[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ skip to main content
research-article

Boundary Layer Flow of Nanofluid Over a Nonlinearly Stretching Sheet With Convective Boundary Condition

Published: 01 January 2015 Publication History

Abstract

The steady laminar two-dimensional flow of nanofluid due to nonlinearly stretching sheet is discussed. Convective surface boundary condition is employed for a thermal boundary layer problem. The newly proposed boundary condition is considered that requires nanoparticle volume fraction at the wall to be passively rather than actively controlled. Suitable similarity transformations are introduced to non-dimensionalize the governing boundary layer equations. The velocity, temperature and nanoparticle volume fraction distributions are determined by two methods namely 1) optimal homotopy analysis method and 2) fourth-fifthorder Runge-Kutta method based shooting technique. The results obtained by two solutions are in excellent agreement. Behavior of interesting parameters on the flow fields is thoroughly presented and discussed.

References

[1]
L. J. Crane, “Flow past a stretching plate,” Zeit. für Ange. Math. Phys., vol. 21, no. 4, pp. 645– 647, 1970.
[2]
K. Vajravelu, “Viscous flow over a nonlinearly stretching sheet,” Appl. Math. Comput., vol. 124, pp. 281–288, 2001.
[3]
R. Cortell, “Viscous flow and heat transfer over a nonlinearly stretching sheet,” Appl. Math. Comput., vol. 184, pp. 864– 873, 2007.
[4]
R. Bhargava, S. Sharma, H. S. Takhar, O. A. Bég, and P. Bhargava, “Numerical solutions for micropolar transport phenomena over a nonlinear stretching sheet, “Nonlinear Anal. Model. Contr., vol. 12, pp. 45–63, 2007.
[5]
R. Cortell, “Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet, “Phys. Lett. A, vol. 372, pp. 631–636, 2008.
[6]
T. Hayat, Z. Abbas, and T. Javed, “Mixed convection flow of a micropolar fluid over a non-linearly stretching sheet,” Phys. Lett. A, vol. 372, pp. 637–647, 2008.
[7]
S. A. Kechil and I. Hashim, “Series solution of flow over nonlinearly stretching sheet with chemical reaction and magnetic field,” Phys. Lett. A, vol. 372, pp. 2258 –2263, 2008.
[8]
T. Hayat, Q. Hussain, and T. Javed, “The modified decomposition method and Padé approximants for the MHD flow over a non-linear stretching sheet,” Nonlinear Anal. RWA, vol. 10, pp. 966–973, 2009.
[9]
P. Rana and R. Bhargava, “Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: A numerical study,” Comm. Nonlinear Sci. Num. Simul., vol. 17, pp. 212 –226, 2012.
[10]
A. Shahzad, R. Ali, and M. Khan, “On the exact solution for axisymmetric flow and heat transfer over a non-linear radially stretching sheet,” Chin. Phys. Lett., vol. 29, p. 084705, 2012.
[11]
H. Masuda, A. Ebata, K. Teramae, and N. Hishinuma, “Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles (dispersion of c-Al2O3, SiO2 and TiO2 ultra-fine particles),” (in Japanese), Netsu Bussei, vol. 4, pp. 227–233, 1993.
[12]
S. U. S. Choi and J. A. Eastman, “Enhancing thermal conductivity of fluids with nanoparticles,” in Proc. ASME Int. Mech. Eng. Congr Expo., San Francisco, CA, USA, 1995, vol. 66, pp. 99–105.
[13]
J. Buongiorno, “Convective transport in nanofluids,” ASME J. Heat Transf., vol. 128, pp. 240–250, 2006.
[14]
S. S. Khaleduzzaman, R. Saidur, J. Selvaraj, I. M. Mahbubul, M. R. Sohel, and I. M. Shahrul, “Nanofluids for thermal performance improvement in cooling of electronic device,” Adv. Mater. Res., vol. 832, pp. 218–223, 2013.
[15]
A. Ebaid and E. H. Aly, “ Exact analytical solution of the peristaltic nanofluids flow in an asymmetric channel with flexible walls and slip condition: application to the cancer treatment,” Comput. Math. Meth. Med. , 2013, Article ID 825376.
[16]
J. Hunt, “Small particle heat exchangers,” J. Renew. Sust. Energy, Lawrence Berkeley Lab, Berkeley, CA, USA. Rep. Number, 1978.
[17]
T. P. Otanicar, P. E. Phelan, R. S. Prasher, G. Rosengarten, and R. A. Taylor, “Nanofluid-based direct absorption solar collector,” J. Renew. Sust. Ener., vol. 2, p. 033102, 2010.
[18]
G. Huminic and A. Huminic, “Application of nanofluids in heat exchangers: A review,” Renew. Sust. Ener. Rev., vol. 16, pp. 5625–5638, 2012.
[19]
D. A. Nield and A. V. Kuznetsov, “The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid,” Int. J. Heat Mass Transf., vol. 52, pp. 5792–5795, 2009.
[20]
V. Kuznetsov and D. A. Nield, “Natural convective boundary-layer flow of a nanofluid past a vertical plate,” Int. J. Therm. Sci., vol. 49, pp. 243–247, 2010.
[21]
W. A. Khan and I. Pop, “Boundary-layer flow of a nanofluid past a stretching sheet,” Int. J. Heat Mass Transf., vol. 53, pp. 2477–2483, 2010.
[22]
O. D. Makinde and A. Aziz, “Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition,” Int. J. Therm. Sci., vol. 50, pp. 1326– 1332, 2011.
[23]
M. Mustafa, T. Hayat, I. Pop, S. Asghar, and S. Obadiat, “Stagnation-point flow of a nanofluid towards a stretching sheet,” Int. J. Heat Mass Transf., vol. 54, pp. 5588– 5594, 2011.
[24]
M. Mustafa, T. Hayat, and S. Obaidat, “Boundary layer flow of a nanofluid over an exponentially stretching sheet with convective boundary conditions,” Int. J. Num. Meth. Heat Fluid Flow, vol. 23, pp. 945– 969, 2013.
[25]
M. J. Uddin, W. A. Khan, and A. I. Ismail, “MHD free convective boundary layer flow of a nanofluid past a flat vertical plate with Newtonian heating boundary condition,” PLoS One, vol. 7, p. e49499, 2012 .
[26]
H. R. Ashorynejad, M. Sheikholeslami, I. Pop, and D. D. Ganji, “Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field,” Heat Mass Transf., vol. 49, pp. 427–436, 2013.
[27]
M. Mustafa, T. Hayat, and A. Alsaedi, “Unsteady boundary layer flow of nanofluid past an impulsively stretching sheet,” J. Mech., vol. 29, pp. 423–432, 2013.
[28]
M. Turkyilmazoglu, “Unsteady convection flow of some nanofluids past a moving vertical flat plate with heat transfer.” J. Heat Transf. Trans. ASME, vol. 136, Article ID 031704, 2013.
[29]
M. M. Rashidi, S. Abelman, and N. F. Mehr, “Entropy generation in steady MHD flow due to a rotating disk in a nanofluid,” Int. J. Heat Mass Transf., vol. 62, pp. 515–525, 2013.
[30]
V. Kuznetsov and D. A. Nield, “The Cheng–Minkowycz problem for natural convective boundary layer flow in a porous medium saturated by a nanofluid: A revised model,” Int. J. Heat Mass Transf., vol. 65, pp. 682–685, 2013.
[31]
A. V. Kuznetsov and D. A. Nield, “Natural convective boundary-layer flow of a nanofluid past a vertical plate: A revised model,” Int. J. Therm. Sci., vol. 77, pp. 126– 129, 2014.
[32]
M. M. Rashidi, N. Freidoonimehr, A. Hosseini, O. A. Bégand, and T. K. Hung, “Homotopy simulation of nanofluid dynamics from a non-linearly stretching isothermal permeable sheet with transpiration,” Meccan, vol. 49, pp. 469–482, 2014.
[33]
M. M. Rashidi, E. Momoniat, M. Ferdows, and A. Basiriparsa, “Lie group solution for free convective flow of a nanofluid past a chemically reacting horizontal plate in a porous media,” Math. Probl. Eng., Article ID 239082, 2014.
[34]
M. Sheikholeslami, D. D. Ganji, M. Y. Javed, and R. Ellahi, “Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model,” J. Magn. Magn. Mater., vol. 374, pp. 36–43, 2015.
[35]
M. Sheikholeslami and D. D. Ganji, “Ferrohydrodynamic and magnetohydrodynamic effects on ferrofluid flow and convective heat transfer,” Energy, vol. 75, pp. 400– 410, 2014.
[36]
M. Sheikholeslami, S. Abelman, and D. D. Ganji, “Numerical simulation of MHD nanofluid flow and heat transfer considering viscous dissipation,” Int. J. Heat Mass Transf., vol. 79, pp. 212–222, 2014.
[37]
M. Sheikholeslami, M. G. Bandpy, R. Ellahi, and A. Zeeshan, “Simulation of MHD CuO–water nanofluid flow and convective heat transfer considering Lorentz forces,” J. Magn. Magn. Mater., vol. 369, pp. 69–80, 2014.
[38]
J. A. Khan, M. Mustafa, T. Hayat, M. A. Farooq, A. Alsaedi, and S. J. Liao, “On model for three-dimensional flow of nanofluid: An application to solar energy,” J. Moleq. Liq., vol. 194, pp. 41–47, 2014.
[39]
M. Sheikholeslami, M. Gori-Bandpy, D. D. Ganji, and S. Soleimani, “Natural convection heat transfer in a cavity with sinusoidal wall filled with CuO–water nanofluid in presence of magnetic field,” J. Taiwan Inst. Chem. Eng., vol. 45, pp. 40–49, 2014.
[40]
M. Turkyilmazoglu, “Nanofluid flow and heat transfer due to a rotating disk,” Comp. Fluids, vol. 94, pp. 139– 146, 2014.
[41]
V. Marinca and N. Herisanu, “Application of optimal homotopy asymptotic method for solving nonlinear equations arising in hear transfer,” Int. Commun. Heat Mass Transf., vol. 35, pp. 710–715, 2008.
[42]
Z. Niu and C. Wang, “ A one-step optimal homotopy analysis method for nonlinear differential equations,” Commun. Nonlinear Sci. Numer. Simulat., vol. 15, pp. 2026– 2036, 2010.
[43]
S. Liao, “An optimal homotopy-analysis approach for strongly nonlinear differential equations,” Commun. Nonlinear Sci. Numer. Simulat., vol. 15, pp. 2003–2016, 2010.
[44]
S. Abbabsandy, E. Shivanianand, and K. Vajravelu, “ Mathematical properties of h-curve in the frame work of the homotopy analysis method,” Commun. Nonlinear Sci. Numer. Simulat., vol. 16, pp. 4268 –4275, 2011.
[45]
R. A. Van Gorder, “Gaussian waves in the Fitzhugh–Nagumo equation demonstrate one rule of the auxiliary function H(x,t) in the homotopy analysis method,” Commun. Nonlinear Sci. Numer. Simulat., vol. 17, pp. 1233–1240, 2012.
[46]
M. Ghoreishi, A. I. B. M. Ismail, A. K. Alomari, and A. Sami Bataineh, “The comparison between homotopy analysis method and optimal homotopy asymptotic method for nonlinear age-structured population models,” Commun. Nonlinear Sci. Numer. Simulat., vol. 17, pp. 1163–1177, 2012.
[47]
M. Sheikholeslami, H. R. Ashorynejad, D. Domairry, and I. Hashim, “Investigation of the laminar viscous flow in a semi-porous channel in the presence of uniform magnetic field using optimal homotopy asymptotic method,” Sains Malaysiana, vol. 41, pp. 1281 –1285, 2012.
[48]
M. Sheikholeslami, H. R. Ashorynejad, D. D. Ganji, and A. Yıldırım, “ Homotopy perturbation method for three-dimensional problem of condensation film on inclined rotating disk,” Sci. Iranica, vol. 19, pp. 437– 442, 2012.
[49]
M. Sheikholeslami, R. Ellahi, H. R. Ashorynejad, G. Domairry, and T. Hayat, “Effects of heat transfer in flow of nanofluids over a permeable stretching wall in a porous medium,” J. Comput. Theor. Nanosci., vol. 11, pp. 486–496, 2014.
[50]
S. E. B. Maïga, C. T. Nguyen, N. Galanis, G. Roy, T. Maré, and M. Coqueux, “Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension,” Int. J. Num. Meth. Heat Fluid Flow, vol. 16, pp. 275–292, 2006.

Index Terms

  1. Boundary Layer Flow of Nanofluid Over a Nonlinearly Stretching Sheet With Convective Boundary Condition
          Index terms have been assigned to the content through auto-classification.

          Recommendations

          Comments

          Please enable JavaScript to view thecomments powered by Disqus.

          Information & Contributors

          Information

          Published In

          cover image IEEE Transactions on Nanotechnology
          IEEE Transactions on Nanotechnology  Volume 14, Issue 1
          Jan. 2015
          195 pages

          Publisher

          IEEE Press

          Publication History

          Published: 01 January 2015

          Author Tags

          1. shooting method
          2. Convective boundary condition
          3. nanofluid
          4. non-linearly stretching sheet
          5. optimal homotopy analysis method (OHAM)

          Qualifiers

          • Research-article

          Contributors

          Other Metrics

          Bibliometrics & Citations

          Bibliometrics

          Article Metrics

          • 0
            Total Citations
          • 0
            Total Downloads
          • Downloads (Last 12 months)0
          • Downloads (Last 6 weeks)0
          Reflects downloads up to 03 Jan 2025

          Other Metrics

          Citations

          View Options

          View options

          Media

          Figures

          Other

          Tables

          Share

          Share

          Share this Publication link

          Share on social media