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Heat Transfer Analysis of a Williamson Micropolar Nanofluid with Different Flow Controls

Published online by Cambridge University Press:  28 August 2018

M. Muthtamilselvan*
Department of Mathematics Bharathiar University Tamilnadu, India
E. Ramya
Department of Mathematics Bharathiar University Tamilnadu, India
D. H. Doh
Division of Mechanical Engineering College of Engineering Korea Maritime and Ocean University Busan, South Korea
G. R. Cho
Division of Mechanical Engineering College of Engineering Korea Maritime and Ocean University Busan, South Korea
*Corresponding author (
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The present model is devoted for the steady stagnation point flow of a Williamson micropolar nanofluid with magneto-hydrodynamics and thermal radiation effects passed over a horizontal porous stretching sheet. The fluid is considered to be gray, absorbing-emitting but non-scattering medium. The Cogley-Vincent-Gilles formulation is adopted to simulate the radiation component of heat transfer. By applying similarity analysis, the governing partial differential equations are transformed into a set of non-linear ordinary differential equations and they are solved by using the bvp4c package in MATLAB. Numerical computations are carried out for various values of the physical parameters. The effects of momentum, microrotation, temperature and nanoparticle volume fraction profiles together with the reduced skin friction coefficient, reduced Nusselt number and reduced Sherwood number of both active and passive controls on the wall mass flux are graphically presented. The present results are compared with previously obtained solutions and they are in good agreement. Results show that the skin friction is increasing functions of the Williamson parameter in both stretching and shrinking surfaces.

Research Article
© The Society of Theoretical and Applied Mechanics 2018 

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Mukesh Kumar, S., Bansal, K. and Bansal, S., “Pulsatile Unsteady Flow of Blood through Porous Medium in a Stenotic Artery under the Influence of Transverse Magnetic Field,” Korea-Australia Rheology Journal, 24, pp. 181189 (2012).Google Scholar
Makinde, O. D., Khan, W. A. and Khan, Z. H., “Buoyancy Effects on MHD Stagnation Point Flow and Heat Transfer of a Nanofluid past a Convectively Heated Stretching/Shrinking Sheet,” International Journal of Heat and Mass Transfer, 62, pp. 526533 (2013).Google 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, pp. 601615 (2013).Google Scholar
Kundu, P. K., Das, K. and Acharya, N., “Flow Features of a Conducting Fluid Near an Accelerated Vertical Plate in Porous Medium with Ramped Wall Temperature,” Journal of Mechanics, 30, pp. 277288 (2014).Google Scholar
Rashidi, M. M., Vishnu Ganesh, N., Abdul Hakeem, A. K. 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).Google Scholar
Mastroberardino, A. and Siddique, J. I., “Magneto-hydrodynamic Stagnation Flow and Heat Transfer Toward a Stretching Permeable Cylinder,” Advanced Mechanical Engineering, (2014) Article ID 419568. Scholar
Prakash, D., Muthtamilselvan, M. and Doh, D. H., “Unsteady MHD Non-Darcian Flow over a Vertical Stretching Plate Embedded in a Porous Medium with Non-Uniform Heat Generation,” Applied Mathematics and Computation, 236, pp. 480492 (2014).Google Scholar
Doh, D. H. and Muthtamilselvan, M., “Thermophoretic Particle Deposition on Magnetohydrodynamic Flow of Micropolar Fluid Due to a Rotating Disk,” International Journal of Mechanical Sciences, 130, pp. 350359 (2017).Google Scholar
Seth, G. S., Tripathi, R., Sharma, R. and Chamkha, A. J., “MHD Double Diffusive Natural Convection Flow over Exponentially Accelerated Inclined plate,” Journal of Mechanics, 33, pp. 8799 (2017).Google Scholar
Sheikholeslami, M., Hatami, M. and Ganji, D. D., “Analytical Investigation of MHD Nanofluid Flow in a Semi-Porous Channel,” Powder Technology, 246, pp. 327336 (2013).Google Scholar
Mukhopadhyay, S., “MHD Boundary Layer Flow and Heat Transfer over an Exponentially Stretching Sheet Embedded in a Thermally Stratified Medium,” Alexandria Engineering Journal, 53, pp. 259265 2013).Google Scholar
Khan, W. A. and Makinde, O. D., “MHD Nanofluid Bioconvection Due to Gyrotactic Microorganisms over a Convectively Heat Stretching Sheet,” International Journal of Thermal Science, 81, pp. 118124 (2014).Google Scholar
Ahmad, R. and Waqar, A., “Khan Unsteady Heat and Mass Transfer MHD Nanofluid Flow over a Stretching Sheet with Heat Source/Sink Using Quasi-Linearization Technique,” Canadian Journal of Physics, 93, pp. 14771485 (2015).Google Scholar
Sajid, M., Ahmed, B. and Abbas, Z., “Steady Mixed Convection Stagnation Point Flow of MHD Oldroyd-B Fluid over a Stretching Sheet,” Journal of the Egyptian Mathematical Society, 23, pp. 440444 (2015).Google Scholar
Williamson, R. V., “The Flow of Pseudoplastic Materials,” Industrial and Engineering Chemistry Research, 21, pp. 11081111 (1929).Google Scholar
Nadeem, S. and Akram, S., “Peristaltic Flow of a Williamson Fluid in an Asymmetric Channel,” Communications in Nonlinear Science and Numerical Simulation, 15, pp. 17051716 (2010).Google Scholar
Zehra, I., Yousaf, M. M. and Nadeem, S., “Numerical Solutions of Williamson Fluid with Pressure Dependent Viscosity,” Results in Physics, 5, pp. 2025 (2015).Google Scholar
Ellahi, R., Riaz, A. and Nadeem, S., “Three Dimensional Peristaltic Flow of Williamson Fluid in a Rectangular Duct,” Indian Journal of Physics, 87, pp. 12751281 (2013).Google Scholar
Khan, N. A., Khan, S. and Riaz, F., “Boundary Layer Flow of Williamson Fluid with Chemically Reactive Species Using Scaling Transformation and Ho-motopy Analysis Method,” Mathematical Science Letters, 3, pp. 199205 (2014).Google Scholar
Eldabe, N. T., Elogail, M. A., Elshaboury, S. M. and Hasan, A. A., “Hall Effects on the Peristaltic Transport of Williamson Fluid through a Porous Medium with Heat and Mass Transfer,” Applied Mathematical Modelling, 40, pp. 315328 (2016).Google Scholar
Akbar, N. S., Hayat, T., Nadeem, S. and Obaidat, S., “Peristaltic Flow of a Williamson Fluid in an Inclined Asymmetric Channel with Partial Slip and Heat Transfer,” International Journal of Heat and Mass Transfer, 55, pp. 18551862 (2012).Google Scholar
Nadeem, S., Maraj, E. N. and Akbar, N. S., “Investigation of Peristaltic Flow of Williamson Nanofluid in a Curved Channel with Compliant Walls,” AppliedNanoscience, 4, pp. 511521 (2014).Google Scholar
Nadeem, S., Hussain, S. T. and Lee, C., “Flow of a Williamson Fluid over a Stretching Sheet,” Brazilian Journal of Chemical Engineering, 30, pp. 619625 (2013).Google Scholar
Nadeem, S. and Hussain, S. T., “Flow and Heat Transfer Analysis of Williamson Nanofluid,” Applied Nanoscience 4, pp. 10051012 (2014).Google Scholar
Nadeem, S. and Hussain, S. T., “Heat Transfer Analysis of Williamson Fluid over Exponentially Stretching Surface,” Applied Mathematics and Mechanics, 35, pp. 489502 (2014).Google Scholar
Kothandapani, M. and Prakash, J., “Effects of Thermal Radiation Parameter and Magnetic Field on the Peristaltic Motion of Williamson Nanofluids in a Tapered Asymmetric Channel,” International Journal of Heat and Mass Transfer, 81, pp. 234245 (2015).Google Scholar
Gorlal, R. S. R. and Gireesha, B. J., “Dual Solutions for Stagnation Point Flow and Convective Heat Transfer of a Williamson Nanofluid past a Stretching/Shrinking Sheet,” Heat and Mass Transfer, 52, pp. 11531162 (2016).Google Scholar
Prasannakumara, B. C., Gireesha, B. J., Gorla, R. S. R. and Krishnamurthy, M. R., “Effects of Chemical Reaction and Nonlinear Thermal Radiation on Williamson Nanofluid Slip Flow over a Stretching Sheet Embedded in a Porous Medium,” Journal of Aerospace Engineering, 29, (2016) 10.1061/ (ASCE)AS.19435525.0000578.Google Scholar
Nadeem, S. and Hussain, S. T., “Analysis of MHD Williamson Nanofluid Flow over a Heated Surface,” Journal of Applied Fluid Mechanics, 9, pp. 729739 (2016).Google Scholar
Halim, N. A., Sivasankaran, S. and Noor, N. F. M., “Active and Passive Controls of the Williamson Stagnation Nanofluid Flow over a Stretching/ Shrinking Surface,” Neural Computing and Application, 28, pp. 10231033 (2017).Google Scholar
Prakash, D. and Muthtamilselvan, M., “Effect of Radiation on Transient MHD Flow of Micropolar Fluid between Porous Vertical Channel with Boundary Conditions of the Third Kind,” Ain Shams Engineering Journal, 5, pp. 12771286 (2013).Google Scholar
Nandy, S. and Pop, I., “Effects of Magnetic Field and Thermal Radiation on Stagnation Flow and Heat Transfer of Nanofluid over a Shrinking Surface,” International Communication of Heat and Mass Transfer, 53, pp. 5055 (2014).Google Scholar
Hayat, T., Muhammad, T., Alsadi, A. and Alhuthali, M. S., “Magnetohydrodynamic Threedimensional Flow of Viscoelastic Nanofluid in the Presence of Nonlinear Thermal Radiation,” Journal of Magnetism and Magnetic Materials, 385, pp. 222229 (2015).Google Scholar
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, pp. 3137 (2015).Google Scholar
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 Modeling, 39, pp. 165181 (2015).Google Scholar
Hayat, T., Asad, S., Mustafa, M. and Alsaedi, A., “MHD Stagnation Point Flow of Jeffrey Fluid over a Convectively Heated Stretching Sheet,” Computers and Fluids, 108, pp. 179185 (2015).Google Scholar
Mohyud-Din, S. T., Jan, S. U., Khan, U. and Ahmed, N., “MHD Flow of Radiative Micropolar Nanofluid in a Porous Channel: Optimal and Numerical Solutions,” Neural Computing and Applications, (2016) DOI 10.1007/s00521-016-2493-3.Google Scholar
Kuznetsov, A. V. and Nield, D. A., “The Cheng Minkowycz Problem for Natural Convective Boundary-Layer Flow in a Porous Medium Saturated by a Nanofluid: a Revised Model,” International Journal of Heat and Mass Transfer, 65, pp. 682685 (2013).Google Scholar
Noor, N. F. M., Haq, R. U., Nadeem, S. and Hashim, I., “Mixed Convection Stagnation Flow of a Micropolar Nanofluid along a Vertically Stretching Surface with Slip Effects,” Meccanica, 50, pp. 20072022 (2015).Google Scholar
Cogley, A. C., Vincent, W. G. and Gilles, S. E., “Differential Approximation for Radiative Transfer in a Non-Gray Gas Near Equilibrium,” AIAA Journal, 6, pp. 551553 (1968).Google Scholar
Ishak, A., Nazar, R., Arifin, N. M. and Pop, I., “Mixed Convection of the Stagnation-Point Flow Towards a Stretching Vertical Permeable Sheet,” Malaysian Journal of Mathematical Science, 1, pp. 217226 (2007).Google Scholar