop, S. Asghar, S. Obaidat, Stagnation-point flow of a nanofluid towards a stretching sheet,
*Int. J. of Heat and Mass Transfer*,**54**, (2011), 5588-5594,**doi:**10.1016/j.ijheatmasstransfer.2011.07.021. - 12
- O.D. Makinde, W.A. Khan, Z.H. Khan, Buoyancy effects on MHD stagnation-point flow and heat transfer of a nanofluid past a convectively heated stretching/shrinking sheet,
*Int. J. of Heat and Mass Transfer*,**62**, (2013), 526-533,**doi:**10.1016/j.ijheatmasstransfer.2013.03.049. - 13
- N. Bachok, A. Ishak, R. Nazar, N. Senu, Stagnation-point flow over a permeable stretching/shrinking sheet in a copper-water nanofluid,
*Boundary Value Problems*,**39**, (2013),**doi:**10.1186/1687-2770-2013-39. - 14
- S.V. Subhashini, R. Sumathi, Dual solutions of a mixed convection flow of nanofluids over a moving vertical plate,
*Int. J. of Heat and Mass Transfer*,**71**, (2014), 117-124,**doi:**10.1016/j.ijheatmasstransfer.2013.12.034. - 15
- F. Ali, R. Nazar, N.M. Arifin, I. Pop, Unsteady shrinking sheet with mass transfer in a rotating fluid,
*Int. J. 7 for Numerical Methods in Fluids*,**66**, (2011), 1465-1474,**doi:**10.1002/fld.2325. - 16
- M. Miklavcic, C.Y. Wang, Viscous flow due to a shrinking sheet,
*Quarterly of Applied Mathematics*,**64**, No. 2 (2006), 283-290. - 17
- C.Y. Wang, Stagnation flow towards a shrinking sheet,
*Int. J. of Non-Lin. Mech.*,**43**, (2008), 377-382,**doi:**10.1016/j.ijnonlinmec.2007.12.021. - 18
- M. Sajid, T. Javed, T. Hayat, Mhd rotating flow of a viscous fluid over a shrinking surface,
*Nonlinear Dynamics*,**51**, (2008), 259-265,**doi:**10.1007/s11071-007-9208-3. - 19
- T. Hayat, T. Javed, M. Sajid, Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface,
*Physics Letters A*,**372**, (2008), 3264-3273,**doi:**10.1016/j.physleta.2008.01.069. - 20
- N. Faraz, Y. Khan, Analytical solution of electrically conducted rotating flow of a second grade fluid over a shrinking surface,
*Ain Shams Engineering Journal*,**2**, (2011), 221-226,**doi:**10.1016/j.asej.2011.10.001. - 21
- H. Rosali, A. Ishak, R. Nazar, I. Pop, Rotating flow over an exponentially shrinking sheet with suction,
*Journal of Molecular Liquids*,**211**, (2015), 965-969,**doi:**10.1016/j.molliq.2015.08.026. - 22
- K. Bhattacharyya, Boundary layer flow and heat transfer over an exponentially shrinking sheet,
*Chin. Phys. Letter*,**28**, No. 7 (2011), 74701-4,**doi:**10.1088/0256-307X/28/7/074701. - 23
- K. Bhattacharyya, I. Pop, Mhd boundary layer flow due to an exponentially shrinking sheet,
*Magnetohydrodynamics*,**47**, No. 4 (2011), 337-344. - 24
- N. Bachok, A. Ishak, I. Pop, Boundary layers stagnation-point flow and heat transfer over an exponentially stretching/shrinking sheet in a nanofluid,
*Int. J. of Heat and Mass Transfer*,**55**, (2012), 8122-8128,**doi:**10.1016/j.ijheatmasstransfer.2012.08.051. - 25
- K. Bhattacharyya, K. Vajravelu, Stagnation-point flow and heat transfer over an exponentially shrinking sheet,
*Commun Nonlinear Sci Numer Simulation*,**17**, (2012), 2728-2734,**doi:**10.1016/j.cnsns.2011.11.011. - 26
- A.M. Rohni, S. Ahmad, A.I. Ismail, I. Pop, Boundary layer flow and heat transfer over an exponentially shrinking vertical sheet with suction,
*Int. J. of Thermal Sciences*,**64**, (2013), 264-272,**doi:**10.1016/j.ijthermalsci.2012.08.016. - 27
- M.M. Rahman, A.V. Rosca, I. Pop, Boundary layer flow of a nanofluid past a permeable exponentially shrinking/stretching surface with second order slip using buongiornos model,
*Int. J. of Heat and Mass Transfer*,**77**, (2014), 1133-1143,**doi:**10.1016/j.ijheatmasstransfer.2014.06.013. - 28
- H.F. Oztop, E. Abu-Nada, Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids,
*Int. J. Heat Fluid Flow*,**29**, (2008), 1326-1336,**doi:**10.1016/j.ijheatfluidflow.2008.04.009.

# How to Cite?

**DOI: 10.12732/ijpam.v112i1.4**

International Journal of Pure and Applied Mathematics

**How to cite this paper?****Source:****ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2017

**Volume:**112

**Issue:**1

**Pages:**57 - 69

Google Scholar; DOI (International DOI Foundation); WorldCAT.

**This work is licensed under the Creative Commons Attribution International License (CC BY).**