Skip to main content
SpringerLink
Log in

MHD Marangoni boundary layer flow and heat transfer of pseudo-plastic nanofluids over a porous medium with a modified model

  • Published:
Mechanics of Time-Dependent Materials Aims and scope Submit manuscript

Abstract

We present a research for the MHD Marangoni boundary layer flow and heat transfer in pseudo-plastic power law nanofluids over a porous medium driven by temperature gradient. A variable magnetic field is considered. Four different types of nanoparticles, copper, aluminum oxide, copper oxide, and titanium oxide are considered with pseudo-plastic power-law carboxy methyl cellulose (CMC)-water used as base fluids. A generalized Fourier law proposed by Zheng for varying thermal conductivity of nanofluids is taken into account, and the surface tension is assumed a quadratic function of the temperature. The governing partial differential equations (PDEs) are formulated, and similarity solutions are obtained numerically using shooting technique combined with Runge–Kutta iteration program and Newton’s scheme. The effects of various physical parameters on horizontal velocity component and temperature curves are discussed and graphically illustrated in details.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Abu-Nada, E.: Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step. Int. J. Heat Fluid Flow 29, 242–249 (2008)

    Article  Google Scholar 

  • Abu-Nada, E., Masoud, Z., Hijazi, A.: Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids. Int. Commun. Heat Mass Transf. 35, 657–665 (2008)

    Article  Google Scholar 

  • Andersson, H.I., Kumaran, V.: On sheet-driven motion of power-law fluids. Int. J. Non-Linear Mech. 41, 1228–1234 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • Chen, C.H.: Magneto-hydrodynamic mixed convection of a power-law fluid past a stretching surface in the presence of thermal radiation and internal heat generation/absorption. Int. J. Non-Linear Mech. 41, 596–603 (2009)

    Article  Google Scholar 

  • Christopher, D.M., Wang, B.X.: Prandtl number effects for Marangoni convection over a flat surface. Int. J. Therm. Sci. 40, 564–570 (2001a)

    Article  Google Scholar 

  • Christopher, D.M., Wang, B.X.: Similarity simulation for Marangoni convection around a vapor bubble during nucleation and growth. Int. J. Heat Mass Transf. 44, 799–810 (2001b)

    Article  MATH  Google Scholar 

  • Guo, Z.L., Lin, P., Wang, Y.F.: Continuous finite element schemes for a phase field model in two-layer fluid Bénard–Marangoni convection computations. Comput. Phys. Commun. 185, 63–78 (2014)

    Article  MathSciNet  Google Scholar 

  • Hatami, M., Hatami, J., Ganji, D.D.: Computer simulation of MHD blood conveying gold nanoparticles as a third grade non-Newtonian nanofluid in a hollow porous vessel. Comput. Methods Programs Biomed. 113, 632–641 (2014)

    Article  Google Scholar 

  • Kabeel, A.E., El-Said, E.M.S., Dafea, S.A.: A review of magnetic field effects on flow and heat transfer in liquids: present status and future potential for studies and applications. Renew. Sustain. Energy Rev. 45, 830–837 (2015)

    Article  Google Scholar 

  • Khan, W.A., Pop, I.: Boundary-layer flow of a nanofluid past a stretching sheet. Int. J. Heat Mass Transf. 53, 2477–2483 (2010)

    Article  MATH  Google Scholar 

  • Kothandapani, M., Prakash, J.: Effect of radiation and magnetic field on peristaltic transport of nanofluids through a porous space in a tapered asymmetric channel. J. Magn. Magn. Mater. 378, 152–163 (2015)

    Article  Google Scholar 

  • Lin, Y.H., Zheng, L.C., Zhang, X.X.: Magnetohydrodynamics thermocapillary Marangoni convection heat transfer of power-law fluids driven by temperature gradient. J. Heat Transf. 135, 051702 (2013)

    Article  Google Scholar 

  • Lin, Y.H., Zheng, L.C., Zhang, X.X.: Radiation effects on Marangoni convection flow and heat transfer in pseudo-plastic non-Newtonian nanofluids with variable thermal conductivity. Int. J. Heat Mass Transf. 77, 708–716 (2014)

    Article  Google Scholar 

  • Lin, Y.H., Zheng, L.C., Chen, G.: Unsteady flow and heat transfer of pseudo-plastic nanoliquid in a finite thin film on a stretching surface with variable thermal conductivity and viscous dissipation. Powder Technol. 274, 324–332 (2015a)

    Article  Google Scholar 

  • Lin, Y.H., Zheng, L.C., Zhang, X.X., Ma, L.X., Chen, G.: MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation. Int. J. Heat Mass Transf. 84, 903–911 (2015b)

    Article  Google Scholar 

  • Magyari, E., Chamkha, A.J.: Exact analytical solutions for thermosolutal Marangoni convection in the presence of heat and mass generation or consumption. Heat Mass Transf. 43, 965–974 (2007)

    Article  Google Scholar 

  • Magyari, E., Chamkha, A.J.: Exact analytical results for the thermosolutal MHD Marangoni boundary layers. Int. J. Therm. Sci. 47, 848–857 (2008)

    Article  Google Scholar 

  • Mahdi, R.A., Mohammed, H.A., Munisamy, K.M., Saeid, N.H.: Review of convection heat transfer and fluid flow in porous media with nanofluid. Renew. Sustain. Energy Rev. 41, 715–734 (2015)

    Article  Google Scholar 

  • Mahdy, A., Ahmed, E.: Thermosolutal Marangoni boundary layer magnetohydrodynamic flow with the Soret and Dufour effects past a vertical flat plate. Eng. Sci. Technol., Int. J. 18, 24–31 (2015)

    Article  Google Scholar 

  • Mohammed, H.A., Gunnasegaram, P., Shuaib, N.H.: Influence of various base nanofluids and substrate materials on heat transfer in trapezoidal microchannel heat sinks. Int. Commun. Heat Mass Transf. 38, 194–201 (2011)

    Article  Google Scholar 

  • Mudhaf, A.A., Chamkha, A.J.: Similarity solutions for MHD thermosolutal Marangoni convection over a flat surface in the presence of heat generation. Heat Mass Transf. 42, 112–121 (2005)

    Article  Google Scholar 

  • Murthy, P.V.S.N., RamReddy, C., Chamkha, A.J., Rashad, A.M.: Magnetic effect on thermally stratified nanofluid saturated non-Darcy porous medium under convective boundary condition. Int. Commun. Heat Mass Transf. 47, 41–48 (2013)

    Article  Google Scholar 

  • Naimi, M., Hasnaoui, M., Platten, J.K.: Marangoni convection of non-Newtonian power law fluids in a shallow rectangular cavity. Eng. Comput. 17(6), 638–668 (2000)

    Article  MATH  Google Scholar 

  • Noghrehabadi, A., Behseresht, A.: Flow and heat transfer affected by variable properties of nanofluids in natural-convection over a vertical cone in porous media. Comput. Fluids 88, 313–325 (2013)

    Article  MathSciNet  Google Scholar 

  • Palm, S.J., Roy, G., Nguyen, C.T.: Heat transfer enhancement with the use of nanofluids in radial flow cooling systems considering temperature-dependent properties. Appl. Therm. Eng. 26, 2209–2218 (2006)

    Article  Google Scholar 

  • Paullet, J.E.: An uncountable number of solutions for a BVP governing Marangoni convection. Math. Comput. Model. 52, 1708–1715 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  • Ravnik, J., Skerget, L., Hribesek, M.: Analysis of three-dimensional natural convection of nanofluids by BEM. Eng. Anal. Bound. Elem. 34, 1018–1030 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  • Santra, A.K., Chakraborty, N., Sen, S.: Prediction of heat transfer due to presence of copper–water nanofluid using resilient-propagation neural network. Int. J. Therm. Sci. 48, 1311–1318 (2009a)

    Article  Google Scholar 

  • Santra, A.K., Sen, S., Chakraborty, N.: Study of heat transfer due to laminar of flow of copper–water nanofluid through two isothermally heated parallel plates. Int. J. Therm. Sci. 48, 391–400 (2009b)

    Article  Google Scholar 

  • Saravanan, S., Sivakumar, T.: Exact solution of Marangoni convection in a binary fluid with through flow and Soret effect. Appl. Math. Model. 33, 3674–3681 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  • Servati, A.A., Javaherdeh, V.K., Ashorynejad, H.R.: Magnetic field effects on force convection flow of a nanofluid in a channel partially filled with porous media using lattice Boltzmann method. Adv. Powder Technol. 25, 666–675 (2014)

    Article  Google Scholar 

  • Sharma, R., Ishak, A., Pop, I.: Stability analysis of magnetohydrodynamic stagnation-point flow toward a stretching/shrinking sheet. Comput. Fluids 102, 94–98 (2014)

    Article  Google Scholar 

  • Sheikholeslami, M., Ganji, D.D.: Three dimensional heat and mass transfer in a rotating system using nanofluid. Powder Technol. 253, 789–796 (2014)

    Article  Google Scholar 

  • Slavtchev, S.G., Miladinova, S.: Thermocapillary flow in a liquid layer at minimum in surface tension. Acta Mech. 127, 209–224 (1998)

    Article  MATH  Google Scholar 

  • Subhashini, S.V., Sumathi, R., Pop, I.: Dual solutions in a double-diffusive MHD mixed convection flow adjacent to a vertical plate with prescribed surface temperature. Int. J. Heat Mass Transf. 56, 724–731 (2013)

    Article  Google Scholar 

  • Xuan, Y.M., Li, Q.: Heat transfer enhancement of nanofluids. Int. J. Heat Fluid Flow 21, 58–64 (2000)

    Article  Google Scholar 

  • Xuan, Y.M., Roetzel, W.: Conceptions of heat transfer correlation of nanofluids. Int. Commun. Heat Mass Transf. 43, 3701–3707 (2000)

    Article  MATH  Google Scholar 

  • Yadav, D., Bhargava, R., Agrawal, G.S.: Boundary and internal heat source effects on the onset of Darcy–Brinkman convection in a porous layer saturated by nanofluid. Int. J. Therm. Sci. 60, 244–254 (2012)

    Article  Google Scholar 

  • Yocob, N.A., Ishak, A., Nazar, R.M., Pop, I.: Falkner–Skan problem for a static and moving wedge with prescribed surface heat flux in a nanofluid. Int. Commun. Heat Mass Transf. 38, 149–153 (2011)

    Article  Google Scholar 

  • Zhang, C.L., Zheng, L.C., Zhang, X.X., Chen, G.: MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction. Appl. Math. Model. 39, 165–181 (2015)

    Article  MathSciNet  Google Scholar 

  • Zhang, Y., Zheng, L.C.: Analysis of MHD thermosolutal Marangoni convection with the heat generation and a first-order chemical reaction. Chem. Eng. Sci. 69, 449–455 (2012)

    Article  Google Scholar 

  • Zhang, Y., Zheng, L.C.: Similarity solutions of Marangoni convection boundary layer flow with gravity and external pressure. Chin. J. Chem. Eng. 22(4), 365–369 (2014)

    Article  Google Scholar 

  • Zheng, L.C., Lin, Y.H., Zhang, X.X.: Marangoni convection of power law fluids driven by power-law temperature gradient. J. Franklin Inst. 349, 2585–2597 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  • Zheng, L.C., Zhang, X.X., Boubaker, K., Yücel, U., Gargouze, E., Yıldırım, A.: Similarity and Boubaker polynomials expansion scheme BPES comparative solutions to the heat transfer equation for incompressible non-Newtonian fluids: case of laminar boundary energy equation. Eur. Phys. J. Appl. Phys. 55, 21102–21106 (2011)

    Article  Google Scholar 

  • Zheng, L.C., Zhang, X.X., Lu, C.Q.: Heat transfer for power law non-Newtonian fluids. Chin. Phys. Lett. 23(12), 3301–3304 (2006)

    Article  Google Scholar 

  • Zheng, L.C., Zhang, X.X., Ma, L.X.: Fully developed convective heat transfer for power law fluids in a circular tube. Chin. Phys. Lett. 25(1), 195–197 (2008)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The research was supported by the Scientific Research Funds of Huaqiao University (No. 14BS310) and the National Natural Science Foundation of China (Nos. 51276014 and 51476191).

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, Fujian, China

    Yanhai Lin

  2. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Liancun Zheng

  3. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Xinxin Zhang

Authors
  1. Yanhai Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liancun Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xinxin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liancun Zheng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, Y., Zheng, L. & Zhang, X. MHD Marangoni boundary layer flow and heat transfer of pseudo-plastic nanofluids over a porous medium with a modified model. Mech Time-Depend Mater 19, 519–536 (2015). https://doi.org/10.1007/s11043-015-9276-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11043-015-9276-6

Keywords

Search

Navigation