Journal of Central South University

, Volume 21, Issue 4, pp 1411–1416 | Cite as

Peristaltic flow in an asymmetric channel with convective boundary conditions and Joule heating

Article

Abstract

The peristaltic transport of viscous fluid in an asymmetric channel is concentrated. The channel walls exhibit convective boundary conditions. Both cases of hydrodynamic and magnetohydrodynamic (MHD) fluids are considered. Mathematical analysis has been presented in a wave frame of reference. The resulting problems are non-dimensionalized. Long wavelength and low Reynolds number approximations are employed. Joule heating effect on the thermal equation is retained. Analytic solutions for stream function and temperature are constructed. Numerical integration is carried out for pressure rise per wavelength. Effects of influential flow parameters have been pointed out through graphs.

Key words

peristaltic flow convective conditions Joule heating 

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References

  1. [1]
    LATHAM T W. Fluid motion in a peristaltic pump [D]. Cambridge: Massachusetts Institute of Technology, MA, USA, 1966.Google Scholar
  2. [2]
    MEKHEIMER K S. Effect of the induced magnetic field on peristaltic flow of a couple stress fluid [J]. Physics Letters A, 2008, 372: 4271–4278.CrossRefMATHGoogle Scholar
  3. [3]
    ABD ELMABOUD Y, MEKHEIMER K S. Non-linear peristaltic transport of a second-order fluid through a porous medium [J]. Applied Mathematical Modelling, 2011, 35: 2695–2710.CrossRefMATHMathSciNetGoogle Scholar
  4. [4]
    EBAID A. Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel [J]. Physics Letters A, 2008, 372: 4493–4499.CrossRefMATHMathSciNetGoogle Scholar
  5. [5]
    HAYAT T, ASGHAR Z, ASGHAR S, MESLOUB S. Influence of inclined magnetic field on peristaltic transport of fourth grade fluid in an inclined asymmetric channel [J]. Journal of the Taiwan Institute of Chemical Engineers, 2010, 5: 553–563.CrossRefGoogle Scholar
  6. [6]
    SRINIVAS S, PUSHPARAJ V. Non-linear peristaltic transport in an inclined asymmetric channel [J]. Communications in Nonlinear Science and Numerical Simulation, 2008, 13: 1782–1795.CrossRefGoogle Scholar
  7. [7]
    YILDIRIM A, SEZER S A. Effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel [J]. Mathematical and Computer Modelling, 2010, 52: 648–625.CrossRefMathSciNetGoogle Scholar
  8. [8]
    HAYAT T, SALEEM N, ALI N. Effect of induced magnetic field on peristaltic transport of a Carreau fluid [J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15: 2407–2423.CrossRefMATHMathSciNetGoogle Scholar
  9. [9]
    HAYAT T, ABBASI F M. Variable viscosity effects on the peristaltic motion of a third order fluid [J]. International Journal for Numerical Methods in Fluids, 2011, 67: 1500–1515.CrossRefMATHGoogle Scholar
  10. [10]
    WANG Y, ALI N, HAYAT T, OBERLACK M. Peristaltic motion of a magnetohydrodynamic micropolar fluid in a tube [J]. Appl Math Modelling, 2011, 35: 3737–3750.CrossRefMATHMathSciNetGoogle Scholar
  11. [11]
    VAJRAVELU K, SREENADH S, LAKSHMINARAYANA P. The influence of heat transfer on peristaltic transport of a Jeffrey fluid in a vertical porous stratum [J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16: 3107–3125.CrossRefMATHMathSciNetGoogle Scholar
  12. [12]
    AKBAR N, HAYAT T, NADEEM S, OBAIDAT S. Peristaltic flow of a Williamson fluid in an inclined asymmetric channel with partial slip and heat transfer [J]. International Journal of Heat and Mass Transfer, 2012, 55: 1855–1862.CrossRefGoogle Scholar
  13. [13]
    HAYAT T, NOREEN S. Peristaltic transport of fourth grade fluid with heat transfer and induced magnetic field [J]. C. R. Mecanique, 2010, 338: 518–528.CrossRefMATHGoogle Scholar
  14. [14]
    HAYAT T, ABBASI F M, AWATIF A, HENDI. Heat transfer analysis for peristaltic mechanism in variable viscosity fluid [J]. Chinese Physics Letters, 2011, 28: 044701.CrossRefGoogle Scholar
  15. [15]
    TRIPATHI D. A mathematical model for swallowing of food bolus through the oesophagus under the influence of heat transfer [J]. International Journal of Thermal Sciences, 2012, 51: 91–101.CrossRefGoogle Scholar
  16. [16]
    HINA S, HAYAT T, ASGHAR S, HENDI A A. Influence of compliant walls on peristaltic motion with heat/mass transfer and chemical reaction [J]. International Journal of Heat and Mass Transfer, 2012, 55: 3386–3394.CrossRefGoogle Scholar
  17. [17]
    HAYAT T, NOREEN S, ALHOTHUALI M, ASGHAR S, ALHOMAIDAN A. Peristaltic flow under the effects of an induced magnetic field and heat and mass transfer [J]. International Journal of Heat and Mass Transfer, 2012, 55: 443–452.CrossRefMATHGoogle Scholar
  18. [18]
    ABBASI F M, HAYAT T, ALSAEDI A, AHMED B. Soret and Dufour effects on peristaltic transport of MHD fluid with variable viscosity [J]. Appl Math Inf Sci, 2014, 8: 211–219.CrossRefGoogle Scholar
  19. [19]
    HAYAT T, ABBASI F M, OBAIDAT S. Peristaltic motion with Soret and Dufour effects [J]. Magnetohydrodynamics, 2011, 47: 295–302.Google Scholar
  20. [20]
    MUSTAFA M, HINA S, HAYAT T, ALSAEDI A. Influence of wall properties on the peristaltic flow of a nanofluid: Analytic and numerical solutions [J]. International Journal of Heat and Mass Transfer, 2012, 55: 4871–4877.CrossRefGoogle Scholar
  21. [21]
    AKBAR N S, NADEEM S, HAYAT T. Simulation of thermal and velocity slip on the peristaltic flow of a Johnson-Segalman fluid in an inclined asymmetric channel [J]. International Journal of Heat and Mass Transfer, 2012, 55: 5495–5502.CrossRefGoogle Scholar
  22. [22]
    KOTHANDAPANI M, SRINIVAS S. Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel [J]. International Journal of Non-Linear Mechanics, 2008, 43: 915–924.CrossRefGoogle Scholar

Copyright information

© Central South University Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Abbasi Fahad Munir
    • 1
  • Hayat Tasawar
    • 1
    • 2
  • Ahmad Bashir
    • 2
  1. 1.Department of MathematicsQuaid-I-Azam University 45320IslamabadPakistan
  2. 2.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

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