Share This Article:

Mixed Convection MHD Flow of a Casson Nanofluid over a Nonlinear Permeable Stretching Sheet with Viscous Dissipation

Abstract Full-Text HTML XML Download Download as PDF (Size:446KB) PP. 1580-1593
DOI: 10.4236/jamp.2015.312182    2,715 Downloads   3,389 Views   Citations

ABSTRACT

The present study deals with the mixed convection MHD flow of a Casson nanofluid over a nonlinear permeable stretching sheet with viscous dissipation. The governing partial differential equations are transformed into nonlinear coupled ordinary differential equations with the help of suitable similarity transformations. These equations were then solved numerically by using an implicit finite difference method known as Keller-Box method. The effects of various parameters such as magnetic parameter (M), Casson parameter (β), local Grashoff number (Gr), local modified Grashoff number (Gc), nonlinear parameter (n), Eckert number (Ec) on velocity, temperature and concentration were discussed and presented graphically. It is found that a larger value of Casson parameter leads to decrease the velocity and temperature. Increase in the local Grashoff number reduces the temperature. Nanoparticle concentration is decreased for the larger values of local Modified Grashoff number. The numerical values of skin friction, Nusselt number and Sherwood number are presented in tables.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Besthapu, P. and Bandari, S. (2015) Mixed Convection MHD Flow of a Casson Nanofluid over a Nonlinear Permeable Stretching Sheet with Viscous Dissipation. Journal of Applied Mathematics and Physics, 3, 1580-1593. doi: 10.4236/jamp.2015.312182.

References

[1] Sakiadis, B.C. (1961) Boundary-Layer Behavior on Continuous Solid Surfaces. AIChE Journal, 7, 26-28.
http://dx.doi.org/10.1002/aic.690070108
[2] Sakiadis, B.C. (1961) Boundary Layer Behavior on Continuous Solid Surfaces: II. Boundary Layer on a Continuous Flat Surface. AIChE Journal, 7, 221-225.
http://dx.doi.org/10.1002/aic.690070211
[3] Erickson, L.E., Fan, L.T. and Fox, V.G. (1966) Heat and Mass Transfer on Moving Continuous Flat Plate with Suction or Injection. Industrial and Engineering Chemistry Fundamentals, 5, 19-25.
http://dx.doi.org/10.1021/i160017a004
[4] Magyari, E. and Keller, B. (2000) Exact Solutions for Self Similar Boundary Layer Flows Induced by Permeable Stretching Walls. European Journal of Mechanics B—Fluids, 19, 109-122.
http://dx.doi.org/10.1016/S0997-7546(00)00104-7
[5] Gupta, P.S. and Gupta, A.S. (1977) Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing. Canadian Journal of Chemical Engineering, 55, 744-746. http://dx.doi.org/10.1002/cjce.5450550619
[6] Vajravelu, K. (2001) Viscous Flow over a Nonlinearly Stretching Sheet. Applied Mathematics and Computation, 124, 281-288.
http://dx.doi.org/10.1016/S0096-3003(00)00062-X
[7] Bhargava, R., Sharma, S., Takhar, H.S., Beg, O.A. and Bhargava, P. (2007) Numerical Solutions for Micropolartransport Phenomena over a Nonlinear Stretching Sheet. Nonlinear Analysis Modeling and Control, 12, 45-63.
[8] Prasad, K.V., Vajravelu, K. and Datti, P.S. (2010) Mixed Convection Heat Transfer over a Non-Linear Stretching Surface with Variable Fluid Properties. International Journal of Non-Linear Mechanics, 45, 320-330.
http://dx.doi.org/10.1016/j.ijnonlinmec.2009.12.003
[9] Choi, S.U.S. (1995) Enhancing Thermal Conductivity of Fluids with Nanoparticles. Proceedings of the ASME International Mechanical Engineering Congress and Exposition, 66, 99-105.
[10] Khan, W.A. and Pop, I. (2010) Boundary-Layer Flow of a Nanofluid past a Stretching Sheet. International Journal of Heat and Mass Transfer, 53, 2477-2483.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.01.032
[11] Buongiorno, J. (2006) Convective Transport in Nanofluids. Journal of Heat Transfer, 128, 240-250.
http://dx.doi.org/10.1115/1.2150834
[12] VanGorder, R.A., Sweet, E. and Vajravelu, K. (2010) Nano Boundary Layers over Stretching Surfaces. Communications in Nonlinear Science and Numerical Simulation, 15, 1494-1500.
http://dx.doi.org/10.1016/j.cnsns.2009.06.004
[13] Hassani, M., Tabar, M.M., Nemati, H., Domairry, G. and Noori, F. (2011) An Analytical Solution for Boundary Layer Flow of a Nanofluid Past a Stretching Sheet. International Journal of Thermal Science, 50, 2256-2263.
http://dx.doi.org/10.1016/j.ijthermalsci.2011.05.015
[14] Akyildiz, F.T., Bellout, H., Vajravelu, K. and VanGorder, R.A. (2011) Existence Results for Third Order Nonlinear Boundary Value Problems Arising in Nano Boundary Layer Fluid Flows over Stretching Surfaces Nonlinear Analysis: Real World Applications, 12, 2919-2930.
http://dx.doi.org/10.1016/j.nonrwa.2011.02.017
[15] Rana, P. and Bhargava, R. (2012) Flow and Heat Transfer of a Nanofluid over a Nonlinearlynstretching Sheet: A Numerical Study. Communications in Nonlinear Science and Numerical Simulation, 17, 212-226.
[16] Mabood, F., Khan, W.A. and Ismail, A.I.M. (2015) MHD Boundary Layer Flow and Heat Transfer of Nanofluids over a Nonlinear Stretching Sheet: A Numerical Study. Journal of Magnetism and Magnetic Materials, 374, 569-576.
http://dx.doi.org/10.1016/j.jmmm.2014.09.013
[17] Fredrickson, A.G. (1964) Principles and Applications of Rheology. Prentice-Hall, Englewood Cliffs.
[18] Nakamura, M. and Sawada, T. (1988) Numerical Study on the Flow of a Non-Newtonian Fluid through an Axisymmetric Stenosis. ASME Journal of Biomechanical Engineering, 110, 137-143.
http://dx.doi.org/10.1115/1.3108418
[19] Mustafa, M., Hayat, T., Pop, I. and Aziz, A. (2011) Unsteady Boundary Layer Flow of a Casson Fluid Due to an Impulsively Started Moving Flat Plate. Heat Transfer Asian Research, 40, 563-576.
[20] Nadeem, S., Haq, R.U. and Lee, C. (2012) MHD Flow of a Casson Fluid over an Exponentially Shrinking Sheet. Scientia Iranica, 19, 1550-1553.
http://dx.doi.org/10.1016/j.scient.2012.10.021
[21] Bhattacharyya, K., Hayat, T. and Alsaedi, A. (2014) Exact Solution for Boundary Layer Flow of Casson Fluid over a Permeable Stretching/Shrinking Sheet. ZAMM, Zeitschrift für Angewandte Mathematik und Mechanik, 96, 522-528.
[22] Bhattacharyya, K., Hayatand, T. and Alsaedi, A. (2013) Analytic Solution for Magneto Hydrodynamic Boundary Layer Flow of Casson Fluid over a Stretching/Shrinking Sheet with Wall Mass Transfer. Chinese Physics B, 22, Article ID: 024702.
[23] Mukhopadhyay, S. (2013) Casson Fluid Flow and Heat Transfer over a Nonlinearly Stretching Surface. Chinese Physics B, 22, Article ID: 074701.
[24] Kameswaran, P.K., Shaw, S. and Sibanda, P. (2014) Dual Solutions of Casson Fluid Flow over a Stretching or Shrinking Sheet. Sadhana, Indian Academy of Science, 39, 1573-1583.
[25] Haq, R.U., Nadeem, S., Khan, Z.H. and Okedayo, T.G. (2015) Convective Heat Transfer and MHD Effects on Casson-Nano Fluid Flow over a Shrinking Sheet. Central European Journal of Physics, 12, 862-871.
[26] Hussain, T., Shehzad, S.A., Alsaedi, A., Hayat, T. and Ramzan, M. (2015) Flow of Casson-Nano Fluid with Viscous Dissipation and Convective Conditions: A Mathematical Model. Journal of Central South University, 22, 1132-1140.
[27] Mustafa, M. and Khan, J.A. (2015) Model for Flow of Casson-Nano Fluid Past a Nonlinearly Stretching Sheet Considering Magnetic Field Effects. AIP Advances, 5, Article ID: 077148.
[28] Cebeci, T. and Bradshaw, P. (1984) Physical and Computational Aspects of Convective Heat Transfer. Springer, Berlin Heidelberg.
http://dx.doi.org/10.1007/978-3-662-02411-9
[29] Vajravelu, K., Prasad, K.V. and Ng, C.-O. (2013) Unsteady Convective Boundary Layer Flow of a Viscous Fluid at a Vertical Surface with Variable Fluid Properties. Nonlinear Analysis: Real World Applications, 14, 455-464.
http://dx.doi.org/10.1016/j.nonrwa.2012.07.008

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.