Newtonian Heating in Magnetohydrodynamic (MHD) Hybrid Nanofluid Flow Near the Stagnation Point over Nonlinear Stretching and Shrinking Sheet
DOI:
https://doi.org/10.37934/arnht.20.1.5367Keywords:
Hybrid Nanofluid, MHD, Newtonian Heating, Stagnation Point, Nonlinear Stretching/Shrinking SheetAbstract
Hybrid nanofluids have demonstrated superior heat transfer performance in numerous applications. However, there remains a need for further research to broaden the scope of their potential applications. The unique behavior of hybrid nanofluids, driven by their potential for improved thermal efficiency, continues to be a focal point of investigation and exploration. This study focuses on the effects of Newtonian heating in MHD hybrid nanofluid near the stagnation point over a nonlinear stretching/shrinking sheet. The Tiwari and Das model, which is a single-phase model, was used to develop the mathematical model. The base fluid and the nanoparticles are assumed to be in thermal equilibrium; hence there is no thermal slip between them. The combination of metal (Cu) and metal oxide (Al2O3) nanoparticles with water (H2O) as the base fluid is used for the analysis. Furthermore, the governing equations are transformed using a similarity transformation technique into similarity equations, which are then solved numerically using a bvp4c function in MATLAB software. Numerical comparison with the published literature is conducted to validate the numerical results, and excellent agreement is found. The impact of physical parameters on the velocity, temperature, skin friction, and local Nusselt number is graphically deliberated. The outcomes suggest that non-unique solutions are found in a specific range of the shrinking parameter. It is also observed that increasing Cu (copper) nanoparticle volume fractions cause an increase in the skin friction coefficient and the local Nusselt number. The presence of magnetic and nonlinear parameters widens the range of solutions to exist while different observation is noticed with an increase in the volume fraction of Cu. Other than that, it has been shown that the Nusselt number increases as the magnetic parameter increases. Lastly, the rise of Newtonian heating contributes to an increase in the temperature profile. This investigation is crucial for understanding the thermal behavior of Cu-Al2O3/ H2O under the influence of physical factors like a magnetic field and Newtonian heating.
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References
Pavlov, K. B. "Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface." Magnitnaya Gidrodinamika 4, no. 1 (1974): 146-147. http://doi.org/10.22364/mhd
Ishak, Anuar, Roslinda Nazar, and Ioan Pop. "MHD boundary-layer flow due to a moving extensible surface." Journal of Engineering Mathematics 62 (2008): 23-33. https://doi.org/10.1007/s10665-007-9169-z
Merkin, J. H., and V. Kumaran. "The unsteady MHD boundary-layer flow on a shrinking sheet." European Journal of Mechanics-B/Fluids 29, no. 5 (2010): 357-363. https://doi.org/10.1016/j.euromechflu.2010.03.006
Mabood, Fazle, W. A. Khan, and AI Md Ismail. "MHD boundary layer flow and heat transfer of nanofluids over a nonlinear stretching sheet: a numerical study." Journal of Magnetism and Magnetic Materials 374 (2015): 569-576. https://doi.org/10.1016/j.jmmm.2014.09.013
Jamalabadi, Mohammad Yaghoub Abdollahzadeh "Magnetic Field Effects on Chemical Reaction of Power-Law Fluid over an Axisymmetric Stretched Sheet." Magnetochemistry 5, no. 4 (2019): 57. https://doi.org/10.3390/magnetochemistry5040057
Jabeen, K., M. Mushtaq, and R. M. Akram "Analysis of the MHD boundary layer flow over a nonlinear stretching sheet in a porous medium using semianalytical approaches." Mathematical Problems in Engineering 2020 (2020): 1-9. https://doi.org/10.1155/2020/3012854
Anuar, Nur Syazana, Norfifah Bachok, and Ioan Pop. "Influence of MHD hybrid ferrofluid flow on exponentially stretching/shrinking surface with heat source/sink under stagnation point region." Mathematics 9, no. 22 (2021): 2932. https://doi.org/10.3390/math9222932
Khan, Umair, Aurang Zaib, Anuar Ishak, Abeer M. Alotaibi, Samia Elattar, Ioan Pop, and Ahmed M. Abed. "Impact of an Induced Magnetic Field on the Stagnation-Point Flow of a Water-Based Graphene Oxide Nanoparticle over a Movable Surface with Homogeneous–Heterogeneous and Chemical Reactions." Magnetochemistry 8, no. 11 (2022): 155. https://doi.org/10.3390/magnetochemistry8110155
Choi S.U.S.; Eastman, J.A. Enhancing thermal conductivity of fluids with nanoparticles. In ASME International Mechanical Engineering Congress & Exposisition, American Society of Mechanical Engineers, San Francisco (1995). https://www.osti.gov/servlets/purl/196525
Khanafer, Khalil, Kambiz Vafai, and Marilyn Lightstone. "Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids." International journal of heat and mass transfer 46, no. 19 (2003): 3639-3653. https://doi.org/10.1016/S0017-9310(03)00156-X
Buongiorno, Jacopo. "Convective transport in nanofluids." (2006): 240-250. https://doi.org/10.1115/1.2150834
Tiwari, Raj Kamal, and Manab Kumar Das. "Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids." International Journal of heat and Mass transfer 50, no. 9-10 (2007): 2002-2018. https://doi.org/10.1016/j.ijheatmasstransfer.2006.09.034
Nield, D. A., and A. V. Kuznetsov. "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, no. 25-26 (2009): 5792-5795. https://doi.org/10.1016/j.ijheatmasstransfer.2009.07.024
Suresh, S., K. P. Venkitaraj, P. Selvakumar, and M. Chandrasekar. "Synthesis of Al2O3–Cu/water hybrid nanofluids using two step method and its thermo physical properties." Colloids and Surfaces A: Physicochemical and Engineering Aspects 388, no. 1-3 (2011): 41-48. https://doi.org/10.1016/j.colsurfa.2011.08.005
Momin, Gaffar G. "Experimental investigation of mixed convection with water-Al2O3 & hybrid nanofluid in inclined tube for laminar flow." Int. J. Sci. Technol. Res 2, no. 12 (2013): 195-202.
Devi, SP Anjali, and S. Suriya Uma Devi. "Numerical investigation of hydromagnetic hybrid Cu–Al2O3/water nanofluid flow over a permeable stretching sheet with suction." International Journal of Nonlinear Sciences and Numerical Simulation 17, no. 5 (2016): 249-257. https://doi.org/10.1515/ijnsns-2016-0037
Nadeem, S., Nadeem Abbas, and A. U. Khan. "Characteristics of three dimensional stagnation point flow of Hybrid nanofluid past a circular cylinder." Results in physics 8 (2018): 829-835. https://doi.org/10.1016/j.rinp.2018.01.024
Elsaid, Essam M., and Mohamed S. Abdel-wahed. "Impact of hybrid nanofluid coolant on the boundary layer behavior over a moving cylinder: Numerical case study." Case Studies in Thermal Engineering 25 (2021): 100951. https://doi.org/10.1016/j.csite.2021.100951
Anuar, Nur Syazana, Norfifah Bachok, and Ioan Pop. "Hybrid carbon nanotube flow near the stagnation region over a permeable vertical plate with heat generation/absorption." Mathematics 9, no. 22 (2021): 2925. https://doi.org/10.3390/math9222925
Rehman, Aqeel ur, and Zaheer Abbas. "Stability analysis of heat transfer in nanomaterial flow of boundary layer towards a shrinking surface: Hybrid nanofluid versus nanofluid." Alexandria Engineering Journal 61, no. 12 (2022): 10757-10768. https://doi.org/10.1016/j.aej.2022.04.020
Yaseen, Moh, Sawan Kumar Rawat, Anum Shafiq, Manoj Kumar, and Kamsing Nonlaopon. "Analysis of heat transfer of mono and hybrid nanofluid flow between two parallel plates in a Darcy porous medium with thermal radiation and heat generation/absorption." Symmetry 14, no. 9 (2022): 1943. https://doi.org/10.3390/sym14091943
Merkin, J. H. "Natural-convection boundary-layer flow on a vertical surface with Newtonian heating." International Journal of Heat and Fluid Flow 15, no. 5 (1994): 392-398. https://doi.org/10.1016/0142-727X(94)90053-1
Hayat, T., Anum Naseem, M. Farooq, and A. Alsaedi. "Unsteady MHD three-dimensional flow with viscous dissipation and Joule heating." The European Physical Journal Plus 128 (2013): 1-15. https://doi.org/10.1140/epjp/i2013-13158-1
Reddy, B. Prabhakar. "Effect of Hall current on radiating hydromagnetic flow past an impulsively moving vertical porous plate with Newtonian heating." I-Manager’s Journal on Future Engineering and Technology 15, no. 3 (2020): 1-10. https://doi.org/10.26634/jfet.15.3.16121
Gangadhar, K., D. Vijaya Kumar, M. Venkata Subba Rao, T. Kannan, and G. Sakthivel. "Effects of Newtonian heating on the boundary layer flow of non-Newtonian magnetohydrodynamic nanofluid over a stretched plate using spectral relaxation method." International Journal of Ambient Energy 43, no. 1 (2022): 1248-1261. https://doi.org/10.1080/01430750.2019.1694585
Rehman, Khalil Ur, Wasfi Shatanawi, Shazia Ashraf, and Nabeela Kousar. "Numerical analysis of Newtonian heating convective flow by way of two different surfaces." Applied Sciences 12, no. 5 (2022): 2383. https://doi.org/10.3390/app12052383
Nabwey, Hossam A., Ahmed M. Rashad, Amal MA EL-Hakiem, and Sumayyah I. Alshber. "Effectiveness of Newtonian Heating on Magneto-Free Convective Flow of Polar Nanofluid across a Solid Sphere." Fractal and Fractional 6, no. 2 (2022): 57. https://doi.org/10.3390/fractalfract6020057
Reddy, B. Prabhakar, and O. D. Makinde. "Newtonian heating effect on heat absorbing unsteady MHD radiating and chemically reacting free convection flow past an oscillating vertical porous plate." International Journal of Applied Mechanics and Engineering 27, no. 1 (2022): 168-187. https://doi.org/10.2478/ijame-2022-0011
Rana, Puneet, and R. Bhargava. "Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: a numerical study." Communications in Nonlinear Science and Numerical Simulation 17, no. 1 (2012): 212-226. https://doi.org/10.1016/j.cnsns.2011.05.009
Mabood, Fazle, W. A. Khan, and AI Md Ismail. "MHD boundary layer flow and heat transfer of nanofluids over a nonlinear stretching sheet: a numerical study." Journal of Magnetism and Magnetic Materials 374 (2015): 569-576. https://doi.org/10.1016/j.jmmm.2014.09.013
Anuar, Nur Syazana, Norfifah Bachok, Norihan Md Arifin, and Haliza Rosali. "Numerical solution of stagnation point flow and heat transfer over a nonlinear stretching/shrinking sheet in hybrid nanofluid: Stability analysis." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 76, no. 2 (2020): 85-98. https://doi.org/10.37934/arfmts.76.2.8598
Ramana, K. Venkata, K. Gangadhar, T. Kannan, and Ali J. Chamkha. "Cattaneo–Christov heat flux theory on transverse MHD Oldroyd-B liquid over nonlinear stretched flow." Journal of Thermal Analysis and Calorimetry (2022): 1-11. https://doi.org/10.1007/s10973-021-10568-x
Nadeem, Sohail, Wang Fuzhang, Fahad M. Alharbi, Farrah Sajid, Nadeem Abbas, A. S. El-Shafay, and Fahad S. Al-Mubaddel. "Numerical computations for Buongiorno nano fluid model on the boundary layer flow of viscoelastic fluid towards a nonlinear stretching sheet." Alexandria Engineering Journal 61, no. 2 (2022): 1769-1778. https://doi.org/10.1016/j.aej.2021.11.013
Waini, Iskandar, Anuar Jamaludin, Roslinda Nazar, and Ioan Pop. "MHD flow and heat transfer of a hybrid nanofluid past a nonlinear surface stretching/shrinking with effects of thermal radiation and suction." Chinese Journal of Physics 79 (2022): 13-27. https://doi.org/10.1016/j.cjph.2022.06.026
Hiemenz, Karl. "Die Grenzschicht an einem in den gleichformigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder." Dinglers Polytech. J. 326 (1911): 321-324.
Rawat, Sawan Kumar, and Manoj Kumar. "Cattaneo–Christov heat flux model in flow of copper water nanofluid through a stretching/shrinking sheet on stagnation point in presence of heat generation/absorption and activation energy." International Journal of Applied and Computational Mathematics 6 (2020): 1-26. https://doi.org/10.1007/s40819-020-00865-8
Negi, Anup Singh, Ashok Kumar, Moh Yaseen, Sawan Kumar Rawat, and Akshay Saini. "Effects of heat source on the stagnation point flow of a nanofluid over a stretchable sheet with magnetic field and zero mass flux at the surface." Forces in Mechanics 11 (2023): 100190. https://doi.org/10.1016/j.finmec.2023.100190
Yaseen, Moh, Sawan Kumar Rawat, Umair Khan, Anup Singh Negi, Manoj Kumar, El-Sayed M. Sherif, Ahmed M. Hassan, and Ioan Pop. "Inspection of unsteady buoyancy and stagnation point flow incorporated by Ag-TiO2 hybrid nanoparticles towards a spinning disk with Hall effects." Case Studies in Thermal Engineering 44 (2023): 102889. https://doi.org/10.1016/j.csite.2023.102889
Bachok, Norfifah, and Anuar Ishak. "Similarity solutions for the stagnation-point flow and heat transfer over a nonlinearly stretching/shrinking sheet." Sains Malaysiana 40, no. 11 (2011): 1297-1300.
Oztop, Hakan F., and Eiyad Abu-Nada. "Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids." International journal of heat and fluid flow 29, no. 5 (2008): 1326-1336. https://doi.org/10.1016/j.ijheatfluidflow.2008.04.009
Malvandi, A., F. Hedayati, and M. R. H. Nobari. "An analytical study on boundary layer flow and heat transfer of nanofluid induced by a non-linearly stretching sheet." Journal of Applied Fluid Mechanics 7, no. 2 (2014): 375-384. https://doi.org/10.36884/jafm.7.02.20308
Shampine, Lawrence F., Lawrence F. Shampine, Ian Gladwell, and S. Thompson. Solving ODEs with matlab. Cambridge university press, 2003.
Wang, C. Y. "Stagnation flow towards a shrinking sheet." International Journal of Non-Linear Mechanics 43, no. 5 (2008): 377-382. https://doi.org/10.1016/j.ijnonlinmec.2007.12.021
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