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Water Boundary Layer Flow over an Exponentially Permeable Stretching Sheet with Variable Viscosity and Prandtl Number

  • Abhishek Kumar SinghEmail author
  • N. Govindaraj
  • S. Roy
Conference paper
  • 7 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 308)

Abstract

The present work focus on water boundary layer flow over an exponential permeable stretching sheet in the presence of suction/injection with variable viscosity and prandtl number. The nonlinear partial differential equations governing flow and thermal fields are presented in non-dimensional form using suitable non-similar transformation. Finally non dimensional partial differential the equations are solved by the implicit finite difference method in combination with the Quasi-linearization technique. The numerical results for skin-friction and local Nusselt number are shown graphically to display effects of physical parameters.

Keywords

Exponential permeable stretching sheet Water boundary layer Variable Prandtl number Quasilinearization technique Variable viscosity 

Nomenclature

Pr

Prandtl number

f

Dimensionless streamfunction

\(C_{p}\)

Specific heat at constant pressure

T

Temperature

g

Acceleration due to gravity

\(U_{W}\)

Moving plate velocity

\(Nu_{x}\)

Nusselt number

\(Cf_{x}\)

Skin friction coefficient

\(U_{\infty }\)

Free stream velocity

v

Velocity component in the y direction

u

Velocity component in the x direction

\(\nu \)

Kinematic viscosity

\(\rho \)

Density

xy

Cartesian coordinates

\(Re_{L}\)

Local Reynolds number

\(\mu \)

Dynamic viscosity

Notes

Acknowledgements

Let me thanks organization team of International Conference on Mathematical Modelling and Scientific Computing who brought the platform to express our idea about mathematical modelling and simulation in applied mathematics. The current work is completely based on modelling of fluid dynamics problem and solution has been obtained by using finite difference method and given in terms of velocity profile (F), temperature profile \((\theta )\), skin friction coefficient \((C_{fx} \left( Re_L\xi exp({\xi })\right) ^{1/2})\) and heat transfer coefficients \((Nu_x (Re_L\xi exp({\xi }))^{-1/2})\).

References

  1. 1.
    ElbElbashbeshy, E.M.A.: Heat transfer over an exponentially stretching continuous surface with suction. Arch. Mech. 53, 643–651 (2001)Google Scholar
  2. 2.
    Zaimi, K., Ishak, A.: Boundary layer flow and heat transfer over a permeable stretching /shrinking sheet with convective boundary condition. J. Appl. Fluid Mech. 8, 499–505 (2015)CrossRefGoogle Scholar
  3. 3.
    Naramgari, S., Sulochana, C.: MHD flow over a permeable stretching sheet of a nanofluid with suction/injection. Alexandria Eng. J. 55, 819–827 (2016)CrossRefGoogle Scholar
  4. 4.
    Hafidzuddin, E.H., Nazar, R., Arifin, N.M., Pop, I.: Boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity. J. Appl. Fluid Mech. 9, 2025–2036 (2016)CrossRefGoogle Scholar
  5. 5.
    Ishak, I., Nazar, R., Pop, I.: The effects of transpiration on the flow and heat transfer over a moving permeable surface in a parallel stream, chem. Eng. J. 148, 63–67 (2009)Google Scholar
  6. 6.
    Patil, P.M., Latha, D.N., Roy, S., Momoniat, E.: Non similar solutions of mixed convection flow from an exponentially stretching surface. Ain Shams Eng. J. 8, 697–705 (2015)CrossRefGoogle Scholar
  7. 7.
    Olusoji, E.: Heat and mass transfer in MHD micropolar fluid flow over a stretching sheet with velocity and thermal slip conditions (2018)Google Scholar
  8. 8.
    Hayat, T., Imtiaz, M., Alsaedi, A.: MHD flow of Nanofluid over permeable stretching sheet with convective boundary conditions. Open J. Fluid Dyn. 8(2), 195 (2014)Google Scholar
  9. 9.
    Srinvasulu, T., Bandari, Shankar: MHD boundary layer flow of nanofluid over a nonlinear stretching sheet with effect of non-uniform heat source and chemical reaction. J. Nanofluids 6(4), 637–646 (2017)CrossRefGoogle Scholar
  10. 10.
    Hayat, T., Shafiq, A., Alsaedi, A., Shahzad, S.A.: Unsteady MHD flow over exponentially stretching sheet with slip conditions. Appl. Math. Mech. 37(2), 193–208 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Bidin, Biliana, Nazar, Roslinda: Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation. Eur. J. Sci. Res. 33, 710–717 (2009)Google Scholar
  12. 12.
    Cortel, R.: Fluid flow and radiative non linear heat transfer over a stretching sheet. J. King Saud Univ. Sci. 26, 161–167 (2014)CrossRefGoogle Scholar
  13. 13.
    Singh, P.J., Roy, S., Pop, I.: Unsteady mixed convection from a rotating vertical slender cylinder in an axial flow. Int. J. Heat Mass Transf. 51, 1423–1430 (2008)CrossRefGoogle Scholar
  14. 14.
    Tsou, F.K., Sparrow, E.M., Goldstein, R.J.: Flow and heat transfer in the boundary layer on a continuous moving surface. Int. Heat Mass Transfer 10, 219–235 (1967)CrossRefGoogle Scholar
  15. 15.
    Soundalgekar, V.M., Murty, T.V.R.: Heat transfer in flow past a continuous moving plate with variable temperature. Warme-und Stoffubertragung 14, 91–93 (1980)CrossRefGoogle Scholar
  16. 16.
    Ali, M.E.: On thermal boundary layer on a power-law stretched surface with suction or injection. Int. J. Heat Fluid Flow 16, 280–290 (1995)CrossRefGoogle Scholar
  17. 17.
    Moutsoglou, T.S.Chen: Buoyancy effects in boundary layers on inclined, continuous, moving sheets. ASME J. Heat Transf. 102, 371–373 (1980)CrossRefGoogle Scholar
  18. 18.
    Chen, C.H.: Laminar mixed convection adjacent to vertical, continuously stretching sheets. Heat Mass Transf. 33, 471–476 (1998)CrossRefGoogle Scholar
  19. 19.
    Varga, R.S.: Matrix Itrative Analysis. Prentice-Hall, Englewood Cliffs, NJ (2000)CrossRefGoogle Scholar
  20. 20.
    Tsou, F.K., Sparrow, E.M., Goldstein, R.J.: Flow and heat transfer in the boundary layer on a continuous moving surface. Int. J. Heat Mass Transf. 10, 219–235 (1967)CrossRefGoogle Scholar
  21. 21.
    Moutsoglou, A., Chen, T.S.: Buoyancy effects in boundary layers on inclined continuous moving sheets. ASME J. Heat Transf. 102, 371–373 (1980)CrossRefGoogle Scholar
  22. 22.
    Chen, C.H.: Laminar mixed convection adjacent to vertical continuously stretching sheets. Heat Mass Transf. 33, 471–476 (1998)CrossRefGoogle Scholar
  23. 23.
    Lide, D.R. (ed.): CRC Handbook of Chemistry and Physics, 71st edn. CRC Press, BocaRaton, FL (1990)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Mathematics Division, School of Advanced ScienceVIT UniversityChennaiIndia
  2. 2.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

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