Skip to main content
SpringerLink
Log in

Influence of Variable Fluid Properties on Nanofluid Flow over a Wedge with Surface Slip

  • Research Article - Chemical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

The present article explores the influence of variable fluid properties on nanofluid flow over a wedge. The flow analysis has been considered under the effect of surface slip. It is supposed to have fluid viscosity and thermal conductivity as an inverse function and linear function of temperature, respectively. The resulting nonlinear ordinary differential equations are solved numerically using RK-4 method together with shooting procedure. The consequence of involved pertinent parameters on the flow province has been discussed through graphs and tables coupled with required discussion. Our analysis conveys that the fluid temperature is higher in the presence of variable viscosity parameter and thermal conductivity parameter. It is also observed that the wall stress decreases with increasing velocity slip parameter.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Falkner, V.M.; Skan, S.W.: Some approximate solution of the boundary layer equations. Philos. Mag. 12, 865–896 (1931)

    Article  MATH  Google Scholar 

  2. Hartree, D.R.: On the equation occurring in Falkner and Skan’s approximate treatment of the equations of boundary layer. Proc. Camb. Philos. Soc. 33, 223–239 (1937)

    Article  MATH  Google Scholar 

  3. Stewartson, K.: Further solution of Falkner and Skan equation. Proc. Camb. Philos. Soc. 50, 454–465 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hastings, S.P.: Reversed flow solutions of Falkner and Skan equation. SIAM J. Appl. Math. 22, 329–334 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  5. Botta, E.F.F.; Hut, F.J.; Veladman, A.E.P.: The role of periodic solution in Falkner and Skanfor \(\lambda \ge 0\). J. Eng. Math. 20, 81–83 (1986)

    Article  Google Scholar 

  6. Yih, K.A.: Uniform suction/blowing on forced convection about a wedge: uniform heat flux. Acta Mech. 128, 173–181 (1998)

    Article  MATH  Google Scholar 

  7. Watanabe, T.: Thermal boundary layers over a wedge with uniform suction or injection in forced flow. Acta Mech. 83, 119–126 (1990)

    Article  Google Scholar 

  8. Rajagopal, K.R.; Gupta, A.S.; Na, T.Y.: A note on Falkner and Skan flows of a non-newtonian fluid. Int. J. Non-linear Mech. 18, 313–320 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zaturska, M.B.; Banks, W.N.: A new solution branch of the Falkner and Skan equation. Acta Mech. 152, 197–201 (2001)

    Article  MATH  Google Scholar 

  10. Na, T.Y.: Computational Methods in Engineering Boundary Value Problems. Academic, New York (1979)

    MATH  Google Scholar 

  11. Asaithambi, A.: Afinite difference method for the Falkner and Skan equation. Appl. Math. Comput. 92, 135–141 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  12. Yacob, N.A.; Ishak, A.; Pop, I.: Falkner and Skan problem for a static or moving wedge in nanofluids. Int. J. Thermal Sci. 50, 133–139 (2011)

    Article  Google Scholar 

  13. Chamkha, A.J.; Mujtaba, M.; Quadri, A.; Issa, C.: Thermal radiation effects on MHD forced convection flow adjacent to a non-isothermal wedge in presence of a heat source and sink. Heat Mass Transf. 39, 305–312 (2003)

    Article  Google Scholar 

  14. Gorla, R.S.R.; Chamkha, A.J.; Rashad, A.M.: Mixed convective boundary layer flow over a vertical wedge embedded in a porous medium saturated with a nanofluid natural convection dominated regime. Nanoscale Res. Lett. 6, 1–9 (2011)

    Article  Google Scholar 

  15. Khan, W.A.; Pop, I.: Boundary layer flow past a wedge moving in a nanofluid. Math. Prob. Eng. 2013, 1–7 (2013)

    MathSciNet  MATH  Google Scholar 

  16. Kasamani, R.M.; Muhaimin, I.; Kandasamy, R.: Laminar boundary layer flow of a nanofluid along a wedge in presence of suction/injection. J. Appl. Mech. Tech. Phys. 54, 377–384 (2013)

    Article  MATH  Google Scholar 

  17. Kandasamy, R.; Muhaimin, I.; Khamis, A.B.; bin Roslan, R.: Unsteady Hiemenz flow of Cu–water nanofluid over a porous wedge in presence of thermal stratification due to solar energy radiation. Int. J. Thermal Sci. 65, 196–205 (2012)

    Article  Google Scholar 

  18. Chiam, T.C.: Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet. Acta Mech. 129, 63–72 (1998)

    Article  MATH  Google Scholar 

  19. Rahaman, M.M.; Uddin, M.J.; Aziz, A.: Effects of variable electric conductivity and non-uniform heat source or sink on convective micropolar fluid flow along an inclined flat plate with surface. Int. J. Thermal Sci. 48, 2331–2340 (2009)

    Article  Google Scholar 

  20. Prasad, K.V.; Vajravelu, K.; Datti, P.S.: The effects of variable fluid properties on the hydro-magnetic flow and heat transfer over a non-linear stretching sheet. Int. J. Thermal Sci. 49, 603–610 (2010)

    Article  Google Scholar 

  21. Rahaman, M.M.: Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition. Meccanica (2011). doi:10.1007/S11012-010-9372-2

    MathSciNet  Google Scholar 

  22. Rahaman, M.M.; Aziz, A.; Al-Lawatia, M.: Heat transfer in micropolar fluid along an inclined permeable plate with variable properties. Int. J. Thermal Sci. 49, 993–1002 (2010)

    Article  Google Scholar 

  23. Rahaman, M.M.; Eltayeb, I.A.: Convective slip flow of rarefied fluids over a wedge with thermal jump and variable fluid properties. Int. J. Thermal Sci. 50, 468–479 (2011)

    Article  Google Scholar 

  24. Pantokratoras, A.: The Falkner–Skan flow with constant wall temperature and variable viscosity. Int. J. Thermal Sci. 45, 378–389 (2006)

    Article  Google Scholar 

  25. Pantokratoras, A.: Further results on the variable viscosity on flow and heat transfer to a continuous moving flat plate. Int. J. Eng. Sci. 42, 1891–1896 (2004)

    Article  MATH  Google Scholar 

  26. Abel, M.S.; Siddheshwar, P.G.; Mahesha, N.: Effects of thermal buoyancy and variable thermal conductivity on the MHD flow and heat transfer in a power-law fluid past a vertical stretching sheet in the presence of non-uniform heat source. Int. J. Non-linear Mech. 44, 1–12 (2009)

    Article  MATH  Google Scholar 

  27. Das, K.; Jana, S.: Influence of variable fluid properties, thermal radiation and chemical reaction on MHD slip flow over a flat plate. Ital. J. Pure Appl. Math. 34, 29–44 (2015)

    MathSciNet  MATH  Google Scholar 

  28. Rahman, M.M.; Rahman, M.A.; Samad, M.A.; Alam, M.S.: Heat transfer in micropolar fluid along a non-linear stretching sheet with temperature dependent viscosity and variable wall temperature. Int. J. Thermophys. 30, 1649–1670 (2009)

    Article  Google Scholar 

  29. Rahaman, M.M.; Salahuddin, K.M.: Study of hydromagnetic heat and mass transfer flow over an inclined heated surface with variable viscosity and electric conductivity. Commun. Non-linear Sci. Numer. Simul. 15, 2073–2085 (2010)

    Article  MATH  Google Scholar 

  30. Rahaman, M.M.: Convective hydromagnetic slip flow with variable properties due to a porous rotating disk. Sultan Qaboos Univ. J. Sci. 15, 55–79 (2010)

    Google Scholar 

  31. Rahaman, M.M.: Combined effects of internal heat generation and higher order chemical reaction on the non-Darcian forced convective flow of a viscous incompressible fluid with variable viscosity and thermal conductivity over a stretching surface embedded in a porous medium. Can. J. Chem. Eng. 90(6), 1632–1645 (2012)

    Article  Google Scholar 

  32. Navier, C.L.M.H.: Memoire sur les lois du mouvement des fluids. Mem. Acad. R. Sci. Inst. Fr. 6, 389–440 (1823)

    Google Scholar 

  33. Uddin, M.J.; Alam, M.S.; Rahamann, M.M.: Natural convective heat transfer flow of nanofluids inside a quarter-circular enclosure using nonhomogeneous dynamic model. J. Sci. Eng. Arab. (2016). doi:10.1007/s13369-016-2330-0

    Google Scholar 

  34. Hina, S.; Hayat, T.; Alsaedi, A.: Slip effects on MHD peristaltic motion with heat and mass transfer. Arab. J. Sci. Eng. 39, 593–603 (2014)

    Article  MathSciNet  Google Scholar 

  35. Acharya, N.; Das, K.; Kundu, P.K.: Ramification of variable thickness on MHD TiO\(_{2}\) and Ag nanofluid flow over a slendering stretching sheet using NDM. Eur. Phys. J. Plus 131, 303 (2016)

    Article  Google Scholar 

  36. Das, K.; Duari, P.R.; Kundu, P.K.: Solar radiation effect on Cu–Water nanofluid flow over a stretching sheet with surface slip and temperature jump. Arab. J. Sci. Eng. 39, 9015–9023 (2014)

    Article  Google Scholar 

  37. Ling, J.X.; Dybbs, A.: Forced convection over a flat plate submersed in a porous medium variable viscosity case. ASME paper-87-WA/HT-23 ASME winter annual meeting, Boston Massachusets, pp. 13–18 (1987)

  38. Weast, R.C.: CRC Handbook of Physics and Chemistry, 71st edn. CRC Press, Boca Raton (1990)

    Google Scholar 

  39. Ali, E.: The effect of variable viscosity on mixed convection heat transfer along a vertical moving surface. Int. J. Thermal Sci. 45, 60–69 (2006)

    Article  Google Scholar 

  40. Knezevic, D.; Savic, V.: Mathematical modelling of changing of dynamical viscosity as a function of temperature and pressure of mineral oils for hydraulic systems. Facta Univ. (Ser. Mech. Eng.) 6, 27–34 (2006)

    Google Scholar 

  41. Chaim, T.C.: Heat transfer with variable conductivity in a stagnation point flow towards a stretching sheet. Int. Commun. Heat Mass Transf. 23, 239–248 (1996)

    Article  Google Scholar 

  42. Martin, M.J.; Boyd, I.D.: Momentum and heat transfer in a laminar boundary layer with slip flow. J. Thermophys. Heat Transf. 20, 710–719 (2006)

    Article  Google Scholar 

  43. Martin, M.J.; Boyd, I.D.: Falkner Skan flow over a wedge with slip boundary condition. J. Thermophys. Heat Transf. 24, 263–270 (2010)

    Article  Google Scholar 

  44. Makinde, O.D.: Laminar falling liquid film with variable viscosity along an inclined heated plate. Appl. Math. Comput. 175, 80–88 (2006)

  45. Fang, T.; Lee, C.F.: A moving layer boundary layer flow of a slightly rarefied gas free stream over a moving flat plate. Appl. Math. Lett. 18, 487–495 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  46. Gad-el-Hak, M.: The fluid mechanics of microdevices: the freeman scholar lecture. J. Fluids Eng. 121(1), 5–53 (1999)

    Article  Google Scholar 

  47. Rahman, M.M.; Alam, M.S.; Al-Salti, N.; Eltayeb, I.A.: Hydromagnetic natural convection heat transfer flow in an isosceles triangular cavity filled with nanofluid using two component nonhomogeneous model. Int. J. Thermal Sci. 107, 272–288 (2016)

    Article  Google Scholar 

  48. Reddy, P.S.; Chamkha, A.J.: Influence of size, shape, type of nanoparticles, type and temperature of the base fluid on natural convection MHD of nanofluids. Alex. Eng. J. 55, 331–341 (2016)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, A.B.N.Seal College, Cooch Behar, West Bengal, 736101, India

    Kalidas Das

  2. Department of Mathematics, M.A.Chandra Mohan High School, Malda, 732121, India

    Nilankush Acharya

  3. Department of Mathematics, Jadavpur University, Kolkata, 700032, West Bengal, India

    Prabir Kumar Kundu

Authors
  1. Kalidas Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nilankush Acharya
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Prabir Kumar Kundu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kalidas Das.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, K., Acharya, N. & Kundu, P.K. Influence of Variable Fluid Properties on Nanofluid Flow over a Wedge with Surface Slip. Arab J Sci Eng 43, 2119–2131 (2018). https://doi.org/10.1007/s13369-017-2499-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-017-2499-x

Keywords

Search

Navigation