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Analysis of Electromagnetohydrodynamic Stagnation Point Flow of Nanofluid Over a Nonlinear Stretching Sheet with Variable Thickness

Published online by Cambridge University Press:  18 July 2019

G. S. Seth*
Affiliation:
Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad - 826004, India
P. K. Mandal
Affiliation:
Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad - 826004, India
*
*Corresponding author (gsseth_ism@yahoo.com)
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Abstract

Present study explores stagnation point flow of nanofluid towards a nonlinear stretching sheet of variable thickness in the presence of electromagnetic field and convective heating. The effect of viscous dissipation and Joule heating are also taken into consideration. Novel concept of non-linear radiative heat flux is also considered. The nanofluid is inspired by Lorentz force which is instigated from the interaction of magnetic and electric fields. Using similarity transformation, the governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically by fourth order Runge-Kutta method along with shooting technique. The velocity, temperature and nanoparticle concentration profiles are plotted and analysed corresponding to various pertinent flow parameters. Also, the skin friction and rate of heat and mass transfers at the surface are computed and explained in detail. It is observed that higher wall thickness parameter results in the reduction of velocity, temperature and nanoparticle concentration when velocity power index is less than unity and opposite effect is observed when velocity power index is greater than unity. Due to intensification of electric field, nanofluid velocity is getting retarded and thereby resulting in enhancement of fluid temperature and nanoparticle concentration.

Type
Research Article
Copyright
© The Society of Theoretical and Applied Mechanics 2019 

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References

REFERENCES

Choi, S. U. S., “Enhancing Thermal Conductivity of Fluids with Nanoparticles,” in: Siginer, D. A. Wang, H.P. (Eds.), Developments and Applications of Non-Newtonian Flows. ASME, New York, FED-231/MD-66, pp. 99105 (1995).Google Scholar
Buongiorno, J., “Convective Transport in Nanofluids,” Journal of Heat Transfer, 128, pp. 240250 (2006).Google Scholar
Khan, W. A. and Pop, I., “Boundary-layer Flow of a Nanofluid Past a Stretching Sheet,” International Journal of Heat and Mass Transfer, 53, pp. 24772483 (2010).Google Scholar
Makinde, O. D. and Aziz, A., “Boundary Layer Flow of a Nanofluid Past a Stretching Sheet with a Convective Boundary Condition,” International Journal of Thermal Sciences, 50, pp. 13261332 (2011).CrossRefGoogle Scholar
Sheikholeslami, M., Gorji-Bandpy, M. and Ganji, D. D., “Lattice Boltzmann Method for MHD Natural Convection Heat Transfer Using Nanofluid,” Powder Technology., 254, pp. 8293 (2014).CrossRefGoogle Scholar
Rashidi, M. M., Ganesh, N. V., Hakeem, A. K. A. and Ganga, B., “Buoyancy Effect on MHD Flow of Nanofluid over a Stretching Sheet in the Presence of Thermal Radiation,” Journal of Molecular Liquids, 198, pp. 234238 (2014).CrossRefGoogle Scholar
Chamkha, A. J., Rashad, A. M., RamReddy, C. and Murthy, P. V. S. N.Viscous Dissipation and Magnetic Field Effects in a Non-Darcy Porous Medium Saturated with a Nanofluid under Convective Boundary Condition,” Special Topics & Reviews in Porous Media, 5(1), pp. 2739 (2014).CrossRefGoogle Scholar
Hayat, T., Aziz, A., Muhammad, T., Alsaedi, A. and Mustafa, M., “On Magnetohydrodynamic Flow of Second Grade Nanofluid over a Convectively Heated Nonlinear Stretching Surface,” Advanced Powder Technology, 27, pp. 19922004 (2016).Google Scholar
Hayat, T., Hussain, Z., Farooq, M. and Alsaedi, A., Homogenious and Heterogeneous Reactions Effects in Flow with Joule Heating and Viscous Dissipation, Journal of Mechanics, 33(1), pp. 7786 (2017).CrossRefGoogle Scholar
Cortell, R., “Effects of Viscous Dissipation and Radiation on the Thermal Boundary Layer over a Nonlinearly Stretching Sheet,” Physics Letters A, 372, pp. 631636 (2008).CrossRefGoogle Scholar
Rahman, M.M. and Eltayeb, I.A., “Radiative Heat Transfer in a Hydromagnetic Nanofluid Past a Non-Linear Stretching Surface with Convective Boundary Condition,” Meccanica, 48(3), pp. 601615 (2013).CrossRefGoogle Scholar
Nadeem, S. and Haq, R.U., “Effect of Thermal Radiation for Magnetohydrodynamic Boundary Layer Flow of a Nanofluid Past a Stretching Sheet with Convective Boundary Conditions,” Journal of Computational and Theoretical Nanoscience, 11(1-9), pp. 3240 (2014).CrossRefGoogle Scholar
Hayat, T. Waqas, M., Shehzad, S. A. and Alsaedi, A., “MHD Stagnation Point Flow of Jeffrey Fluid by a Radially Stretching Surface with Viscous Dissipation and Joule Heating,” J. Hydrology and Hydromechanics, 63, pp. 311317 (2015).CrossRefGoogle Scholar
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, pp. 3643 (2015).CrossRefGoogle Scholar
Seth, G. S., Sharma, R., Kumbhakar, B. and Chamkha, A. J., “Hydromagnetic Flow of Heat Absorbing and Radiating Fluid over Exponentially Stretching Sheet with Partial Slip and Viscous and Joule Dissipation,” Engineering Computations, 33(3), pp. 907925 (2016).Google Scholar
Seth, G. S., Mishra, M. K. and Chamkha, A. J.Hydromagnetic Convective Flow of Viscoelastic Nanofluid with Convective Boundary Condition over an Inclined Stretching SheetJournal of Nanofluids, 5(4), pp. 512521 (2016).CrossRefGoogle Scholar
Kumar, R., Kumar, R., Shehzad, S. A. and Sheikholeslami, M., “Rotating Frame Analysis of Radiating and Reacting Ferro-Nanofluid Considering Joule Heating and Viscous Dissipation,” International Journal of Heat and Mass Transfer, 120, pp. 540551 (2018).Google Scholar
Pantokratoras, A. and Fang, T., “Sakiadis Flow with Nonlinear Rosseland Thermal Radiation,” Physica Scripta, 87(1), 015703 (2013).CrossRefGoogle Scholar
Mushtaq, A., Mustafa, M., Hayat, T. and Alsaedi, A., “Effects of Thermal Radiation on the Stagnation-Point Flow of Upper-Convected Maxwell Fluid over a Stretching Sheet,” Journal of Aerospace Engineering, 27(4), 04014015, (2014).Google Scholar
Cortell, R.Fluid Flow and Radiative Nonlinear Heat Transfer over a Stretching Sheet,” Journal of King Saud University-Science, 26(2), pp. 161167 (2014).CrossRefGoogle Scholar
Mushtaq, A., Mustafa, M. Hayat, T. and Alsaedi, A.Nonlinear Radiative Heat Transfer in the Flow of Nanofluid Due to Solar Energy: A Numerical Study,” Journal of Taiwan Institute of Chemical Engineers, 45, pp. 11761183 (2014).CrossRefGoogle Scholar
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
Mahanthesh, B., Gireesha, B. J. and Gorla, R. S. R., “Nonlinear Radiative Heat Transfer in MHD Three-Dimensional Flow of Water Based Nanofluid over a Non-Linearly Stretching Sheet with Convective Boundary Condition,” Journal of the Nigerian Mathematical Society, 35, pp. 178198 (2016).Google Scholar
Kumar, R., Sood, S., Sheikholeslami, M. and Shehzad, S. A., “Nonlinear Thermal Radiation and Cubic Autocatalysis Chemical Reaction Effects on the Flow of Stretched Nanofluid under Rotational Osciollations,” Journal of Clloid and Interface Science, 505, pp. 253265 (2017).CrossRefGoogle Scholar
Turkyilmazoglu, M. and Pop, I., “Exact Analytical Solutions for the Flow and Heat Transfer Near the Stagnation Point on a Stretching/Shrinking Sheet in a Jeffrey Fluid,” International Journal of Heat and Mass Transfer, 57, pp. 8288 (2013).Google Scholar
Rashidi, M. M. and Freidoonimehr, N., “Analysis of Entropy Generation in MHD Stagnation-Point Flow in Porous Media with Heat Transfer,” International Journal for Computational Methods Engineering Science and Mechanics, 15, pp. 345355 (2014).CrossRefGoogle Scholar
Ibrahim, W., “Nonlinear Radiative Heat Transfer in Magnetohydrodynamic (MHD) Stagnation Point Flow of Nanofluid Past a Stretching Sheet with Convective Boundary Condition,” Propulsion and Power Research, 4(4), pp. 230239 (2015).CrossRefGoogle Scholar
Khan, W. A., Makinde, O. D. and Khan, Z. H., “Nonaligned MHD Stagnation Point Flow of Variable Viscosity Nanofluids Past a Stretching Sheet with Radiative Heat,” International Journal of Heat and Mass Transfer, 96, pp. 525534 (2016).CrossRefGoogle Scholar
Fang, T., Zhang, J. and, Zhong, Y., “Boundary Layer Flow over a Stretching Sheet with Variable Thickness,” Applied Mathematics and Computation, 218, pp. 72417252 (2012).CrossRefGoogle Scholar
Elbashbeshy, E. M. A., Emam, T. G. and Abdel-Wahed, M. S., “Flow and Heat Transfer over a Moving Surface with Non-Linear Velocity and Variable Thickness in a Nanofluid in the Presence of Thermal Radiation,” Canadian Journal of Physics, 91, pp. 699708 (2013).Google Scholar
Abdel-Wahed, M. S., Elbashbeshy, E. M. A. and Emam, T. G., “Flow and Heat Transfer over a Moving Surface with Non-Linear Velocity and Variable Thickness in a Nanofluids in the Presence of Brownian Motion,” Applied Mathematics and Computation, 254, pp. 4962 (2015).CrossRefGoogle Scholar
Babu, M. J. and Sandeep, N., “3D MHD Flow of a Nanofluid over a Slendering Stretching Sheet with Thermophoresis and Brownian Motion Effects,” Journal of Molecular Liquids, 222, pp. 10031009 (2016).CrossRefGoogle Scholar
Turkyilmazoglu, M., Magnetic Field and Slip Effects on the Flow and Heat Transfer of Stagnation Point Jeffrey Fluid over Deformable Surfaces, Zeitschrift fur Naturforschung A, 71(6), pp. 549556 (2016).CrossRefGoogle Scholar
Farooq, M., Javed, M., Khan, M. J., M., Anjuma, A. and Hayat, T., “Melting Heat Transfer and Double Stratification in Stagnation Flow of Viscous Nanofluid,” Results in Physics, 7, pp. 22962301 (2017).CrossRefGoogle Scholar
Daniel, Y. S., Aziz, Z. A., Ismail, Z. and Salah, F., “Impact of Thermal Radiation on Electrical MHD Flow of Nanofluid over Nonlinear Stretching Sheet with Variable Thickness,” Alexandria Engineering Journal, 57(3), pp. 21872197 (2018).Google Scholar
Reddy, S., Naikoti, K. and Rashidi, M. M., “MHD Flow and Heat Transfer Characteristics of Williamson Nanofluid over a Stretching Sheet with Variable Thickness and Variable Thermal Conductivity,” Transactions of A. Razmadze Mathematical Institute, 171, pp. 195211 (2017).CrossRefGoogle Scholar
Hayat, T., Ullah, I., Alsaedi, A. and Farooq, M., “MHD Flow of Powell-Eyring Nanofluid over a Non-Linear Stretching Sheet with Variable Thickness,” Results in Physics, 7, pp. 189196 (2017).CrossRefGoogle Scholar
Kumar, R., Raju, C. S., K, Sekhar, K. R and Reddy, G. V., Three Dimensional MHD Ferrous Nanofluid Flow over a Sheet of Variable Thickness in Slip Flow Regime, Journal of Mechanics, doi:10.1017/jmech.2017.95 (2017).CrossRefGoogle Scholar
Turkyilmazoglu, M., Naganthran, K. and Pop, I., “Unsteady MHD Rear Stagnation Point Flow over Off-Centred Deformable Surfaces,” International Journal of Numerical Methods for Heat and Fluid Flow, 27(7), pp. 15541570 (2017).CrossRefGoogle Scholar
Kumar, R., Sood, S., Shehzad, S. A. and Sheikholeslami, M., “Radiative Heat Transfer Study for Flow of Non-Newtonian Nanofluid Past a Riga Plate with Variable Thickness,” Journal of Molecular Liquids, 248, pp. 143152 (2017).CrossRefGoogle Scholar
Prasad, K. V., Vajravelu, K., Vaidya, H., Gorder, R. A. V., “MHD Flow and Heat Transfer in a Nanofluid over a Slender Elastic Sheet with Variable Thickness,” Results in Physics, 7, pp. 14621474 (2017).CrossRefGoogle Scholar
Turkyilmazoglu, M., “Analytical Solutions to Mixed Convection MHD Fluid Flow Induced by a Nonlinearly Deforming Permeable Surface,” Communications in Nonlinear Science and Numerical Simulation, 63, pp. 373379 (2018).CrossRefGoogle Scholar
Daniel, Y. S., Aziz, Z. A., Ismail, Z. and Salah, F., “Effects of Thermal Radiation, Viscous and Joule Heating on Electrical MHD Nanofluid with Double Stratification,” Chinese Journal of Physics, 55(3), pp. 630651 (2017).Google Scholar
Hayat, T., Safiq, A. and Alseidi, A., “Effect of Joule Heating and Thermal Radiation in Flow of Third Grade Fluid over Radiative Surface,” Plos One, 9(1), e83153 (2014).CrossRefGoogle Scholar
Mabood, F., Khan, W. A. and Ismail, A. I., “MHD Boundary Layer Flow and Heat Transfer of Nanofluids over a Nonlinear Stretching Sheet: A Numerical Study,” Journal of Magnetism and Magnetic Materials, 374, pp. 569576 (2015).CrossRefGoogle Scholar
Brinkman, H. C, “The Viscosity of Concentrated Suspensions and Solutions,” The Journal of Chemical Physics. 20, pp. 571581 (1952).CrossRefGoogle Scholar
Tiwari, R. K., 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, pp. 20022018 (2007).CrossRefGoogle Scholar
Khanafer, K., Vafai, K. and Lightstone, M., “Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids,” International Journal of Heat and Mass Transfer, 46, pp. 36393653 (2003).Google Scholar
Maxwell, J. C. A treatise on Electricity and Magnetism, Cambridge Oxford University Press, Cambridge (1904).Google Scholar
Sheikholeslami, M., Abelman, S. and Ganji, D. D., “Numerical simulation of MHD nanofluid flow and heat transfer considering viscous dissipation,” International Journal of Heat and Mass Transfer, 79, pp. 212222 (2014).CrossRefGoogle Scholar
Rosseland, S., Astrophysik and Atom-Theorestischegrundlagen. Springer, Berlin (1931).CrossRefGoogle Scholar
Kakac, S. and Pramuanjaroenkij, A., “Single-Phase and Two-Phase Treatments of Convective Heat Transfer Enhancement with Nanofluids–A State-of-the-Art Review,” International Journal of Thermal Sciences, 100, pp. 7597 (2016).CrossRefGoogle Scholar
Nield, D. A. and Kuznetsov, A. V., “The Cheng– Minkowycz Problem for Natural Convective Boundary-Layer Flow in a Porous Medium Saturated by a Nanofluid.” International Journal of Heat and Mass Transfer, 52(25), pp. 57925795 (2009).CrossRefGoogle Scholar
Rana, P. and Bhargava, R., “Flow and Heat Transfer of a Nanofluid over a Nonlinearly Stretching Sheet: A Numerical Study,” Communications in Nonlinear Science and Numerical Simulation, 17(1), pp. 212226 (2012).CrossRefGoogle Scholar
Turkyilmazoglu, M., “Determination of the Correct Range of Physical Parameters in the Approximate Analytical Solutions of Nonlinear Equations Using the Adomian Decomposition Method,” Mediterranean Journal of Mathematics, 13(6), pp. 40194037 (2016).CrossRefGoogle Scholar
Chaim, T. C., “Stagnation Point Flow Towards a Stretching Sheet,” Journal of the Physical Society of Japan, 63, pp. 24432444 (1994).CrossRefGoogle Scholar