Heat Transfer of Thin Film Flow Over an Unsteady Stretching Sheet with Dynamic Viscosity


  • Ali Rehman Department of Mathematics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia
  • Zabidin Salleh Department of Mathematics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia
  • Taza Gul Department of Mathematics, City University of Science and Information Technology, Peshawar P/C, 25000, Pakistan




Water based GO-EG/GO-W nanofluids, Optimal homotopy analysis method, Stretching sheet, Dynamic viscosity


This research paper explains the impact of dynamics viscosity of water base GO-EG/GO-W nanofluid over a stretching sheet. The impact of different parameter for velocity and temperature are displayed and discussed. The similarity transformation is used to convert the partial differential equation to nonlinear ordinary differential equation. The solution of the problem is obtained by using the optimal homotopy analysis method (OHAM). The BVPh 2.0 package function of Mathematica is used to obtain the numerical results. The result of important parameter such as magnetic parameter, Prandtl number, Eckert number, dynamic viscosity, nanoparticles volume fraction and unsteady parameter for both velocity and temperature profiles are plotted and discussed. The BVPh 2.0 package is used to obtain the convergences of the problem up to 25 iteration. The skin friction coefficient and Nusselt number is explained in table form.


Haq, Rizwan Ul, S. Naveed Kazmi, and Toufik Mekkaoui. "Thermal management of water based SWCNTs enclosed in a partially heated trapezoidal cavity via FEM." International Journal of Heat and Mass Transfer 112 (2017): 972-982. https://doi.org/10.1016/j.ijheatmasstransfer.2017.05.041

Prasannakumara, B. C., B. J. Gireesha, M. R. Krishnamurthy, and K. Ganesh Kumar. "MHD flow and nonlinear radiative heat transfer of Sisko nanofluid over a nonlinear stretching sheet." Informatics in Medicine Unlocked 9 (2017): 123-132. https://doi.org/10.1016/j.imu.2017.07.006

Rudraswamy, N. G., S. A. Shehzad, K. Ganesh Kumar, and B. J. Gireesha. "Numerical analysis of MHD three-dimensional Carreau nanoliquid flow over bidirectionally moving surface." Journal of the Brazilian Society of Mechanical Sciences and Engineering 39, no. 12 (2017): 5037-5047. https://doi.org/10.1007/s40430-017-0897-3

Soomro, Feroz Ahmed, Rizwan-ul Haq, Zafar Hayat Khan, and Qiang Zhang. "Passive control of nanoparticle due to convective heat transfer of Prandtl fluid model at the stretching surface." Chinese Journal of Physics 55, no. 4 (2017): 1561-1568. https://doi.org/10.1016/j.cjph.2017.05.007

Usman, Muhammad, Rizwan Ul Haq, Muhammad Hamid, and Wei Wang. "Least square study of heat transfer of water-based Cu and Ag nanoparticles along a converging/diverging channel." Journal of Molecular Liquids 249 (2018): 856-867. https://doi.org/10.1016/j.molliq.2017.11.047

Takhar, Harmindar S., Ali J. Chamkha, and Girishwar Nath. "Unsteady three-dimensional MHD-boundary-layer flow due to the impulsive motion of a stretching surface." Acta Mechanica 146, no. 1 (2001): 59-71. https://doi.org/10.1007/BF01178795

Kumar, K. Ganesh, B. J. Gireesha, M. R. Krishnamurthy, and B. C. Prasannakumara. "Impact of convective condition on Marangoni convection flow and heat transfer in Casson nanofluid with uniform heat source sink." Journal of Nanofluids 7, no. 1 (2018): 108-114. https://doi.org/10.1166/jon.2018.1439

Sheikholeslami, M., and Houman B. Rokni. "Numerical simulation for impact of Coulomb force on nanofluid heat transfer in a porous enclosure in presence of thermal radiation." International Journal of Heat and Mass Transfer 118 (2018): 823-831. https://doi.org/10.1016/j.ijheatmasstransfer.2017.11.041

Sheikholeslami, M., and S. A. Shehzad. "Simulation of water based nanofluid convective flow inside a porous enclosure via non-equilibrium model." International Journal of Heat and Mass Transfer 120 (2018): 1200-1212. https://doi.org/10.1016/j.ijheatmasstransfer.2017.12.132

Falkneb, V. M., and Sylvia W. Skan. "LXXXV. Solutions of the boundary-layer equations." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 12, no. 80 (1931): 865-896. https://doi.org/10.1080/14786443109461870

Yih, K. A. "Uniform suction/blowing effect on forced convection about a wedge: uniform heat flux." Acta Mechanica 128, no. 3 (1998): 173-181. https://doi.org/10.1007/BF01251888

Watanabe, T. "Thermal boundary layers over a wedge with uniform suction or injection in forced flow." Acta Mechanica 83, no. 3 (1990): 119-126. https://doi.org/10.1007/BF01172973

Rajagopal, Kumbakonam R., A. S. Gupta, and Tsung-Yen Na. "A note on the Falkner-Skan flows of a non-Newtonian fluid." International Journal of Non-Linear Mechanics 18, no. 4 (1983): 313-320. https://doi.org/10.1016/0020-7462(83)90028-8

Na, Tsung Yen. Computational methods in engineering boundary value problems. Academic press, New York, 1980.

Asaithambi, Asai. "A finite-difference method for the Falkner-Skan equation." Applied Mathematics and Computation 92, no. 2-3 (1998): 135-141. https://doi.org/10.1016/S0096-3003(97)10042-X

Rehman, Ali, Taza Gul, Zabidin Salleh, Safyan Mukhtar, Fawad Hussain, Kottakkaran Sooppy Nisar, and Poom Kumam. "Effect of the Marangoni convection in the unsteady thin film spray of CNT nanofluids." Processes 7, no. 6 (2019): 392. https://doi.org/10.3390/pr7060392

Rehman, Ali, Zabidin Salleh, Taza Gul, and Zafar Zaheer. "The impact of viscous dissipation on the thin film unsteady flow of GO-EG/GO-W nanofluids." Mathematics 7, no. 7 (2019): 653. https://doi.org/10.3390/math7070653

Balandin, Alexander A., Suchismita Ghosh, Wenzhong Bao, Irene Calizo, Desalegne Teweldebrhan, Feng Miao, and Chun Ning Lau. "Superior thermal conductivity of single-layer graphene." Nano Letters 8, no. 3 (2008): 902-907. https://doi.org/10.1021/nl0731872

Yu, Wei, Huaqing Xie, and Dan Bao. "Enhanced thermal conductivities of nanofluids containing graphene oxide nanosheets." Nanotechnology 21, no. 5 (2009): 055705. https://doi.org/10.1088/0957-4484/21/5/055705

Gul, Taza, and Kiran Firdous. "The experimental study to examine the stable dispersion of the graphene nanoparticles and to look at the GO-H2O nanofluid flow between two rotating disks." Applied Nanoscience 8, no. 7 (2018): 1711-1727. https://doi.org/10.1007/s13204-018-0851-4

Gul, Taza, Waqas Noman, Muhammad Sohail, and Muhammad Altaf Khan. "Impact of the Marangoni and thermal radiation convection on the graphene-oxide-water-based and ethylene-glycol-based nanofluids." Advances in Mechanical Engineering 11, no. 6 (2019): 1687814019856773. https://doi.org/10.1177/1687814019856773

Qasim, M., Z. H. Khan, R. J. Lopez, and W. A. Khan. "Heat and mass transfer in nanofluid thin film over an unsteady stretching sheet using Buongiorno's model." The European Physical Journal Plus 131, no. 1 (2016): 1-11. https://doi.org/10.1140/epjp/i2016-16016-8

Liao, Shijun. "An optimal homotopy-analysis approach for strongly nonlinear differential equations." Communications in Nonlinear Science and Numerical Simulation 15, no. 8 (2010): 2003-2016. https://doi.org/10.1016/j.cnsns.2009.09.002

Maleque, Kh. "Effects of binary chemical reaction and activation energy on MHD boundary layer heat and mass transfer flow with viscous dissipation and heat generation/absorption." International Scholarly Research Notices 2013 (2013). https://doi.org/10.1155/2013/284637

Gireesha, B. J., M. Archana, B. Mahanthesh, and B. C. Prasannakumara. "Exploration of activation energy and binary chemical reaction effects on nano Casson fluid flow with thermal and exponential space-based heat source." Multidiscipline Modeling in Materials and Structures (2019).

Prasannakumara, B. C., B. J. Gireesha, Rama SR Gorla, and M. R. Krishnamurthy. "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, no. 5 (2016): 04016019. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000578

Khodabandeh, Erfan, Davood Toghraie, A. Chamkha, Ramin Mashayekhi, Omidali Akbari, and Seyed Alireza Rozati. "Energy saving with using of elliptic pillows in turbulent flow of two-phase water-silver nanofluid in a spiral heat exchanger." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 4 (2019): 2025-2049. https://doi.org/10.1108/HFF-10-2018-0594

Rehman, Ali, Zabidin Salleh, and Taza Gul. "Influence of Dynamics Viscosity on the Water Base Graphene Oxide-Ethylene Glycol/Graphene Oxide-Water Nanofluid Flow Over a Stretching Cylinder." Journal of Nanofluids 8, no. 8 (2019): 1661-1667. https://doi.org/10.1166/jon.2019.1722

Rehman, Ali, Zabidin Salleh, and Taza Gul. "In?uence of dynamics viscosity on the water base CNTs nanofluid flow over a stretching surface." Cogent Engineering 7, no. 1 (2020): 1772945. https://doi.org/10.1080/23311916.2020.1772945

Rehman, Ali, Zabidin Salleh, and Taza Gul. "The impact of marangoni convection, magnetic field and viscous dissipation on the thin film unsteady flow of go-eg/go-w nanofluids over an extending sheet." JP Journal of Heat and Mass Transfer 18, no. 2 (2019): 477-496. https://doi.org/10.17654/HM018020477

Rehman, Ali, Zabidin Salleh, and Taza Gul. "The impact of the magnetic field and viscous dissipation on the thin film unsteady flow of GO-EG/GO-W nanofluids." In Journal of Physics: Conference Series, vol. 1366, no. 1, p. 012031. IOP Publishing, 2019. https://doi.org/10.1088/1742-6596/1366/1/012031

Rehman, Ali, Zabidin Salleh, and Taza Gul. "Analytical study of unsteady squeezed flow of water base cnts nanofluid with magnetic field and variable thermal conductivity over a stretching surface." Frontiers in Heat and Mass Transfer (FHMT) 14 (2020). https://doi.org/10.5098/hmt.14.20

Raza, Jawad. "Thermal radiation and slip effects on magnetohydrodynamic (MHD) stagnation point flow of Casson fluid over a convective stretching sheet." Propulsion and Power Research 8, no. 2 (2019): 138-146. https://doi.org/10.1016/j.jppr.2019.01.004

Raza, J., Fateh Mebarek-Oudina, Paras Ram, and S. Sharma. "MHD flow of non-Newtonian molybdenum disulfide nanofluid in a converging/diverging channel with Rosseland radiation." In Defect and Diffusion Forum, vol. 401, pp. 92-106. Trans Tech Publications Ltd, 2020. https://doi.org/10.4028/www.scientific.net/DDF.401.92

Alkasassbeh, Mohammad, Zurni Omar, Fateh Mebarek?Oudina, Jawad Raza, and Ali Chamkha. "Heat transfer study of convective fin with temperature?dependent internal heat generation by hybrid block method." Heat Transfer-Asian Research 48, no. 4 (2019): 1225-1244. https://doi.org/10.1002/htj.21428

Lund, Liaquat Ali, Zurni Omar, Jawad Raza, and Ilyas Khan. "Magnetohydrodynamic flow of Cu-Fe3O4/H2O hybrid nanofluid with effect of viscous dissipation: dual similarity solutions." Journal of Thermal Analysis and Calorimetry 10, no. 1007 (2020): 1-13. https://doi.org/10.1007/s10973-020-09602-1

Lund, Liaquat Ali, Zurni Omar, Jawad Raza, and Ilyas Khan. "Triple solutions of micropolar nanofluid in the presence of radiation over an exponentially preamble shrinking surface: Convective boundary condition." Heat Transfer 49, no. 5 (2020): 3075-3093. https://doi.org/10.1002/htj.21763




How to Cite

Rehman, A., Salleh, Z., & Gul, T. (2021). Heat Transfer of Thin Film Flow Over an Unsteady Stretching Sheet with Dynamic Viscosity. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 81(2), 67–81. https://doi.org/10.37934/arfmts.81.2.6781
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