Research Papers: Forced Convection

Nonlinear Heat Transfer in a Two-Layer Flow With Nanofluids by OHAM

[+] Author and Article Information
Umer Farooq

e-mail: umer@Sjtu.edu.cn

Lin Zhi-Liang

e-mail: linzhiliang@sjtu.edu.cn
School of Naval Architecture,
Ocean and Civil Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 26, 2012; final manuscript received August 31, 2013; published online November 5, 2013. Assoc. Editor: Robert D. Tzou.

J. Heat Transfer 136(2), 021702 (Nov 05, 2013) (8 pages) Paper No: HT-12-1407; doi: 10.1115/1.4025432 History: Received July 26, 2012; Revised August 31, 2013

The problem of fully developed steady, laminar, incompressible flow in a vertical channel is studied analytically, one region is filled with water based copper nanofluid and the other region is filled with clear viscous fluid. The resulting coupled nonlinear ordinary differential equations (ODEs) are solved by optimal homotopy analysis method (OHAM). The convergence of our results is discussed by the so-called total average squared residual error. Analytical results are presented for different values of the physical parameters, such as the mixed convection parameters, the Brownian motion parameter, and thermophoresis parameter. Reversed flow is observed for sufficiently high buoyancy (mixed convection parameter). Further we investigate the effects of the Brownian motion parameter and thermophoresis parameter on the fluid flow and heat transfer at the interface of the two regions.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Tao, L. N., 1960, “On Combined Free and Forced Convection in Channels,” ASME J. Heat Transfer, 82, pp. 233–238. [CrossRef]
Aung, W., and Worku, G., 1986, “Developing Flow and Flow Reversal in a Vertical Channel With Asymmetric Wall Temperature,” ASME J. Heat Transfer, 108, pp. 299–304. [CrossRef]
Aung, W., and Worku, G., 1986, “Theory of Fully Developed, Combined Convection Including Flow Reversal,” ASME J. Heat Transfer, 108, pp. 485–488. [CrossRef]
Kimura, T., Heya, N., Takeuchi, M., and Isomi, H., 1986, “Natural Convection Heat Transfer Phenomena in an Enclosure Filled With Two Stratified Fluids,” Trans. Jpn. Soc. Mech. Eng., Ser. B, 52, pp. 617–625. [CrossRef]
Malashetty, M. S., Umavathi, J. C., and Kumar, J. P., 2006, “Magnetoconvection of Two-Immiscible Fluids in a Vertical Enclosure,” J. Heat Mass Transfer, 42, pp. 977–993. [CrossRef]
Nikodijevic, D., Stamenkovic, Z., Milenkovic, D., Lagojevic, B., and Nikodikevic, J., 2011, “Flow and Heat Transfer of Two Immiscible Fluids in the Presence of Uniform Inclined Magnetic Field,” Math. Probl. Eng., 2011, p. 132302. [CrossRef]
Kumar, J. P., Umavathi, J. C., Chamkha, A. J., and Pop, I., 2010, “Fully-Developed Free Convective Flow of Micropolar and Viscous Fluids in a Vertical Channel,” Appl. Math. Model., 34, pp. 1175–1186. [CrossRef]
Umavathi, J. C., Liu, I. C., Kumar, J. P., and Meera, D. S., 2010, “Unsteady Flow and Heat Transfer of Porous Media Sandwiched Between Viscous Fluids,” Appl. Math. Mech., 31(12), pp. 1497–1516. [CrossRef]
Choi, S. U., 1995, “Enhancing Thermal Conductivity of Fluids With Nanoparticle,” Conference on International Mechanical Engineering Congress and Exhibition, San Francisco, CA, Nov. 12–17.
Choi, S. U., Zhang, Z. G., Lockwood, W., and Grulke, F. E., 2001, “Anomalously Thermal Conductivity Enhancement in Nanotube Suspension,” J. Appl. Phys. Lett., 79, pp. 2252–2254. [CrossRef]
Das, S. K., Choi, S. U., Yu, W., and Pardeep, T., 2007, Nanofluids: Science and Technology, Wiley, Hoboken, NJ.
Xu, H., and Pop, I., 2012, “Fully Developed Mixed Convection Flow in a Vertical Channel Filled With Nanofluids,” Int. Commun. Heat Mass Transfer, 39, pp. 1086–1092. [CrossRef]
Grosan, T., and Pop, I., 2012, “Fully Developed Mixed Convection in a Vertical Channel Filled by a Nanofluid,” ASME J. Heat Transfer, 134, pp. 1–5. [CrossRef]
Xu, H., Fan, T., and Pop, I., 2013, “Analysis of Mixed Convection Flow of a Nanofluid in a Vertical Channel With the Buongiorno Mathematical Model,” J. Int. Commun. Heat Mass Transfer, 44, pp. 15–22. [CrossRef]
Gorder, R. A. V., Prasad, K. V., and Vajravelu, K., 2012, “Convective Heat Transfer in the Vertical Channel Flow of a Clear Fluid Adjacent to a Nanofluid Layer: A Two-Fluid Model,” Heat and Mass Transfer, 48, pp. 1247–1255. [CrossRef]
Liao, S., 1997, “A Kind of Approximate Solution Technique Which Does not Depend Upon Small Parameters (II)—An Application in Fluid Mechanics,” Int. J. Nonlinear Mech., 32, pp. 815–822. [CrossRef]
Liao, S., 2010, “An Optimal Homotopy-Analysis Approach for Strongly Nonlinear Differential Equations,” J. Commun. Nonlinear Sci. Numer. Simul., 15, pp. 2003–2016. [CrossRef]
Khanafer, K., Vafai, K., and Lightstone, M., 2003, “Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids,” Int. J. Heat Mass Transfer, 46, pp. 3639–3653. [CrossRef]
Buongiorno, J., 2006, “Convective Transport in Nano fluids,” ASME J. Heat Transfer, 128, pp. 240–250. [CrossRef]
Liao, S., 1999, “An Explicit, Totally Analytic Approximation of Blasius Viscous Flow Problems,” Int. J. Nonlinear Mech., 34, pp. 759–778. [CrossRef]
Liao, S., 1999, “A Uniformly Valid Solutions of 2D Viscous Flow Past a Semi-Infinite Flat Plate,” J. Fluid Mech., 385, pp. 101–128. [CrossRef]
Liao, S., and Campo, A., 2002, “Analytic Solutions of the Temperature Distribution in Blasius Viscous Flow Problems,” J. Fluid Mech., 453, pp. 411–425. [CrossRef]
Liao, S., 2003, “On the Analytic Solution of Magnetohydrodynamic Flows of Non-Newtonian Fluids Over a Stretching Sheet,” J. Fluid Mech., 488, pp. 189–212. [CrossRef]
Liao, S., 2003, Beyond Perturbation. Introduction to Homotopy Analysis Method, Chapman and Hall/CRC Press, Boca Raton, FL.
Liao, S., 2012, Homotopy Analysis Method in Nonlinear Differential Equations, Higher Education Press, Beijing.


Grahic Jump Location
Fig. 1

Physical configuration

Grahic Jump Location
Fig. 2

Comparison of OHAM results with Aung and Worku [3] for stream vise velocity profiles

Grahic Jump Location
Fig. 3

Graphs of u(y), θ(y), and φ(y) for different λi with Nb = Nt = 0.01 and h = 0.1

Grahic Jump Location
Fig. 4

Graphs of u(y), θ(y), and φ(y) for different λi with Nb = Nt = 0.01 and h = 1.0

Grahic Jump Location
Fig. 5

Graphs of u(y), θ(y), and φ(y) for different Nb with λ1 = 1.0, Nt = 0.01, and h = 0.1

Grahic Jump Location
Fig. 6

Graphs of u(y), θ(y), and φ(y) for different Nb with λ1 = 150, Nt = 0.01, and h = 1.0

Grahic Jump Location
Fig. 7

Graphs of u(y), θ(y), and φ(y) for different Nt with λ1 = 150, Nb = 0.01, and h = 1.0



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