MHD Flow and Heat Transfer of SiC-TiO2/DO Hybrid Nanofluid due to a Permeable Spinning Disk by a Novel Algorithm

Document Type : Research Paper


1 Department of Mechanical Engineering, Islamic Azad University, Central Tehran Branch, Tehran, Iran

2 Department of Applied Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania


This study intends to semi-analytically investigate the steady 3D boundary layer flow of a SiC-TiO2/DO hybrid nanofluid over a porous spinning disk subject to a constant vertical magnetic field. Here, the novel attitude to single-phase hybrid nanofluid model corresponds to considering nanoparticles and base fluid masses to compute solid equivalent volume fraction, solid equivalent density, and also solid equivalent specific heat at constant pressure. The basic PDEs are transformed into dimensionless ODEs using Von Kármán similarity transformations, which are then solved numerically using bvp4c function. Results indicate that mass suction and magnetic field effects diminish all hydrodynamic and thermal boundary layer thicknesses. Finally, a significant report is presented to investigate quantities of engineering interest due to governing parameters’ effects.


Main Subjects

[1] Sobamowo, M.G., Free convection flow and heat transfer of nanofluids of different shapes of nano-sized particles over a vertical plate at low and high Prandtl numbers, Journal of Applied and Computational Mechanics, 5(1), 2019, 13–39.
[2] Kezzar, M., Rafik Sari, M., Bourenane, R., Rashidi, M.M., Haiahem, A., Heat transfer in hydro-magnetic nano-fluid flow between non-parallel plates using DTM, Journal of Applied and Computational Mechanics, 4(4), 2018, 352–364.
[3] Ghahremani E., Ghaffari, R., Ghadjari, H., Mokhtari, J., Effect of variable thermal expansion coefficient and nanofluid properties on steady natural convection in an enclosure, Journal of Applied and Computational Mechanics, 3(4), 2017, 240–250.
[4] Akinshilo, A.T., Sobamowo, G.M., Perturbation solutions for the study of MHD blood as a third grade nanofluid transporting gold nanoparticles through a porous channel, Journal of Applied and Computational Mechanics, 3(2), 2017, 103–117.
[5] Ding, Y., Alias, H., Wen, D., Williams, R.A., Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids), International Journal of Heat and Mass Transfer, 49, 2006, 240–250.
[6] Minea, A.A., Advances in Industrial Heat Transfer, CRC Press, 2013.
[7] Minea, A.A., A review on the thermophysical properties of water-based nanofluids and their hybrids, The Annals of “DUNAREA DE JOS” University of GALATI, 083X, 2016, 35-47.
[8] Sidik, C., Azwadi, N., Adamu, I.M., Jamil, M.M., Kefayati, G.H.R., Mamat, R., Najafi, G., Recent progress on hybrid nanofluids in heat transfer applications: A comprehensive review, International Communications in Heat and Mass Transfer, 78, 2016, 68–79.
[9] Madhesh, D., Parameshwaran, R., Kalaiselvam, S., Experimental investigation on convective heat transfer and rheological characteristics of Cu-TiO2 hybrid nanofluids, Experimental Thermal and Fluid Science, 52, 2014, 104–115.
[10] Senthilaraja, S., Vijayakumar, K., Ganadevi, R., A comparative study on thermal conductivity of Al2O3/water, CuO/water and Al2O3– CuO/water nanofluids, Digest Journal of Nanomaterials and Biostructures, 10, 2015, 1449–1458.
[11] Bhosale, G.H., Borse, S.L., Pool Boiling CHF Enhancement with Al2O3-CuO/H2O Hybrid Nanofluid, International Journal of Engineering Research & Technology, 2(10), 2013, 946–950.
[12] He, Y., Vasiraju, S., Que L., Hybrid nanomaterial-based nanofluids for micropower generation, RSC Advances, 4, 2014, 2433-2439.
[13] Esfe, M.H., Abbasian Arani, A.A., Rezaie, M., Yan, Wei-Mon, Karimipour, A., Experimental determination of thermal conductivity and dynamic viscosity of Ag–MgO/water hybrid nanofluid, International Communications in Heat and Mass Transfer, 66, 2015, 189–195.
[14] Syam Sundar, L., Irurueta G.O., Venkata Ramana E., Singh, M,K., Sousa, A.C.M., Thermal conductivity and viscosity of hybrid nanofluids prepared with magnetic nanodiamond-cobalt oxide (ND-Co3O4) nanocomposite, Case Studies in Thermal Engineering, 7, 2016, 66–77.
[15] Hayat, T., Nadeem, S., Heat transfer enhancement with Ag–CuO/water hybrid nanofluid, Results in Physics, 7, 2017, 2317–2324.
[16] Chamkha, A.J., Miroshnichenko, I.V., Sheremet, M.A., Numerical analysis of unsteady conjugate natural convection of hybrid water-based nanofluid in a semicircular cavity, Journal of Thermal Science and Engineering Applications, 9, 2017, 041004–9.
[17] Wei, B., Zou, C., Yuan, X., Li, X., Thermo-physical property evaluation of diathermic oil based hybrid nanofluids for heat transfer applications, International Journal of Heat and Mass Transfer, 107, 2017, 281–287.
[18] Li, X., Zou, C., Zhou, L., Qi, A., Experimental study on the thermo-physical properties of diathermic oil based SiC nanofluids for high temperature applications, International Journal of Heat and Mass Transfer, 97, 2016, 631–637.
[19] Colangelo, G., Favale, E., de Risi, A., Laforgia, D., Results of experimental investigations on the heat conductivity of nanofluids based on diathermic oil for high temperature applications, Applied Energy, 97, 2012, 828–833.
[20] Tamim, H., Dinarvand, S., Hosseini, R., Pop, I., MHD mixed convection stagnation-point flow of a nanofluid over a vertical permeable surface: a comprehensive report of dual solutions, Heat and Mass Transfer, 50, 2014, 639–650.
[21] Alfven, H., Existence of electromagnetic-hydrodynamic waves, Nature, 150, 1942, 405-406.
[22] Domairry Ganji, D., Hashemi Kachapi, S.H., Application of Nonlinear Systems in Nanomechanics and Nanofluids (Analytical Methods and Applications), Elsevier, 2015.
[23] Dinarvand, S., A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field, Central European Journal of Physics, 7(1), 2009, 114-122.
[24] Nademi Rostami, M., Dinarvand, S., Pop, I., Dual solutions for mixed convective stagnation-point flow of an aqueous silica –alumina hybrid nanofluid, Chinese Journal of Physics, 56, 2018, 2465-2478.
[25] Mehryan, S.A.M., Sheremet, M.A., Soltani, M., Izadi, M., Natural convection of magnetic hybrid nanofluid inside a double-porous medium using two-equation energy model, Journal of Molecular Liquids, 277, 2019, 959–970.
[26] Sheikholeslami, M., Mehryan, S.A.M., Shafee, A., Sheremet, M.A., Variable magnetic forces impact on magnetizable hybrid nanofluid heat transfer through a circular cavity, Journal of Molecular Liquids, 277, 2019, 388–396.
[27] Von Kármán, T., Über laminare und turbulente Reibung, Zeitchrift für Angewandte Mathematik und Mechanik, 1(4), 1921, 233–252.
[28] Schlichting, H., Gersten, K., Boundary-Layer Theory, 9th ed., Springer, 2017.
[29] Cochran, W.G., The flow due to a rotating disk, Cambridge Philosophical Society, 30(3), 1934, 365-375.
[30] Rogers, M.G., Lance, G.N., The Rotationally Symmetric Flow of a Viscous Fluid in the Presence of an Infinite Rotating Disk, Journal of Fluid Mechanics, 7, 1960, 617-631.
[31] White, F.M., Viscous Fluid Flow, 3rd ed., McGraw-Hill, 2006.
[32] Turkyilmazoglu, M., Nanofluid flow and heat transfer due to a rotating disk, Computers & Fluids, 94, 2014, 139–146.
[33] Rashidi, M.M., Dinarvand, S., Purely analytic approximate solutions for steady three-dimensional problem of condensation film on inclined rotating disk by homotopy analysis method, Nonlinear Analysis: Real World Applications, 10, 2009, 2346–2356.
[34] Dinarvand, S., On explicit, purely analytic solutions of off-centered stagnation flow towards a rotating disc by means of HAM, Nonlinear Analysis: Real World Applications, 11, 2010, 3389-3398.
[35] Bachok, N., Ishak, A., Pop, I., Flow and heat transfer over a rotating porous disk in a nanofluid, Physica B, 406, 2011, 1767–1772.
[36] Rashidi, M.M., Abelman, S., Freidooni Mehr, N., Entropy generation in steady MHD flow due to a rotating porous disk in ananofluid, International Journal of Heat and Mass Transfer, 62, 2013, 515–525.
[37] Dinarvand, S., Pop, I., Free-convective flow of copper/water nanofluid about a rotating down-pointing cone using Tiwari-Das nanofluid scheme, Advanced Powder Technology, 28, 2017, 900–909.
[38] Hekmatipour, F., Akhavan-Behabadi, M.A., Sajadi, B., Combined free and forced convection heat transfer of the copper oxide-heat transfer oil (CuO-HTO) nanofluid inside horizontal tubes under constant wall temperature, Applied Thermal Engineering, 100, 2016, 621–627.
[39] Kamyar, A., Saidur, R., Hasanuzzaman, M., Application of Computational Fluid Dynamics (CFD) for nanofluids, International Journal of Heat and Mass Transfer, 55, 2012, 4104–4115.
[40] Tiwari, R.J., Das, M.K., Heat transfer augmentation in a two sided lid-driven differentially heated square cavity utilizing nanofluids. International Journal of Heat and Mass Transfer, 50, 2007, 2002–2018.
[41] Syam Sundar, L., Sharma, K.V., Singh, M.K., Sousa, A.C.M., Hybrid nanofluids preparation, thermal properties, heat transfer and friction factor – A review, Renewable and Sustainable Energy Reviews, 68, 2017, 185–198.
[42] Oztop, H.F., Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, International Journal of Heat and Fluid Flow, 29, 2008, 1326–1336.
[43] Syam Sundar, L., Venkata Ramana, E., Graça, M.P.F., Singh, M.K., Sousa, A.C.M., Nanodiamond-Fe3O4 nanofluids: Preparation and measurement of viscosity, electrical and thermal conductivities, International Communications in Heat and Mass Transfer, 73, 2016, 62–74.
[44] Shampine, L.F., Gladwell, I., Thompson, S., Solving ODEs with MATLAB, Cambridge University Press, 2003.
[45] Roşca, N.C., Roşca, A.V., Aly, E.H., Pop, I., Semi-analytical solution for the flow of a nanofluid over a permeable stretching/shrinking sheet with velocity slip using Buongiorno mathematical model, European Journal of Mechanics B/Fluids, 58, 2016, 39–49.
[46] Yin, C., Zheng, L., Zhang, C., Zhang, X., Flow and heat transfer of nanofluids over a rotating disk with uniform stretching rate in the radial direction, Propulsion and Power Research, 6(1), 2017, 25–30.