Applied Mathematics and Mechanics

, Volume 40, Issue 4, pp 465–480 | Cite as

Melting heat transfer in Cu-water and Ag-water nanofluids flow with homogeneous-heterogeneous reactions

  • M. ImtiazEmail author
  • F. Shahid
  • T. Hayat
  • A. Alsaedi


This article addresses melting heat transfer in magnetohydrodynamics (MHD) nanofluid flows by a rotating disk. The analysis is performed in Cu-water and Ag-water nanofluids. Thermal radiation, viscous dissipation, and chemical reactions impacts are added in the nanofluid model. Appropriate transformations lead to the nondimensionalized boundary layer equations. Series solutions for the resulting equations are computed. The role of pertinent parameters on the velocity, temperature, and concentration is analyzed in the outputs. It is revealed that the larger melting parameter enhances the velocity profile while the temperature profile decreases. The surface drag force and heat transfer rate are computed under the influence of pertinent parameters. Furthermore, the homogeneous reaction parameter serves to decrease the surface concentration.

Key words

magnetohydrodynamics (MHD) nanofluid stretchable rotating disk thermal radiation melting heat transfer homogeneous-heterogeneous reaction 

Chinese Library Classification


2000 Mathematics Subject Classification



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  1. [1]
    CHOI, S. U. S. Enhancing thermal conductivity of fluids with nanoparticle. ASME International Mechanical Engineering Congress and Exposition, 66, 99–105 (1995)Google Scholar
  2. [2]
    MASUDA, H., EBATA, A., TERAMAE, K., and HISHINUMA, N. Alteration of thermal conductivity and viscosity of liquid by dispersing ultrane particles. Netsu Bussei, 7, 227–233 (1993)CrossRefGoogle Scholar
  3. [3]
    SHIRVAN, K. M., ELLAHI, R., MAMOURIAN, M., and MOGHIMAN, M. Effect of wavy surface characteristics on heat transfer in a wavy square cavity lled with nanofluid. International Journal of Heat and Mass Transfer, 107, 1110–1118 (2017)CrossRefGoogle Scholar
  4. [4]
    SHIRVAN, K. M., MAMOURIAN, M., MIRZAKHANLARI, S., and ELLAHI, R. Numerical investigation of heat exchanger effectiveness in a double pipe heat exchanger lled with nanofluid: a sensitivity analysis by response surface methodology. Powder Technology, 313, 99–111 (2017)CrossRefGoogle Scholar
  5. [5]
    RASHIDI, S., AKAR, S., BOVAND, M., and ELLAHI, R. Volume of fluid model to simulate the nanofluid flow and entropy generation in a single slope solar still. Renewable Energy, 115, 400–410 (2018)CrossRefGoogle Scholar
  6. [6]
    SHEIKHOLESLAMI, M., ELLAHI, R., ASHORYNEJAD, H. R., DOMAIRRY, G., and HAYAT, T. Effects of heat transfer in flow of nanofluids over a permeable stretching wall in a porous medium. Journal of Computational and Theoretical Nanoscience, 11, 486–496 (2014)CrossRefGoogle Scholar
  7. [7]
    ZEESHAN, A., SHEHZAD, N., and ELLAHI, R. Analysis of activation energy in Couette-Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions. Results in Physics, 8, 502–512 (2018)CrossRefGoogle Scholar
  8. [8]
    HAYAT, T., KHAN, M. I., QAYYUM, S., and ALSAEDI, A. Entropy generation in flow with silver and copper nanoparticles. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 539, 335–346 (2018)CrossRefGoogle Scholar
  9. [9]
    ZHANG, C., ZHENG, L., ZHANG, X., and CHEN, G. MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction. Applied Mathematical Modelling, 39, 165–181 (2015)Google Scholar
  10. [10]
    SHEIKHOLESLAMI, M., GANJI, D. D., JAVED, M. Y., and ELLAHI, R. Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model. Journal of Magnetism and Magnetic Materials, 374, 36–43 (2015)CrossRefGoogle Scholar
  11. [11]
    SRINIVASACHARYA, D. and UPENDAR, M. Effect of double stratication on MHD free convection in a micropolar fluid. Journal of Egyptian Mathematical Society, 21, 370–378 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    HAYAT, T., RASHID, M., IMTIAZ, M., and ALSAEDI, A. Magnetohydrodynamic (MHD) flow of Cu-water nanofluid due to a rotating disk with partial slip. AIP Advances, 5, 067169 (2015)CrossRefGoogle Scholar
  13. [13]
    RASHIDI, S., DEHGHAN, M., ELLAHI, R., RIAZ, M., and ABAD, M. T. J. Study of stream wise transverse magnetic fluid flow with heat transfer around a porous obstacle. Journal of Magnetism and Magnetic Materials, 378, 128–137 (2015)CrossRefGoogle Scholar
  14. [14]
    ARIKOGLU, A., OZKOL, I., and KOMURGOZ, G. Effect of slip on entropy generation in a single rotating disk in MHD flow. Applied Energy, 85, 1225–1236 (2008)CrossRefGoogle Scholar
  15. [15]
    SHEHZAD, S. A., ABDULLAH, Z., ABBASI, F. M., HAYAT, T., and ALSAEDI, A. Magnetic eld effect in three-dimensional flow of an Oldroyd-B nanofluid over a radiative surface. Journal of Magnetism and Magnetic Materials, 399, 97–108 (2016)CrossRefGoogle Scholar
  16. [16]
    ABDEL-WAHED, M. S. and EMAM, T. G. Effect of Joule heating and Hall current on MHD flow of a nanofluid due to a rotating disk with viscous dissipation. Thermal Science, 22, 857–870 (2018)CrossRefGoogle Scholar
  17. [17]
    ABDEL-WAHED, M. S. and AKL, M. Effect of Hall current on MHD flow of a nanofluid with variable properties due to a rotating disk with viscous dissipation and nonlinear thermal radiation. AIP Advances, 6, 095308 (2016)CrossRefGoogle Scholar
  18. [18]
    KARMAN, T. V. Uber laminare and turbulente reibung. Zeit Angew Mathematical Mechanics, 1, 233–252 (1921)CrossRefzbMATHGoogle Scholar
  19. [19]
    STEWARTSON, K. On the flow between two rotating coaxial disks. Proceedings in Combine Philosophy Society, 49, 333–341 (1953)MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    TURKYILMAZOGLU, M. Nanofluid flow and heat transfer due to a rotating disk. Computers and Fluids, 94, 139–146 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    JIJI, L. M. and GANATOS, P. Microscale flow and heat transfer between rotating disks. International Journal of Heat and Fluid Flow, 31, 702–710 (2010)CrossRefGoogle Scholar
  22. [22]
    HAYAT, T., QAYYUM, S., IMTIAZ, M., ALZAHRANI, F., and ALSAEDI, A. Partial slip effect in flow of magnetite Fe3O4 nanoparticles between rotating stretchable disks. Journal of Magnetism and Magnetic Materials, 413, 39–48 (2016)CrossRefGoogle Scholar
  23. [23]
    CHAUDHARY, M. A. and MERKIN, J. H. A simple isothermal model for homogeneous-heterogeneous reactions in boundary layer flow I: equal diffusivities. Fluid Dynamics Research, 16, 311–333 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    HAYAT, T., IMTIAZ, M., ALSAEDI, A., and ALMEZAL, S. On Cattaneo-Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous-heterogeneous reactions. Journal of Magnetism and Magnetic Materials, 401, 296–303 (2016)CrossRefGoogle Scholar
  25. [25]
    RASHIDI, M. M., RAHIMZADEH, N., FERDOWS, M., UDDIN, M. J., and BEG, O. A. Group theory and differential transform analysis of mixed convective heat and mass transfer from a horizontal surface with chemical reaction effects. Chemical Engineering Communications, 199, 1012–1043 (2012)CrossRefGoogle Scholar
  26. [26]
    BACHOK, N., ISHAK, A., and POP, I. On the stagnation-point flow towards a stretching sheet with homogeneous-heterogeneous reactions effects. Communications in Nonlinear Science and Numerical Simulation, 16, 4296–4302 (2011)CrossRefzbMATHGoogle Scholar
  27. [27]
    HAYAT, T., KHAN, M. I., WAQAS, M., ALSAEDI, A., and KHAN, M. I. Radiative flow of micropolar nanofluid accounting thermophoresis and Brownian moment. International Journal of Hydrogen Energy, 42, 16821–16833 (2017)CrossRefGoogle Scholar
  28. [28]
    HAYAT, T., SHAFIQUE, M., TANVEER, A., and ALSAEDI, A. Hall and ion slip effects on peristaltic flow of Jeffrey nanofluid with Joule heating. Journal of Magnetism and Magnetic Materials, 407, 51–59 (2016)CrossRefGoogle Scholar
  29. [29]
    HAYAT, T., IMTIAZ, M., ALSAEDI, A., and KUTBI, M. A. MHD three-dimensional flow of nanofluid with velocity slip and nonlinear thermal radiation. Journal of Magnetism and Magnetic Materials, 396, 31–37 (2015)CrossRefGoogle Scholar
  30. [30]
    MUKHOPADHYAY, S. MHD boundary layer flow and heat transfer over an exponentially stretching sheet embedded in a thermally stratied medium. Alexandria Engineering Journal, 52, 259–265 (2013)CrossRefGoogle Scholar
  31. [31]
    EPSTEIN, M. and CHO, D. H. Melting heat transfer in steady laminar flow over a flat plate. Journal of Heat Transfer, 98, 531–533 (1976)CrossRefGoogle Scholar
  32. [32]
    KAZMIERCZAK, M., POULIKAKOS, D., and SADOWSKI, D. Melting of a vertical plate in porous medium controlled by forced convection of a dissimilar fluid. International Communications in Heat Mass Transfer, 14, 507–517 (1987)CrossRefGoogle Scholar
  33. [33]
    KAZMIERCZAK, M., POULIKAKOS, D., and POP, I. Melting from a flat plate in a porous medium in the presence of steady natural convection. Numerical Heat Transfer, 10, 571–581 (1986)CrossRefGoogle Scholar
  34. [34]
    MUSTAFA, M. Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper-convected Maxwell fluid. AIP Advances, 5, 047109 (2015)CrossRefGoogle Scholar
  35. [35]
    HAYAT, T., IMTIAZ, M., ALSAEDI, A., and ALZAHRANI, F. Effects of homogeneous-heterogeneous reactions in flow of magnetite-Fe3O4 nanoparticles by a rotating disk. Journal of Molecular Liquids, 216, 845–855 (2016)CrossRefGoogle Scholar
  36. [36]
    SUI, J., ZHENG, L., ZHANG, X., and CHEN, G. Mixed convection heat transfer in power law fluids over a moving convey or along an inclined plate. International Journal of Heat and Mass Transfer, 85, 1023–1033 (2015)CrossRefGoogle Scholar
  37. [37]
    KHAN, M. I., KHAN, M. I., WAQAS, M., HAYAT, T., and ALSAEDI, A. Chemically reactive flow of Maxwell liquid due to variable thicked surface. International Communications in Heat and Mass Transfer, 86, 231–238 (2017)CrossRefGoogle Scholar
  38. [38]
    LIN, Y., ZHENG, L., and CHEN, G. Unsteady flow and heat transfer of pseudoplastic nano liquid in a finite thin film on a stretching surface with variable thermal conductivity and viscous dissipation. Powder Technology, 274, 324–332 (2016)CrossRefGoogle Scholar
  39. [39]
    LIAO, S. J. Homotopy Analysis Method in Non-Linear Differential Equations, Springer and Higher Education Press, Heidelberg (2012)CrossRefzbMATHGoogle Scholar
  40. [40]
    HAYAT, T., KHAN, M. I., FAROOQ, M., YASMEEN, T., and ALSAEDI, A. Stagnation point flow with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions. Journal of Molecular Liquids, 220, 49–55 (2016)CrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WahWah CanttPakistan
  2. 2.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan
  3. 3.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia

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