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**Heat transfer and flow analysis of magnetohydrodynamic dissipative Carreau nanofluid over a stretching sheet with internal heat generation.**
*(English)*
Zbl 1499.65303

Summary: The unsteady two-dimensional flow and heat transfer analysis of Carreau nanofluid over a stretching sheet subjected to magnetic field, temperature dependent heat source/sink and viscous dissipation is presented in this paper. Similarity transformations are used to reduce the systems of the developed governing partial differential equations to nonlinear third and second orders ordinary differential equation which are solved using differential transform method. Using kerosene as the base fluid embedded with the silver (Ag) and copper (Cu) nanoparticles, the effects of pertinent parameters on reduced Nusselt number, flow and heat transfer characteristics of the nanofluid are investigated and discussed. From the results, it is established temperature field and the thermal boundary layers of Ag-Kerosene nanofluid are highly effective when compared with the Cu-Kerosene nanofluid. Heat transfer rate is enhanced by increasing in power-law index and unsteadiness parameter. Skin friction coefficient and local Nusselt number can be reduced by magnetic field parameter and they can be enhanced by increasing the aligned angle. Friction factor is depreciated and the rate of heat transfer increases by increasing the Weissenberg number. Also, for the purpose of verification, the results of the analytical of the approximate analytical solutions are compared with the results of numerical solution using Runge-Kutta coupled with Newton method. A very good agreement is established between the results. This analysis can help in expanding the understanding of the thermo-fluidic behaviour of the Carreau nanofluid over a stretching sheet.

### MSC:

65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |

80A32 | Chemically reacting flows |

### Keywords:

MHD; nanofluid; non-uniform heat source sink; Carreau fluid; thermal radiation and free convection; MHD
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\textit{G. M. Sobamowo} et al., J. Comput. Eng. Math. 6, No. 1, 3--26 (2019; Zbl 1499.65303)

### References:

[1] | T. Hayat, I. Ullah, B. Ahmad, A. Alsaedi, “Radiative Flow of Carreau Liquid in Presence of Newtonian Heating and Chemical Reaction”, Results in Physics, 7 (2017), 715-722 |

[2] | H. I. Andersson, J. B. Aarseth, N. Braud, B. S. Dandapat, “Flow of a Power-Law Fluid on an Unsteady Stretching Surface”, Journal of Non-Newtonian Fluid Mechanics, 62:1 (1996), 1-8 |

[3] | H. I. Andersson, K. H. Bech, B. S. Dandapat, “Magneto Hydrodynamics Flow of a Power-Law Fluid over a Stretching Sheet”, International Journal of Non-Linear Mechanics, 27:6 (1992), 929-936 · Zbl 0775.76216 |

[4] | C. H. Chen, “Heat Transfer in a Power-Law Fluid Film over an Unsteady Stretching Sheet”, Heat and Mass Transfer, 39:8-9 (2003), 791-796 |

[5] | B. S. Dandapat, B. Santra, H. I. Andersson, “Thermocapillarity in a Liquid Film on an Unsteady Stretching Surface”, International Journal of Heat and Mass Transfer, 46:16 (2003), 3009-3015 · Zbl 1048.76502 |

[6] | B S. Dandapat, B. Santra, K. Vejravelu, “The Effects of Variable Fluid Properties and the Thermocapillarity on the Flow of a Thin Film on Stretching Sheet”, International Journal of Heat and Mass Transfer, 50:5-6 (2007), 991-996 · Zbl 1124.80317 |

[7] | C. Wang, “Analytic Solutions for a Liquid Film on an Unsteady Stretching Surface”, Heat and Mass Transfer, 42:8 (2006), 759-766 |

[8] | C. H. Chen, “Effect of Viscous Dissipation on Heat Transfer in a Non-Newtonian Liquid Film over an Unsteady Stretching Sheet”, Journal of Non-Newtonian Fluid Mechanics, 135:2-3 (2006), 128-135 · Zbl 1195.76127 |

[9] | M. Sajid, T. Hayat, S. Asghar, “Comparison between the HAM and HPM Solutions of Thin Film Flows of Non- Newtonian Fluids on a Moving Belt”, Nonlinear Dynamics, 50:1-2 (2007), 27-35 · Zbl 1181.76031 |

[10] | B. S. Dandapat, S. Maity, A. Kitamura, “Liquid Film Flow Due to an Unsteady Stretching Sheet”, International Journal of Non-Linear Mechanics, 43:9 (2008), 880-886 · Zbl 1203.74100 |

[11] | S. Abbasbandy, M. Yurusoy, M. Pakdemirli, “The Analysis Approach of Boundary Layer Equation of Power-Law Fluids of Second Grade”, Zeitschrift für Naturforschung A, 43:9 (2008), 880-886 |

[12] | B. Santra, B. S. Dandapat, “Unsteady Thin-Film Flow over a Heated Stretching Sheet”, International Journal of Heat and Mass Transfer, 52:7-8 (2009), 1965-1970 · Zbl 1157.80366 |

[13] | M. Sajid, N. Ali, T. Hayat, “On Exact Solutions for Thin Film Flows of a Micropolar Fluid”, Communications in Nonlinear Science and Numerical Simulation, 14:2 (2009), 451-461 · Zbl 1221.76038 |

[14] | N. F. M. Noor, I. Hashim, “Thermocapillarity and Magnetic Field Effects in a Thin Liquid Film on an Unsteady Stretching Surface”, International Journal of Heat and Mass Transfer, 53:9-10 (2010), 2044-2051 · Zbl 1190.80025 |

[15] | B. S. Dandapat, S. Chakraborty, “Effects of Variable Fluid Properties on Unsteady Thin-Film Flow over a Non- Linear Stretching Sheet”, International Journal of Heat and Mass Transfer, 53:25-26 (2010), 5757-5763 · Zbl 1201.80015 |

[16] | B. S. Dandapat, S. K. Singh, “Thin Film Flow over a Heated Nonlinear Stretching Sheet in Presence of Uniform Transverse Magnetic Field”, International Communications of Heat and Mass Transfer, 38:3 (2011), 324-328 |

[17] | G. M. Abdel-Rahman, “Effect of Magnetohydrodynamic on Thin Films of Unsteady Micropolar Fluid through a Porous Medium”, Journal of Modern Physics, 2:1 (2011), 1290-1304 |

[18] | Y. Khan, Q. Wu, N. Faraz, A. Yildirim, “The Effects of Variable Viscosity and Thermal Conductivity on a Thin Film Flow over a Shrinking/Stretching Sheet”, Computers and Mathematics with Applications, 61:11 (2011), 3391-3399 · Zbl 1222.76014 |

[19] | I. C. Liu, A. Megahed, H. H. Wang, “Heat Transfer in a Liquid Film due to an Unsteady Stretching Surface with Variable Heat Flux”, Journal of Applied Mechanics, 80:4 (2013), 041003, 7 pp. |

[20] | K. Vajravelu, K. V. Prasad, C. O. Ng, “Unsteady Flow and Heat Transfer in a Thin Film of Ostwald-De Waele Liquid over a Stretching Surface”, Communications in Nonlinear Science and Numerical Simulation, 17:11 (2012), 4163-4173 · Zbl 1316.76013 |

[21] | I C. Liu, A M. Megahed, “Homotopy Perturbation Method for Thin Film Flow and Heat Transfer over an Unsteady Stretching Sheet with Internal Heating and Variable Heat Flux”, Journal of Applied Mechanics, 2012, 418527, 12 pp. · Zbl 1251.80002 |

[22] | R. C. Aziz, I. Hashim, S. Abbasbandy, “Effects of Thermocapillarity and Thermal Radiation on Flow and Heat Transfer in a Thin Liquid Film on an Unsteady Stretching Sheet”, Mathematical Problems in Engineering, 2012, 127320, 14 pp. · Zbl 1264.76102 |

[23] | M. M. Khader, A. M. Megahed, “Numerical Simulation Using the Finite Difference Method for the Flow and Heat Transfer in a Thin Liquid Film over an Unsteady Stretching Sheet in a Saturated Porous Medium in the Presence of Thermal Radiation”, Journal of King Saud University - Engineering Sciences, 25:1 (2013), 29-34 |

[24] | Y. Lin, L. Zheng, X. Zhang, L. Ma, G. Chen, “MHD Pseudo-Plastic Nanofluid Unsteady Flow and Heat Transfer in a Finite Thin Film over Stretching Surface with Internal Heat Generation”, International Journal of Heat and Mass Transfer, 84 (2015), 903-911 |

[25] | N. Sandeep, C. Sulochana, I. L. Animasaun, “Stagnation Point Flow of a Jeffrey Nano Fluid over a Stretching Surface with Induced Magnetic Field and Chemical Reaction”, International Journal of Engineering Research in Africa, 20 (2016), 93-111 |

[26] | J. Tawade, M. S. Abel, P. G. Metri, “Thin Film Flow and Heat Transfer over an Unsteady Stretching Sheet with Thermal Radiation, Internal Heating in Presence of External Magnetic Field”, Physics. Fluid Dynamics, 2016, no. 3, 16 pp., arXiv: · Zbl 1367.76069 |

[27] | C. S. K. Raju, N. Sandeep, “Unsteady Three-Dimensional Flow of Casson-Carreau Fluids Past a Stretching Surface”, Alexandria Engineering Journal, 55:2 (2016), 1115-1126 |

[28] | C. S. K. Raju, N. Sandeep, “Falkner-Skan Flow of a Magnetic-Carreau Fluid Past a Wedge in the Presence of Cross Diffusion Effects”, The European Physical Journal Plus, 131:8 (2016), 267 |

[29] | C. S. K. Raju, N. Sandeep, V. Sugunamma, “Dual Solutions for Three-Dimensional MHD Flow of a Nanofluid over a Nonlinearly Permeable Stretching Sheet”, Alexandria Engineering Journal, 55:1 (2016), 151-162 |

[30] | N. Sandeep, O. K. Koriko, I. L. Animasaun, “Modified Kinematic Viscosity Model for 3D-Casson Fluid Flow within Boundary Layer Formed on a Surface at Absolute Zero”, Journal of Molecular Liquids, 221 (2016), 1197-1206 |

[31] | M. J. Babu, N. Sandeep, C. S. K. Raju, “Heat and Mass Transfer in MHD Eyring-Powell Nanofluid Flow due to Cone in Porous Medium”, International Journal of Engineering Research in Africa, 19 (2016), 57-74 |

[32] | I. L. Animasaun, C. S. K. Raju, N. Sandeep, “Unequal Diffusivities Case of Homogeneous-Heterogeneous Reactions within Viscoelastic Fluid Flow in the Presence of Induced Magnetic Field and Nonlinear Thermal Radiation”, Alexandria Engineering Journal, 55:2 (2016), 1595-1606 |

[33] | O. D. Makinde, I. L. Animasaun, “Thermophoresis and Brownian Motion Effect on MHD Bioconvection of Nanofluid with Nonlinear Thermal Radiation and Quartic Chemical Reaction Past an Upper Horizontal Surface of a Paraboloid of Revolution”, Journal of Molecular Liquids, 221 (2016), 733-743 |

[34] | O. D. Makinde, I. L. Animasaun, “Bioconvection in MHD Nanofluid Flow with Nonlinear Thermal Radiation and Quartic Autocatalysis Chemical Reaction Past an Upper Surface of a Paraboloid of Revolution”, International Journal of Thermal Sciences, 109 (2016), 159-171 |

[35] | N. Sandeep, “Effect of Aligned Magnetic Field on Liquid Thin Film Flow of Magnetic- Nanofluid Embedded with Graphene Nanoparticles Thermal Radiation”, Advanced Powder Technology, 28:3 (2017), 865-875 |

[36] | J. V. Ramana Reddy, V. Sugunamma, N. Sandeep, “Effect of Frictional Heating on Radiative Ferrofluid Flow over a Slendering Stretching Sheet with Aligned Magnetic Field”, The European Physical Journal Plus, 132:1 (2017), 7 |

[37] | M. E. Ali, N. Sandeep, “Rheological Equations from Molecular Network Theories”, Results in Physics, 7 (2017), 21-30 |

[38] | P. J. Carreau, “Cattaneo-Christov Model for Radiative Heat Transfer of Magnetohydrodynamic Casson-Ferrofluid: a Numerical Study”, Transactions of the Society of Rheology, 16:1 (1972), 99-127 |

[39] | M. S. Kumar, N. Sandeep, B. R. Kumar, “Free Convection Heat Transfer of MHD Dissipative Carreau Nanofluid Flow over a Stretching Sheet”, Frontiers in Heat and Mass Transfer, 8 (2017), 13 |

[40] | T. Hayat, N. Saleem, S. Asghar, M. S. Alhothuali, A. Alhomaidan, “Influence of Induced Magnetic Field and Heat Transfer on Peristaltic Transport of a Carreau Fluid”, Communications in Nonlinear Science and Numerical Simulation, 16:9 (2011), 3559-3577 · Zbl 1419.76706 |

[41] | B. I. Olajuwon, “Convective Heat and Mass Transfer in a Hydromagnetic Carreau Fluid Past a Vertical Porous Plated in Presence of Thermal Radiation and Thermal Diffusion”, Thermal Science, 15:2 (2011), 241-252 |

[42] | T. Hayat , S. Asad, M. Mustafa, A. Alsaedi, “Boundary Layer Flow of Carreau Fluid over a Convectively Heated Stretching Sheet”, Applied Mathematics and Computation, 246 (2014), 12-22 · Zbl 1338.76022 |

[43] | N. S. Akbar, S. Nadeem, U. I. Haq Rizwan, Ye. Shiwei, “MHD Stagnation Point Flow of Carreau Fluid Yoward a Permeable Shrinking Sheet: Dual Solutions”, Ain Shams Engineering Journal, 5:4 (2014), 1233-1239 |

[44] | N. S. Akbar, “Blood Flow of Carreau Fluid in a Tapered Artery with Mixed Convection”, International Journal of Biomathematics, 7:6 (2014), 1450068 · Zbl 1305.76134 |

[45] | Kh. S. Mekheimer, F. Salama, M. A. Elkot, “The Unsteady Flow of a Carreau Fluid Through Inclined Catheterized Arteries Having a Balloon with Time-Variant Overlapping Stenosis”, Walailak Journal of Science and Technology, 12:10 (2015), 863-883 |

[46] | Y. A. Elmaboud, Kh. S. Mekheimer, M. S. Mohamed, “Series Solution of a Natural Convection Flow for a Carreau Fluid in a Vertical Channel with Peristalsis”, Journal of Hydrodynamics, Ser. B, 27:6 (2015), 969-979 |

[47] | Hashim, M. I. Khan, “A Revised Model to Analyze the Heat and Mass Transfer Mechanisms in the Flow of Carreau Nanofluids”, International Journal of Heat and Mass Transfer, 103 (2016), 291-297 |

[48] | G. R. Machireddy, S. Naramgari, “Heat and Mass Transfer in Radiative MHD Carreau Fluid with Cross Diffusion”, Ain Shams Engineering Journal, 9:4 (2016), 1189-1204 |

[49] | C. Sulochana, G. P. Ashwinkumar, N. Sandeep, “Transpiration Effect on Stagnationpoint Flow of a Carreau Nanofluid in the Presence of Thermophoresis and Brownian Motion”, Alexandria Engineering Journal, 55:2 (2016), 1151-1157 |

[50] | J. K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, 1986 (in Chinese) |

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