Back
 JAMP  Vol.4 No.2 , February 2016
Transient Combined Convective Heat Transfer over a Stretching Surface in a Non-Newtonian Nanofluid Using Buongiorno’s Model
Abstract: The present paper investigates the transient mixed convective boundary layer flow of an incompressible non-Newtonian quiescent nanofluid adjacent to a vertical stretching surface. The effects of the Brownian motion and thermophoresis are included for the nanofluid. Using appropriate non-similarity transformations the non-dimensional, coupled and highly non-linear system of equations is solved numerically using the efficient Keller-box implicit finite difference method for the whole transient from t=0 (initial state) to (final steady-state flow). The box method is unconditionally stable. Numerical results for dimensionless velocity (f’), micro-rotation (g), temperature (θ), nanoparticle volume fraction (Φ) at final steady state flow, skin friction function (), Nusselt number function () and Sherwood number function () have been presented on various parameters inform of tables and graphs. The results indicate that as Nb and Nt increase, the Nusselt number decreases whereas Sherwood number increases at initial and early state time but decreases at the final steady state time. As the K increases, the friction factor decreases whereas surface mass transfer rate and the surface heat transfer rates slightly increase. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work. The study has many practical applications such as extrusion of plastic sheets, paper production, glass blowing, metal spinning and drawing plastic films.
Cite this paper: Gorla, R. , Vasu, B. and Siddiqa, S. (2016) Transient Combined Convective Heat Transfer over a Stretching Surface in a Non-Newtonian Nanofluid Using Buongiorno’s Model. Journal of Applied Mathematics and Physics, 4, 443-460. doi: 10.4236/jamp.2016.42050.
References

[1]   Das, S.K., Choi, S.U.S., Yu, W. and Pradet, T. (2007) Nanofluids: Science and Technology. Wiley, Hoboken.
http://dx.doi.org/10.1002/9780470180693

[2]   Buongiorno, J. (2006) Convective Transport in Nanofluids. Journal of Heat Transfer, 128, 240-250.
http://dx.doi.org/10.1115/1.2150834

[3]   Xuan, Y.M. and Roetzel, W. (2000) Conceptions for Heat Transfer Correlation of Nanofluids. International Journal of Heat and Mass Transfer, 43, 3701-3707.
http://dx.doi.org/10.1016/S0017-9310(99)00369-5

[4]   Yu, W. and Xie, H.Q. (2011) A Review on Nanofluids: Preparation, Stability Mechanisms, and Applications, Hindawi Publishing Corporation. Journal of Nanomaterials, 2012, Article ID: 435873.

[5]   Mahbubul, I.M., Saidur, R. and Amalina, M.A. (2012) Latest Developments on the Viscosity of Nanofluids. International Journal of Heat and Mass Transfer, 55, 874-885. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.10.021

[6]   Aberoumand, S., Aberoumand, H. and Javaherdeh, K. (2013) Improve Heat Transfer by Using Nanofluids: A Review. American Journal of Advanced Scientific Research (AJASR), 1, 375-386.

[7]   Gupta, M., Arora, N., Kumar, R., Kumar, S. and Dilbaghi, N. (2014) A Comprehensive Review of Experimental Investigations of Forced Convective Heat Transfer Characteristics for Various Nanofluids. International Journal of Mechanical and Materials Engineering, 9, 1-21.
http://dx.doi.org/10.1007/s11242-009-9413-2

[8]   Kuznetsov, A.V. and Nield, D.A. (2010) Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: Brinkman Model. Transport in Porous Media, 81, 409-422.
http://dx.doi.org/10.1007/s11242-009-9413-2

[9]   Kuznetsov, A.V. and Nield, D.A. (2011) Double-Diffusive Natural Convective Boundary-Layer Flow of a Nanofluid past a Vertical Plate. International Journal of Thermal Sciences, 50, 712-717.
http://dx.doi.org/10.1016/j.ijthermalsci.2011.01.003

[10]   Bachok, N., Ishak, A. and Pop, I. (2012) Flow and Heat Transfer Characteristics on a Moving Plate in a Nanofluid. International Journal of Heat and Mass Transfer, 55, 642-648.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.10.047

[11]   Gorla, R.S.R., Chamkha, A.J. and Hossain, A. (2009) Mixed Convection Flow of Non-Newtonian Fluid from a Slotted Vertical Surface with Uniform Surface Heat Flux. Canadian Journal of Chemical Engineering, 87, 534-540.
http://dx.doi.org/10.1002/cjce.20195

[12]   Gorla, R.S.R. and Kumari, M. (2013) Mixed Convection in an Axisymmetric Stagnation Flow of a Non-Newtonian Nanofluid on a Vertical Cylinder. Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanoengineering and Nanosystems, 227, 150-160.

[13]   Chamkha, A.J., Rashad, A.M. and Aly, A. (2013) Transient Natural Convection Flow of a Nanofluid over a Vertical Cylinder. Meccanica, 48, 71-81.
http://dx.doi.org/10.1007/s11012-012-9584-8

[14]   RamReddy, Ch., Murthy, P.V.S.N., Chamkha, A.J. and Rashadd, A.M. (2013) Soret Effect on Mixed Convection Flow in a Nanofluid under Convective Boundary Condition. International Journal of Heat and Mass Transfer, 64, 384-392. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.04.032

[15]   Vendabai, K. and Sarojamma, G. (2014) Unsteady Convective Boundary Layer Flow of a Nanofluid over a Stretching Surface in the Presence of a Magnetic Field and Heat Generation. International Journal of Emerging Trends in Engineering and Development, 3, 214-230.

[16]   Kumari, M., Gireesha, B.J. and Gorla, R.S.R. (2015) Heat and Mass Transfer in a Nanofluid Film on an Unsteady Stretching Surface. Journal of Nanofluids, 4, 560-567.

[17]   Eringen, A.C. (1966) Theory of Micropolar Fluids. Journal of Mathematics and Mechanics, 16, 1-18.
http://dx.doi.org/10.1512/iumj.1967.16.16001

[18]   Eringen, A.C. (2001) Microcontinuum Field Theories II: Fluent Media. Springer, New York.

[19]   Ariman, T., Turk, M.A. and Sylvester, N.D. (1973) Microcontinuum Fluid Mechanics—A Review. International Journal of Engineering Science, 11, 905-930.
http://dx.doi.org/10.1016/0020-7225(73)90038-4

[20]   Ariman, T., Turk, M.A. and Sylvester, N.D. (1974) Applications of Micro-Continuum Fluid Mechanics. International Journal of Engineering Science, 12, 273-293.
http://dx.doi.org/10.1016/0020-7225(74)90059-7

[21]   Bég, O.A., Bhargava, R., Rawat, S., Takhar, H.S. and Bég, T.A. (2007) Numerical Study of Grashof and Darcy Number Effects on Natural Convection Heat and Species Transfer Past a Stretching Surface in Micropolar Saturated-Porous Medium with Viscous Heating. International Journal of Fluid Mechanics Research, 34, 287-307.
http://dx.doi.org/10.1615/InterJFluidMechRes.v34.i4.10

[22]   Kim, Y.-J. (2004) Heat and Mass Transfer in MHD Micropolar Flow over a Vertical Moving Porous Plate in a Porous medium. Transport in Porous Media, 56, 17-37.
http://dx.doi.org/10.1023/B:TIPM.0000018420.72016.9d

[23]   Gorla, R.S.R., Slaouti, A. and Takhar, H.S. (1998) Free Convection in Micropolar Fluids over a Uniformly Heated Vertical Plate. International Journal of Numerical Methods for Heat & Fluid Flow, 8, 504-518.
http://dx.doi.org/10.1108/09615539810220261

[24]   Rees, D.A.S. and Bassom, A.P. (1996) The Blasius Boundary Layer Flow of a Micropolar Fluid. International Journal of Engineering Science, 34, 133-124.
http://dx.doi.org/10.1016/0020-7225(95)00058-5

[25]   Lien, F.S. and Chen, C.C. (1987) Mixed Convection of Micropolar Fluid about a Sphere with Blowing and Suction. International Journal of Engineering Science, 34, 1301-1310.

[26]   Nazar, R., Amin, N., Grosan, T. and Pop, I. (2003) Mixed Convection Boundary Layer Flow about an Isothermal Sphere in Micropolar Fluid. International Journal of Thermal Sciences, 42, 283-293.
http://dx.doi.org/10.1016/S1290-0729(02)00027-3

[27]   Kumari, M., Slaouti, A., Takhar, H.S., Nakamura, S. and Nath, G. (1996) Unsteady Free Convection Flow over a Continuous Moving Vertical Surface. Acta Mechanica, 116, 75-82.
http://dx.doi.org/10.1007/BF01171421

[28]   Ishak, A., Nazar, R. and Pop, I. (2006) Unsteady Mixed Convection Boundary Layer Flow Due to a Stretching Vertical Surface. The Arabian Journal of Science and Engineering, 31, 165-182.

[29]   Ishak, A., Nazar, R. and Pop, I. (2008) Heat Transfer over a Stretching Surface with Variable Surface Heat Flux in Micropolar Fluids. Physics Letters A, 372, 559-561.
http://dx.doi.org/10.1016/j.physleta.2007.08.003

[30]   Pop, I. and Na, T.Y. (1996) Unsteady Flow Past a Stretching Sheet. Mechanics Research Communications, 23, 413-422.
http://dx.doi.org/10.1016/0093-6413(96)00040-7

[31]   Wang, C.Y., Du, G., Miklavcic, M. and Chang, C.C. (1997) Impulsive Stretching of a Surface in a Viscous Fluid. SIAM (Society for Industrial and Applied Mathematics) Journal on Applied Mathematics, 57, 1-14.
http://dx.doi.org/10.1137/S0036139995282050

[32]   Rashad, A.M. and EL-Kabeir, S.M.M. (2010) Heat and Mass Transfer in Transient Flow by Mixed Convection Boundary Layer over a Stretching Sheet Embedded in a Porous Medium with Chemically Reactive Species. Journal of Porous Media, 13, 75-85.
http://dx.doi.org/10.1615/JPorMedia.v13.i1.70

[33]   Rohni, A.M., Ahmad, S. and Pop, I. (2012) Flow and Heat Transfer over an Unsteady Shrinking Sheet with Suction in Nanofluids. International Journal of Heat and Mass Transfer, 55, 1888-1895.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.11.042

[34]   Cebeci, T. and Bradshaw, P. (1984) Physical and Computational Aspects of Convective Heat Transfer. Springer, New York.
http://dx.doi.org/10.1007/978-3-662-02411-9

[35]   Keller, H.B. (1978) Numerical Methods in Boundary-Layer Theory. Annual Review of Fluid Mechanics, 10, 417-433.
http://dx.doi.org/10.1146/annurev.fl.10.010178.002221

[36]   Vasu, B., Prasad, V.R., Bég, O.A., Aziz, A. and Prashad, R.D. (2010) Numerical Analysis of Magnetohydrodynamic Nonlinear Convection Heat and Mass Transfer from a Sphere in a Non-Darcian Variable-Porosity Medium. International Journal of Applied Mathematics, 17, 64-111.

 
 
Top