0
Research Papers: Micro/Nanoscale Heat Transfer

Heat Transfer Analysis for Three-Dimensional Stagnation-Point Flow of Water-Based Nanofluid Over an Exponentially Stretching Surface

[+] Author and Article Information
Fiaz Ur Rehman

Department of Mathematics,
Govt. Postgraduate College No. 1,
Abbottabad 22010, Pakistan
e-mail: tanolig@gmail.com

Sohail Nadeem

Department of Mathematics,
Quaid-I-Azam University,
Islamabad 44000, Pakistan

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 22, 2017; final manuscript received August 29, 2017; published online January 17, 2018. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 140(5), 052401 (Jan 17, 2018) (7 pages) Paper No: HT-17-1037; doi: 10.1115/1.4038359 History: Received January 22, 2017; Revised August 29, 2017

The basic theme of this investigation is to analyze heat and mass transport for three-dimensional (3D) stagnation-point flow of nanofluid caused by an exponentially stretched surface when water is treated as base fluid. In this study, we invoked the boundary layer phenomena and suitable similarity transformation of exponential character; as a result, our 3D nonlinear equations of momentum and energy are transmuted into nonlinear and nonhomogeneous differential equations involving ordinary derivatives. Final equations are then puzzled out by applying homotopy analysis technique. Interesting outcomes of aggressing parameters involved in this study, and effecting profiles of temperature field and velocity are explained in detail. Graphical results of involved parameters appearing in considered nanofluid are presented separately. Different aspects of skin friction coefficient as well as Nusselt number are calculated. It is worth mentioning that skin friction (as we go) along x and y-direction is maximal for Cu-water nanofluid and minimal for AL2O3-water nanofluid. Also, the resulting quantity of local Nusselt number came out maximum for Cu-water nanofluid whereas minimum for TiO2-water nanofluid.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Sakiadis, B. C. , 1961, “Boundary-Layer Behavior on Continuous Solid Surface—I: Boundary Layer Equations for Two Dimensional and Axisymmetric Flow,” J. Am. Inst. Chem. Eng., 7(1), pp. 26–28. [CrossRef]
Sakiadis, B. C. , 1961, “Boundary Layer Behavior on Continuous Solid Surface—II: Boundary Layer on a Continuous Flat Surface,” J. Am. Inst. Chem. Eng., 7(2), pp. 221–225. [CrossRef]
Crane, L. , 1970, “Flow Past a Stretching Plate,” Z. Angew. Math. Phys., 21(4), pp. 645–647. [CrossRef]
Grubka, L. J. , and Bobba, K. M. , 1985, “Heat Transfer Characteristics of a Continuous Stretching Surface With Variable Temperature,” ASME J. Heat Transfer, 107(1), pp. 248–250. [CrossRef]
Ali, M. E. , 1995, “On Thermal Boundary Layer on a Power-Law Stretched Surface With Suction and Injection,” Int. J. Heat Fluid Flow, 16(4), pp. 280–290. [CrossRef]
Andersson, H. I. , 1992, “MHD Flow of a Viscoelastic Fluid Past a Stretching Surface,” Acta Mech., 95(1–4), pp. 227–230. [CrossRef]
Prasad, K. V. , Abel, S. , and Datti, P. S. , 2003, “Diffusion of Chemically Reactive Species of a Non-Newtonian Fluid Immersed in a Porous Medium Over a Stretching Sheet,” Int. J. Non-Linear Mech., 38(5), pp. 651–657. [CrossRef]
Liu, I.-C. , 2005, “Flow and Heat Transfer of an Electrically Conducting Fluid of Second Grade in Porous Medium Over a Stretching Sheet Subject to a Transverse Magnetic Field,” Int. J. Non-Linear Mech., 40(4), pp. 465–474. [CrossRef]
Magyari, E. , and Keller, B. , 1999, “Heat and Mass Transfer in the Boundary Layer on an Exponentially Stretching Continuous Surface,” J. Phys. D, 32(5), pp. 577–585. [CrossRef]
Elbashbeshy, E. M. A. , 2001, “Heat Transfer Over an Exponentially Stretching Continuous Surface With Suction,” Arch. Mech., 53(6), pp. 643–651. http://am.ippt.pan.pl/am/article/view/v53p643
Liu, C. , Wang, H. H. , and Peng, Y. F. , 2013, “Flow and Heat Transfer for Three-Dimensional Flow Over an Exponentially Stretching Surface,” Chem. Eng. Commun., 200(2), pp. 253–268. [CrossRef]
Choi, S. U. S. , and Eastman, J. A. , 1995, “Enhancing Thermal Conductivity of Fluids With Nanoparticles,” ASME International Mechanical Engineering Congress and Exposition, San Francisco, CA, Nov. 12–17, pp. 99–105.
Pang, C. , Lee, J. W. , and Kang, Y. T. , 2015, “Review on Combined Heat and Mass Transfer Characteristics in Nanofluids,” Int. J. Therm. Sci., 87, pp. 49–67. [CrossRef]
Sarkar, J. , Ghosh, P. , and Adil, A. , 2015, “A Review on Hybrid Nanofluids: Recent Research, Development and Applications,” Renewable Sustainable Energy Rev., 43, pp. 164–177. [CrossRef]
Bahiraei, M. , and Hangi, M. , 2015, “Flow and Heat Transfer Characteristics of Magnetic Nanofluids: A Review,” J. Magn. Mater., 374, pp. 125–138. [CrossRef]
Bhattacharyya, K. , and Vajravelu, K. , 2012, “Stagnation-Point Flow and Heat Transfer Over an Exponentially Shrinking Sheet,” Commun. Nonlinear. Sci. Numer. Simul., 17(7), pp. 2728–2734. [CrossRef]
Bachok, N. , Ishak, A. , Nazar, R. , and Pop, I. , 2010, “Flow and Heat Transfer at a General Three-Dimensional Stagnation Point in a Nanofluid,” Physica B, 405(24), pp. 4914–4918. [CrossRef]
Nadeem, S. , and Lee, C. H. , 2012, “Boundary Layer Flow of Nanofluid Over an Exponentially Stretching Surface,” Nanoscale Res. Lett., 7, p. 94. [CrossRef] [PubMed]
Nadeem, S. , Haq, R. U. , and Khan, Z. H. , 2014, “Heat Transfer Analysis of Water-Based Nanofluid Over an Exponentially Stretching Sheet,” Alexandria Eng. J., 53(1), pp. 219–224. [CrossRef]
Pal, D. , Mandal, G. , and Vajravelu, K. , 2014, “Flow and Heat Transfer of Nanofluids at a Stagnation Point Flow Over a Stretching/Shrinking Surface in a Porous Medium With Thermal Radiation,” Appl. Math. Comput., 238, pp. 208–224.
Hsiao, K.-L. , 2014, “Nanofluid Flow With Multimedia Physical Features for Conjugate Mixed Convection and Radiation,” Comput. Fluids, 104, pp. 1–8. [CrossRef]
Noghrehabadi, A. , Izadpanahi, E. , and Ghalambaz, M. , 2014, “Analyze of Fluid Flow and Heat Transfer of Nanofluids Over a Stretching Sheet Near the Extrusion Slit,” Comput. Fluids, 100, pp. 227–236. [CrossRef]
Nadeem, S. , and Hussain, S. T. , 2014, “Flow and Heat Transfer Analysis of Williamson Nanofluid,” Appl. Nanosci., 4(8), pp. 1005–1012. [CrossRef]
Ghaffari, A. , Javed, T. , and Hsiao, K.-L. , 2016, “Heat Transport Analysis of Unsteady Oblique Stagnation Point Flow of Elastic-Viscous Fluid Due to Sinusoidal Wall Temperature Over an Oscillating-Stretching Surface: A Numerical Approach,” J. Mol. Liq., 219, pp. 748–755. [CrossRef]
Hsiao, K. L. , 2016, “Stagnation Electrical MHD Nanofluid Mixed Convection With Slip Boundary on a Stretching Sheet,” Appl. Therm. Eng., 98, pp. 850–861. [CrossRef]
Ur Rehman, F. , Nadeem, S. , and Haq, R. U. , 2017, “Heat Transfer Analysis for Three-Dimensional Stagnation-Point Flow Over an Exponentially Stretching Surface,” Chin. J. Phys., 55(4), pp. 1552–1560. [CrossRef]
Tiwari, R. K. , and Das, M. K. , 2007, “Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids,” Int. J. Heat Mass Transfer, 50(9–10), pp. 2002–2018. [CrossRef]
Abu-Nada, E. , 2008, “Application of Nanofluids for Heat Transfer Enhancement of Separated Flows Encountered in a Backward Facing Step,” Int. J. Heat Fluid Flow, 29(1), p. 242. [CrossRef]
Abu-Nada, E. , and Oztop, H. F. , 2009, “Effects of Inclination Angle on Natural Convection in Enclosures Filled With Cu-Water Nanofluid,” Int. J. Heat Fluid Flow, 30(4), pp. 669–678. [CrossRef]
Talebi, F. , Houshang, A. , and Shahi, M. , 2010, “Numerical Study of Mixed Convection Flows in a Square Lid-Driven Cavity Utilizing Nanofluid,” Int. Commun. Heat Mass Transfer, 37(1), pp. 79–90. [CrossRef]
Brikman, H. C. , 1952, “The Viscosity of Concentrated Suspensions and Solutions,” J. Chem. Phys., 20, pp. 571–581. [CrossRef]
Xuan, Y. , and Li, Q. , 2003, “Investigation on Convective Heat Transfer and Flow Features of Nanofluids,” ASME J. Heat Transfer, 125(1), pp. 151–155. [CrossRef]
Li, Q. , and Xuan, Y. , 2000, “Experimental Investigation on Transport Properties of Nanofluids,” International Symposium on Heat Transfer, Beijing, China, pp. 757–762. https://www.tib.eu/en/search/id/BLCP%3ACN042077963/Experimental-investigation-on-transport-properties/
Liao, S. J. , 1995, “An Approximate Solution Technique Not Depending on Small Parameters: A Special Example,” Int. J. Non-Linear Mech., 30(3), pp. 371–380. [CrossRef]
Liao, S. J. , 1998, “Homotopy Analysis Method: A New Analytic Method for Nonlinear Problems,” Appl. Math. Mech., 19(10), pp. 957–962. [CrossRef]
Liu, C. S. , 2010, “The Essence of the Homotopy Analysis Method,” Appl. Math. Comp., 216(4), pp. 1299–1303. [CrossRef]
Liao, S. J. , 2004, Beyond Perturbation: Introduction to the Homotopy Analysis Method, CRC Press, Boca Raton, FL.
Oztop, H. F. , and Abu-Nada, E. , 2008, “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled With Nanofluids,” Int. J. Heat Fluid Flow, 29(5), pp. 1326–1336. [CrossRef]

Figures

Grahic Jump Location
Fig. 2

h-curves diagrammed for the functions f,g, and θ

Grahic Jump Location
Fig. 5

Influence of nanoparticle on f′(η) and g′(η)

Grahic Jump Location
Fig. 6

Influence of nanoparticles, A on θ(η) and ϕ, r1 on coefficient of skin friction along x-direction

Grahic Jump Location
Fig. 7

Influence of ϕ,α1, and α2 for different nanoparticles on coefficient of skin friction along x-direction

Grahic Jump Location
Fig. 8

Influence of ϕ,r1, and α1 for different nanoparticles on coefficient of skin friction along y-direction

Grahic Jump Location
Fig. 1

Geometry of the problem

Grahic Jump Location
Fig. 3

Effect of ϕ and r1 on f′(η) and g′(η)

Grahic Jump Location
Fig. 4

Influence of ϕ and r1 on g′(η) and θ(η)

Grahic Jump Location
Fig. 9

Influence of ϕ,r1 on coefficient of skin friction along y-direction

Grahic Jump Location
Fig. 10

Influence of ϕ,r1, and A for different nanoparticles on Nusselt number

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In