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Slip Viscous Flow Over an Exponentially Stretching Porous Sheet with Thermal Convective Boundary Conditions

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Abstract

The aim of the paper is to investigate the boundary layer flow, heat and mass transfer towards the exponentially stretching sheet in a viscous fluid. Similarity transformations are used to convert non-linear governing equations of the flow into non-linear ordinary differential equations. The successive linearization method is used to linearize the resulting ordinary differential equations and then solved by Chebyshev spectral collocation method. A quantitative analysis is made with the previously published results for special cases. The numerical results for the physical parameters on the development of the flow, temperature, concentration, skin friction coefficient, heat and mass transfer are given. It can be concluded from the present analysis that an increase in slip parameter decreases the velocity and increases the temperature and concentration. The heat transfer coefficient is increasing and the velocity, temeperature and concentration are decreasing with the increase in the suction parameter. The temperature and heat transfer coefficient are increasing with the increase in the Biot number.

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References

  1. Sakiadis, B.C.: Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE. J. 7(1), 26–28 (1961)

  2. Sakiadis, B.C.: Boundary-layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface. AIChE. J. 7(2), 221–225 (1961)

  3. Crane, L.J.: Flow past a stretching plate. J. Appl. Math. Phys (ZAMP) 21, 645–647 (1970)

    Article  Google Scholar 

  4. Beavers, G.S., Joseph, D.D.: Boundary conditions at a numerically permeable wall. J. Fluid Mech. 30(1), 197–207 (1967)

    Article  Google Scholar 

  5. Martin, M.J., Boyd, I.D.: Blasius boundary layer solution with slip flow conditions, American Institute of Physics 0-7354-0025-3/01, (2001)

  6. Yao, S., Fang, T., Zhong, Y.: Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions. Commun. Nonlinear Sci. Numer. Simul. 16, 752–760 (2011)

    Article  MATH  Google Scholar 

  7. Matthews, M.T., Hill, J.M.: A note on the boundary layer equations with linear slip boundary condition. Appl. Math. Lett. 21, 810–813 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ishak, A.: MHD boundary layer flow due to an exponentially stretching sheet with radiation effect. Sains Malays. 40(4), 391–395 (2011)

    Google Scholar 

  9. Nadeem, S., Ul Haq, R., Lee, C.: MHD flow of a Casson fluid over an exponentially shrinking sheet. Mech. Eng. 19(6), 1550–1553 (2012)

    Google Scholar 

  10. Mukhopadhyay, S., Gorla, R.S.R.: Effects of partial slip on boundary layer flow past a permeable exponential stretching sheet in presence of thermal radiation. Heat Mass Transf. 48, 1773–1781 (2012)

    Article  Google Scholar 

  11. Pavithra, G.M., Gireesha, B.J.: Effect of internal heat generation/absorption on dusty fluid flow over an exponentially stretching sheet with viscous dissipation. J. Math. (2013). doi:10.1155/2013/583615

    MATH  MathSciNet  Google Scholar 

  12. Srinivasacharya, D., RamReddy, Ch.: Cross-diffusion effects on mixed convection from an exponentially stretching surface in Non-Darcy porous Medium. Heat Transf. Asian Res. 42(2), 111–124 (2013)

    Article  Google Scholar 

  13. Abbas, Z., Javed, T., Ali, N., Sajid, M.: Flow and heat transfer of Maxwell fluid over an exponentially stretching sheet: a non-similar solution. Heat Transf. Asian Res. 43, 233–242 (2014)

    Article  Google Scholar 

  14. Rahman, M.M., Rosca, A.V., Pop, I.: Boundary layer flow of a nanofluid past a permeable exponentially shrinking/stretching surface with second order slip using Buongiorno model. Int. J. Heat Mass Transf. 77, 1133–1143 (2014)

    Article  Google Scholar 

  15. Hayat, T., Shehzad, S.A., Qasim, Md, Asghar, S.: Three-dimensional stretched flow via convective boundary condition and heat generation/absorption. Int. J. Numer. Methods Heat Fluid Flow 24(2), 342–358 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mustafa, M., Khan, J.A., Hayat, T., Alsaedi, A.: Simulations for Maxwell fluid flow past a convectively heated exponentially stretching sheet with nanoparticles. AIP Adv. 5, 037133 (2015). doi:10.1063/1.4916364

    Article  Google Scholar 

  17. Loganthan, P., Vimala, C.: MHD flow of nanofluids over an exponentially stretching sheet embedded in a stratified medium with suction and radiation effects. J. Appl. Fluid Mech. 8(1), 85–93 (2015)

    Google Scholar 

  18. Remus, D.E., Marinca, V.: Approximate solutions for steady boundary layer MHD viscous flow and radiative heat transfer over an exponentially porous stretching sheet. Appl. Math. Comput. 269, 389–401 (2015)

    MathSciNet  Google Scholar 

  19. Hamad, M.A.A., Uddin, Md.J, Ismail, Md: Investigation of combined heat and masstransfer by Lie group analysis with variable diffusivity taking into account hydrodynamic slip and thermal convective boundary conditions. Int. J. Heat Mass Transf. 55, 1355–1362 (2012)

  20. Pnueli, D., Gutfinger, C.: Fluid Mech. Cambridge University Press, Cambridge (1992)

    Book  MATH  Google Scholar 

  21. Schlichting, H.: Boundary Layer Theory, 6th edn. McGraw-Hill, New York (1968)

    MATH  Google Scholar 

  22. Sherman, F.S.: Viscous Flow. McGraw-Hill, Singapore (1990)

    MATH  Google Scholar 

  23. Durst, F.: Fluid Mechanics—An Introduction to the Theory of Fluid Flows. Springer, Berlin (2008)

    MATH  Google Scholar 

  24. Yih, C.S.: Fluid Mechanics—A Concise Introduction to the Theory. West River Press, Ann Arbor (1979)

    Google Scholar 

  25. Motsa, S.S., Shateyi, S.: Successive linearization solution of free convection non-Darcy flow with heat and mass transfer. Adv. Top. Mass Transf. 19, 425–438 (2006)

    Google Scholar 

  26. Makukula, Z.G., Sibanda, P., Motsa, S.S.: A novel numerical technique for two dimensional laminar flow between two moving porous walls. Math. Probl. Eng. 2010, 1–15 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  27. Awad, F.G., Sibanda, P., Motsa, S.S., Makinde, O.D.: Convection from an inverted cone in a porous medium with cross-diffusion effects. Comput. Math. Appl. 61, 1431–1441 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  28. Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods-Fundamentals in Single Domains. Springer, Berlin (2006)

  29. Magyari, E., Keller, B.: Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface. J. Phys. D Appl. Phys. 32, 577–585 (1999)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Warangal, Telangana State, 506004, India

    D. Srinivasacharya & P. Jagadeeshwar

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  1. D. Srinivasacharya
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  2. P. Jagadeeshwar
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Correspondence to D. Srinivasacharya.

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Srinivasacharya, D., Jagadeeshwar, P. Slip Viscous Flow Over an Exponentially Stretching Porous Sheet with Thermal Convective Boundary Conditions. Int. J. Appl. Comput. Math 3, 3525–3537 (2017). https://doi.org/10.1007/s40819-017-0311-y

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  • DOI: https://doi.org/10.1007/s40819-017-0311-y

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