Skip to main content
Log in

Effects of Viscous Dissipation and Convective Boundary Conditions on Blasius and Sakiadis Problems for Casson Fluid

  • Short Communication
  • Published:
National Academy Science Letters Aims and scope Submit manuscript

Abstract

In this article, two types of problems are investigated. The flow and heat transfer over: (1) a static flat plate (Blasius problem) and (2) a moving flat plate (Sakiadis problem) are considered. Convective boundary conditions are used to formulate the energy equation. Suitable similarity transform has been employed to reduce the governing nonlinear partial differential equations to a set of somewhat simpler nonlinear differential equations. These equations are then solved numerically by using sixth order Runge–Kutta method. Influences of different emerging parameters on both the problems are presented graphically coupled with comprehensive discussions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

References

  1. Blasius H (1908) Grenzschichten in Flussigkeiten mit kleiner reibung. Zeitschrift für angewandte Mathematik und Physik ZAMP 56:1–37

    Google Scholar 

  2. Sakiadis BC (1961) Boundary-layer behaviour on continuous solid surfaces, boundary layer equations for 2-dimensional and axisymmetric flow. Am Inst Chem Eng J 7:26–28

    Article  Google Scholar 

  3. Takhar HS, Nitu S, Pop I (1991) Boundary layer flow due to a moving plate: variable fluid properties. Acta Mech 90:37–42

    Article  Google Scholar 

  4. He JH (2003) A simple perturbation approach to Blasius equation. Appl Math Comput 140:217–222

    Article  Google Scholar 

  5. Wang L (2004) A new algorithm for solving classical Blasius equation. Appl Math Comput 157:1–9

    Article  Google Scholar 

  6. Butt AS, Munawar S, Ali A, Mehmood A (2012) Entropy generation in the Blasius flow under thermal radiation. Phys Scr 85:035008 (6 pp)

    Article  Google Scholar 

  7. Smolentsev S, Abdou M, Morley NB, Sawan S, Malang S, Wong C (2006) Numerical analysis of MHD flow and heat transfer in a poloidal channel of the DCLL blanket with a SiCf/SiC flow channel insert. Fusion Eng Des 81:549–553

    Article  Google Scholar 

  8. Abbasbandy S (2006) The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phys Lett A 360:109–113

    Article  Google Scholar 

  9. Abbasbandy S (2007) Homotopy analysis method for heat radiation equations. Int Commun Heat Mass Transfer 34:380–387

    Article  Google Scholar 

  10. Aziz A (2009) A similarity solution for laminar thermal boundary layer over flat plate with a convective surface boundary condition. Commun Nonlinear Sci Numer Simul 14:064–1068

    Article  Google Scholar 

  11. Aziz A (2010) Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition. Commun Nonlinear Sci Numer Simul 15:573–580

    Article  Google Scholar 

  12. Parand K, Abbasbandy S, Kazem S, Rezaei AR (2011) Comparison between two common collocation approaches based on radial basis functions for the case of heat transfer equations arising in porous medium. Commun Nonlinear Sci Numer Simul 16:1396–1407

    Article  Google Scholar 

  13. Khan U, Ahmed N, Zaidi ZA, Asadullah M, Mohyud-Din ST (2014) MHD squeezing flow between two infinite plates. Ain Shams Eng J 5:187–192

  14. Makinde OD (2010) Similarity solution of hydromagnetic heat and mass transfer over a vertical plate with a convective surface boundary condition. Int J Phys Sci 5:700–710

    Google Scholar 

  15. Noor NFM, Abbasbandy S, Hashim I (2012) Heat and mass transfer of thermophoretic MHD flow over an inclined radiate isothermal permeable surface in the presence of heat source/sink. Int J Heat Mass Transf 55:2122–2128

    Article  Google Scholar 

  16. Hussain A, Mohyud-Din ST, Cheema TA (2012) Analytical and numerical approaches to squeezing flow and heat transfer between two parallel disks with velocity slip and temperature jump. Chin Phys Lett 29:114705

    Article  Google Scholar 

  17. Mrill WE, Benis AM, Gilliland ER, Sherwood TK, Salzman EW (1965) Pressure flow relations of human blood hollow fibers at low flow rates. J Appl Physiol 20:954–967

    Google Scholar 

  18. McDonald DA (1974) Blood Flows in Arteries, 2nd edn. Arnold, London

    Google Scholar 

  19. Nadeem S, Haq RU, Lee C (2012) MHD flow of a Casson fluid over an exponentially shrinking sheet. Sci Iran 19:1150–1553

    Article  Google Scholar 

  20. Ahmed N, Khan U, Khan SIU, Jun YX, Zaidi ZA, Mohyud-Din ST (2013) Magneto hydrodynamic (MHD) Squeezing flow of a Casson fluid between parallel disks. Int J Phys Sci 8:1788–1799

    Google Scholar 

  21. Nadeem S, Haq RU, Akbar NS, Khan ZH (2013) MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet. Alex Eng J 52:577–582

    Article  Google Scholar 

  22. Schlichting H, Gersten K (2000) Boundary layer theory, 8th edn. Springer, New York

    Book  Google Scholar 

  23. Makinde OD (2012) Analysis of Sakiadis flow of nanofluids with viscous dissipation and Newtonian heating. Appl Math Mech 33:1545–1554

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Syed Tauseef Mohyud-Din.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, S.I., Khan, U., Ahmed, N. et al. Effects of Viscous Dissipation and Convective Boundary Conditions on Blasius and Sakiadis Problems for Casson Fluid. Natl. Acad. Sci. Lett. 38, 247–250 (2015). https://doi.org/10.1007/s40009-014-0331-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40009-014-0331-7

Keywords

Navigation