THERMAL SCIENCE
International Scientific Journal
Thermal Science - Online First
online first only
Influence of activation energy and Stefan blowing on magneto cross Williamson fluid over an exponential stretching sheet
ABSTRACT
In this study, a two-dimensional Williamson fluid flows through a Darcy- Forchhiemer permeable medium, influenced by mixed convection, MHD, and non-linear thermal radiation over an exponential stretching sheet. The impacts of Stefan blowing, Brownian motion, and thermophoresis are being studied. This investigation looks into the impacts of joule heating and activation energy. The governing partial differential equations that are used for fluid flow modelling are transformed into a collection of non-linear ordinary differential equations by use of the required similarity transformations. The Keller Box numerical technique is applied to solve the corresponding nonlinear ordinary differential equations. The influence of numerous characteristics is investigated using graphical representations of velocity, temperature, and concentration. To validate the problem, numerical values of the Nusselt number are calculated and compared to available literature. Additionally, the skin friction coefficient are determined and tabulated numerically.
KEYWORDS
PAPER SUBMITTED: 2025-03-28
PAPER REVISED: 2025-04-27
PAPER ACCEPTED: 2025-05-10
PUBLISHED ONLINE: 2025-07-05
- Pearson, J.R.A., et al., Models for Flow of Non-Newtonian and Complex Fluids through Porous Media, Journal of Non-Newtonian Fluid Mechanics,102 (2002),pp.447-73. doi.org/10.1016/s0377-0257(01)00191-4
- Hoyt, J.W.,Some Applications of Non-Newtonian Fluid Flow,Advances in the Flow and Rheology of Non-Newtonian Fluids,8 (1999), pp.797-826. doi.org/10.1016/s0169- 3107(99)80008-2
- Chhabra, R.P., et al., Non-Newtonian Fluid Behaviour, Non-Newtonian Flow in the Process Industries, 1999,pp. 1-36. doi.org/10.1016/b978-075063770-1/50002-6
- Hameed, M., and S. Nadeem, Unsteady MHD Flow of a Non-Newtonian Fluid on a Porous Plate." Journal of Mathematical Analysis and Applications 325, (2007), pp.724-33. doi.org/10.1016/j.jmaa.2006.02.002
- Turkyilmazoglu, Mustafa, MHD Fluid Flow and Heat Transfer Due to a Stretching Rotating Disk, International Journal of Thermal Sciences, 51, (2012),pp.195-201. doi.org/10.1016/j.ijthermalsci.2011.08.016
- Kabeel AE et al., A review of magnetic field effects on flow and heat transfer in liquids: Present status and future potential for studies and applications, Renewable and Sustainable Energy Reviews,45,(2015),pp.830-837. dx.doi.org/10.1016/j.rser.2015.02.029
- Khan, Umar et al., Nonlinear Radiation Effects on Flow of Nanofluid over a Porous Wedge in the Presence of Magnetic Field, International Journal of Numerical Methods for Heat & Fluid Flow 27, ( 2017),pp.48-63. doi.org/10.1108/hff-10-2015-0433
- Hosseinzadeh, Kh. et al.,Nonlinear Thermal Radiation and Chemical Reaction Effects on Maxwell Fluid Flow with Convectively Heated Plate in a Porous Medium,Heat Transfer- Asian Research 48,(2018), pp.744-59. doi.org/10.1002/htj.21404
- Khan, Masood and Aamir Hamid, Influence of Non-Linear Thermal Radiation on 2D Unsteady Flow of a Williamson Fluid with Heat Source/Sink, Results in Physics 7 (2017), pp.3968-75. doi.org/10.1016/j.rinp.2017.10.014
- Mabood, F., A.et al., Impacts of Stefan Blowing and Mass Convention on Flow of Maxwell Nanofluid of Variable Thermal Conductivity about a Rotating Disk,Chinese Journal of Physics 71 (2021), pp.260-72. doi.org/10.1016/j.cjph.2021.03.003
- Naveen Kumar, R. et al., Stefan Blowing Effect on Nanofluid Flow over a Stretching Sheet in the Presence of a Magnetic Dipole, Micro and Nanofluid Convection with Magnetic Field Effects for Heat and Mass Transfer Applications Using MATLAB, 2022, 91-111. doi.org/10.1016/b978-0-12-823140-1.00005-1
- Dey, Sudip, et al.,Effects of Stefan Blowing on Mixed Convection Heat Transfer in a Nanofluid Flow with Thompson and Troian Slip, Numerical Heat Transfer, Part A: Applications,(2023),pp. 1-20. doi.org/10.1080/10407782.2023.2261626
- Bachok, Norfifah et al.,.Boundary Layer Stagnation-Point Flow and Heat Transfer over an Exponentially Stretching/Shrinking Sheet in a Nanofluid, International Journal of Heat and Mass Transfer, 55,(2012),pp.8122-28. doi.org/10.1016/j.ijheatmasstransfer.2012.08.051
- Mustafa, M., et al.,Simulations for Maxwell Fluid Flow Past a Convectively Heated Exponentially Stretching Sheet with Nanoparticles, AIP Advances, 5, (2015) 037133. doi.org/10.1063/1.4916364
- Hayat, T. et al., Newtonian and Joule Heating Effects in Two-Dimensional Flow of Williamson Fluid, Journal of Applied FluidMechanics 9,(2016),pp.196975. doi.org/10.18869/acadpub.jafm.68.235.24646
- Ramesh, K., et al.,Simultaneous Effects of MHD and Joule Heating on the Fundamental Flows of a Casson Liquid with Slip Boundaries, Propulsion and Power Research,10,(2021),pp.118-129. doi.org/10.1016/j.jppr.2021.05.002
- Ali, Aatif et al., MHD Williamson Nanofluid Flow in the Rheology of Thermal Radiation, Joule Heating, and Chemical Reaction Using the Levenberg-Marquardt Neural Network Algorithm,Frontiers in Energy Research, 10 (2022), pp.1-23. doi.org/10.3389/fenrg.2022.965603
- ShivaRao et al.,A Numerical Study on Unsteady MHD Williamson Nanofluid Flow Past a Permeable Moving Cylinder in the Presence of Thermal Radiation and Chemical Reaction, Biointerface Research in Applied Chemistry, 13 (2023), pp.1-19. doi.org/10.33263/briac135.436
- Zegeye et al., Combined Effects of Joule Heating and Binary Chemical Reaction of MHD Williamson Nanofluid on Darcy-Forchheimer Porous Medium Past Unsteady Stretching Cylinder, International Journal of Thermofluids, 20 (2023), pp.100474. doi.org/10.1016/j.ijft.2023.100474
- Ijaz, Misbah et al., Activation Energy and Dual Stratification Effects for Walter-B Fluid Flow in View of Cattaneo-Christov Double Diffusionon, Heliyon 5 (2019), pp.e01815. doi.org/10.1016/j.heliyon.2019.e01815
- Salahuddin,T. et al., Variable Thermo-Physical Characteristics of Carreau Fluid Flow by Means of Stretchable Paraboloid Surface with Activation Energy and Heat Generation, Case Studies in Thermal Engineering ,25 (2021) pp.100971. doi.org/10.1016/j.csite.2021.100971
- C.Srinivas Reddy et al.,,Cattaneo-Christov Double Diffusion Theory for MHD Cross Nanofluid Flow towards a Vertical Stretching Sheet with Activation Energy,International Journal of Ambient Energy 43(1),(2021)pp.3924-33. doi.org/10.1080/01430750.2020.1852113
- Saleem, Musharafa et al., Impression of Nonlinear Radiation and Stefan Blowing on the Magneto Cross Nano-Williamson Fluid above Exponentially Stretching Sheet,Results in Engineering 17 (2023), pp.100864. doi.org/10.1016/j.rineng.2022.100864
- The MathWorks, Inc. (2018a). MATLAB R2018a [Computer software]. Natick, Massachusetts: The MathWorks, Inc