Two-Dimensional Mixed Convection and Radiative Al2O3-Cu/H2O Hybrid Nanofluid Flow over a Vertical Exponentially Shrinking Sheet with Partial Slip Conditions
DOI:
https://doi.org/10.37934/cfdl.14.3.2238Keywords:
Boundary layer, Heat transfer, Hybrid nanofluid, Mixed convection, Radiation, Velocity slip, Thermal slipAbstract
Hybrid nanofluid is considered a modern and improvised form of nanofluid which usually used to enhance the performance of heat transfer in fluid flow systems. Previous studies found hybrid nanofluid offered a wide range of applications and this opened up numerous new opportunities to further explore the unknown behaviour of hybrid nanofluid under different body geometries and physical parameters. This paper numerically studied a two-dimensional mixed convection and radiative Al2O3-Cu/H2O hybrid nanofluid flow over a vertical exponentially shrinking sheet with partial slip conditions. The main objective is to investigate the effect of mixed convection and radiation on the velocity and temperature profiles, as well as the effect of suction on reduced skin friction and reduced heat transfer with respect to solid volume fraction of copper, velocity, and thermal slips. Exponential similarity variables transformed the governing system of partial differential equations into a system of ordinary differential equations which is solved via MATLAB’s bvp4c solver. Outcomes showed that the value of the reduced heat transfer upsurges in the first solution but declines in the second solution when the velocity slip rises. The reduced heat transfer decreases in both dual solutions when thermal slip is enhanced. As the intensity of thermal slip increases, the reduced skin friction rises in the first solution and decreases in the second. As the mixed convection parameter increases, no obvious variation is noticed in the temperature distribution within the first solution, but increasing trend is observed within the second solution. An increment in the temperature distribution also observed within the dual solutions as the thermal radiation parameter increases. In summary, findings from this study are particularly useful to understand various behaviour of Al2O3-Cu/H2O hybrid nanofluid under the influence of mixed convection, radiation, and partial slip conditions when it flows over a vertical exponential shrinking sheet.
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Sakiadis, Byron C. "Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow." AIChE Journal 7, no. 1 (1961): 26-28. https://doi.org/10.1002/aic.690070108
Crane, Lawrence J. "Flow past a stretching plate." Zeitschrift für angewandte Mathematik und Physik ZAMP 21, no. 4 (1970): 645-647. https://doi.org/10.1007/BF01587695
Choi, S. US, and Jeffrey A. Eastman. "Enhancing thermal conductivity of fluids with nanoparticles. " No. ANL/MSD/CP-84938; CONF-951135-29. Argonne National Lab., IL (United States), 1995. https://www.osti.gov/servlets/purl/196525
Wang, Xiang-Qi, and Arun S. Mujumdar. "Heat transfer characteristics of nanofluids: A review." International Journal of Thermal Sciences 46, no. 1 (2007): 1-19. https://doi.org/10.1016/j.ijthermalsci.2006.06.010
Abu-Nada, Eiyad, and Hakan F. Oztop. "Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid." International Journal of Heat and Fluid Flow 30, no. 4 (2009): 669-678. https://doi.org/10.1016/j.ijheatfluidflow.2009.02.001
Lund, Liaquat Ali, Zurni Omar, Sumera Dero, Dumitru Baleanu, and Ilyas Khan. "Rotating 3D flow of hybrid nanofluid on exponentially shrinking sheet: Symmetrical solution and duality." Symmetry 12, no. 10 (2020): 1637. https://doi.org/10.3390/sym12101637
Miklavčič, M., and C. Wang. "Viscous flow due to a shrinking sheet." Quarterly of Applied Mathematics 64, no. 2 (2006): 283-290. https://doi.org/10.1090/S0033-569X-06-01002-5
Bachok, Norfifah, Anuar Ishak, and Ioan Pop. "Stagnation-point flow over a stretching/shrinking sheet in a nanofluid." Nanoscale Research Letters 6, no. 1 (2011): 1-10. https://doi.org/10.1186/1556-276X-6-623
Bachok, Norfifah, Anuar Ishak, and Ioan Pop. "Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet." International Journal of Heat and Mass Transfer 55, no. 7-8 (2012): 2102-2109. https://doi.org/10.1016/j.ijheatmasstransfer.2011.12.013
Naramgari, Sandeep, and C. Sulochana. "MHD flow over a permeable stretching/shrinking sheet of a nanofluid with suction/injection." Alexandria Engineering Journal 55, no. 2 (2016): 819-827. https://doi.org/10.1016/j.aej.2016.02.001
Ahmad, Syakila, and Ioan Pop. "Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids." International Communications in Heat and Mass Transfer 37, no. 8 (2010): 987-991. https://doi.org/10.1016/j.icheatmasstransfer.2010.06.004
Lund, Liaquat Ali, Zurni Omar, and Ilyas Khan. "Quadruple solutions of mixed convection flow of magnetohydrodynamic nanofluid over exponentially vertical shrinking and stretching surfaces: Stability analysis." Computer Methods and Programs in Biomedicine 182 (2019): 105044. https://doi.org/10.1016/j.cmpb.2019.105044
Khan, Ansab Azam, Khairy Zaimi, Suliadi Firdaus Sufahani, and Mohammad Ferdows. "MHD flow and heat transfer of double stratified micropolar fluid over a vertical permeable shrinking/stretching sheet with chemical reaction and heat source." Journal of Advanced Research in Applied Sciences and Engineering Technology 21, no. 1 (2020): 1-14. https://doi.org/10.37934/araset.21.1.114
Rohni, Azizah Mohd, Sumera Dero, and Azizan Saaban. "Triple solutions and stability analysis of mixed convection boundary flow of Casson nanofluid over an exponentially vertical stretching/shrinking sheet." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 72, no. 1 (2020): 94-110. https://doi.org/10.37934/arfmts.72.1.94110
Yashkun, Ubaidullah, Khairy Zaimi, Nor Ashikin Abu Bakar, and Mohammad Ferdows. "Nanofluid stagnation-point flow using Tiwari and Das model over a stretching/shrinking sheet with suction and slip effects." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 70, no. 1 (2020): 62-76. https://doi.org/10.37934/arfmts.70.1.6276
Hussain, Syed M., Wasim Jamshed, Vivek Kumar, Vikash Kumar, Kottakkaran Sooppy Nisar, Mohamed R. Eid, Rabia Safdar, Abdel-Haleem Abdel-Aty, and I. S. Yahia. "Computational analysis of thermal energy distribution of electromagnetic Casson nanofluid across stretched sheet: Shape factor effectiveness of solid-particles." Energy Reports 7 (2021): 7460-7477. https://doi.org/10.1016/j.egyr.2021.10.083
Hussain, Syed M., Wasim Jamshed, Esra Karatas Akgül, and Nor Ain Azeany Mohd Nasir. "Mechanical improvement in solar aircraft by using tangent hyperbolic single-phase nanofluid." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering (2021): 09544089211059377. https://doi.org/10.1177/09544089211059377
Khan, Aamir Abbas, Muhammad Naveed Khan, Sohail Nadeem, Syed Modassir Hussain, and Muhammad Ashraf. "Thermal slip and homogeneous/heterogeneous reaction characteristics of second-grade fluid flow over an exponentially stretching sheet." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering (2021): 09544089211064187. https://doi.org/10.1177/09544089211064187
Hussain, Syed M., Rohit Sharma, Manas R. Mishra, and Sattam S. Alrashidy. "Hydromagnetic dissipative and radiative graphene Maxwell nanofluid flow past a stretched sheet - Numerical and statistical analysis." Mathematics 8, no. 11 (2020): 1929. https://doi.org/10.3390/math8111929
Sharma, R., S. M. Hussain, C. S. K. Raju, G. S. Seth, and Ali J. Chamkha. "Study of graphene Maxwell nanofluid flow past a linearly stretched sheet: A numerical and statistical approach." Chinese Journal of Physics 68 (2020): 671-683. https://doi.org/10.1016/j.cjph.2020.10.013
Hussain, Syed Modassir, J. Jain, G. S. Seth, and M. M. Rashidi. "Effect of thermal radiation on magneto-nanofluids free convective flow over an accelerated moving ramped temperature plate." Scientia Iranica 25, no. 3 (2018): 1243-1257.
Sharma, Rohit, Syed Modassir Hussain, and Garima Mishra. "Soret and Dufour effects on viscoelastic radiative and heat absorbing nanofluid driven by a stretched sheet with inclined magnetic field." Defect and Diffusion Forum 388 (2018): 223-245. https://doi.org/10.4028/www.scientific.net/DDF.388.223
Mishra, M. R., S. M. Hussain, O. D. Makinde, and G. S. Seth. "Stability analysis and multiple solutions of a hydromagnetic dissipative flow over a stretching/shrinking sheet." Bulgarian Chemical Communication 52, no. 2 (2020): 259-271.
Hussain, S. M., R. Sharma, M. K. Mishra, and G. S. Seth. "Radiative magneto-nanofluid over an accelerated moving ramped temperature plate with Hall effects." Journal of Nanofluids 6, no. 5 (2017): 840-851. https://doi.org/10.1166/jon.2017.1381
Hussain, S. M., J. Jain, G. S. Seth, and M. M. Rashidi. "Free convective heat transfer with Hall effects, heat absorption and chemical reaction over an accelerated moving plate in a rotating system." Journal of Magnetism and Magnetic Materials 422 (2017): 112-123. https://doi.org/10.1016/j.jmmm.2016.08.081
Nandi, Susmay, Bidyasagar Kumbhakar, and Subharthi Sarkar. "MHD stagnation point flow of Fe3O4/Cu/Ag-CH3OH nanofluid along a convectively heated stretching sheet with partial slip and activation energy: Numerical and statistical approach." International Communications in Heat and Mass Transfer 130 (2022): 105791. https://doi.org/10.1016/j.icheatmasstransfer.2021.105791
Singha, A. K., G. S. Seth, Krishnendu Bhattacharyya, Dhananjay Yadav, Ajeet Kumar Verma, and Anil Kumar Gautam. "Soret and Dufour effects on hydromagnetic flow of H2O-based nanofluids induced by an exponentially expanding sheet saturated in a non-Darcian porous medium." Journal of Nanofluids 10, no. 4 (2021): 506-517. https://doi.org/10.1166/jon.2021.1800
Hussain, Syed M., Rohit Sharma, Gauri S. Seth, and Manas R. Mishra. "Thermal radiation impact on boundary layer dissipative flow of magneto-nanofluid over an exponentially stretching sheet." International Journal of Heat and Technology 36, no. 4 (2018): 1163-1173. https://doi.org/10.18280/ijht.360402
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
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
Huminic, Gabriela, and Angel Huminic. "Hybrid nanofluids for heat transfer applications – A state-of-the-art review." International Journal of Heat and Mass Transfer 125 (2018): 82-103. https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.059
Waini, Iskandar, Anuar Ishak, and Ioan Pop. "Unsteady flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid." International Journal of Heat and Mass Transfer 136 (2019): 288-297. https://doi.org/10.1016/j.ijheatmasstransfer.2019.02.101
Waini, Iskandar, Anuar Ishak, and Ioan Pop. "Transpiration effects on hybrid nanofluid flow and heat transfer over a stretching/shrinking sheet with uniform shear flow." Alexandria Engineering Journal 59, no. 1 (2020): 91-99. https://doi.org/10.1016/j.aej.2019.12.010
Yahaya, Rusya Iryanti, Norihan M. Arifin, Roslinda Nazar, and Ioan Pop. "Flow and heat transfer past a permeable stretching/shrinking sheet in Cu−Al2O3/water hybrid nanofluid." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 3 (2019): 1197-1222. https://doi.org/10.1108/HFF-05-2019-0441
Waini, Iskandar, Anuar Ishak, and Ioan Pop. "Hiemenz flow over a shrinking sheet in a hybrid nanofluid." Results in Physics 19 (2020): 103351. https://doi.org/10.1016/j.rinp.2020.103351
Adnan Asghar & Teh, Yuan Ying. "Three dimensional MHD hybrid nanofluid Flow with rotating stretching/shrinking sheet and Joule heating." CFD Letters 13, no. 8 (2021): 1-19. https://doi.org/10.37934/cfdl.13.8.119
Hussain, Syed M., R. Sharma, and Ali J. Chamkha. "Numerical and statistical exploration on the dynamics of water conveying Cu-Al2O3 hybrid nanofluid flow over an exponentially stretchable sheet with Navier’s partial slip and thermal jump conditions." Chinese Journal of Physics (2021): 120-138. https://doi.org/10.1016/j.cjph.2021.11.007
Hussain, Syed M., and Wasim Jamshed. "A comparative entropy-based analysis of tangent hyperbolic hybrid nanofluid flow: Implementing finite difference method." International Communications in Heat and Mass Transfer 129 (2021): 105671. https://doi.org/10.1016/j.icheatmasstransfer.2021.105671
Jamshed, Wasim, M. Prakash, Syed M. Hussain, Mohamed R. Eid, Kottakkaran Sooppy Nisar, and Taseer Muhammad. "Entropy amplified solitary phase relative probe on engine oil based hybrid nanofluid.” Chinese Journal of Physics (2021). https://doi.org/10.1016/j.cjph.2021.11.009
Nandi, Susmay, Bidyasagar Kumbhakar, and Gauri Shanker Seth. "Quadratic regression analysis of unsteady MHD free convective and radiative-dissipative stagnation flow of hybrid nanofluid over an exponentially stretching surface under porous medium." Chinese Journal of Physics (2021). https://doi.org/10.1016/j.cjph.2021.12.011
Kumbhakar, Bidyasagar, and Susmay Nandi. "Unsteady MHD radiative-dissipative flow of Cu-Al2O3/H2O hybrid nanofluid past a stretching sheet with slip and convective conditions: A regression analysis." Mathematics and Computers in Simulation 194 (2022):563-587. https://doi.org/10.1016/j.matcom.2021.12.018
Lund, Liaquat Ali, Zurni Omar, and Ilyas Khan. "Mathematical analysis of magnetohydrodynamic (MHD) flow of micropolar nanofluid under buoyancy effects past a vertical shrinking surface: Dual solutions." Heliyon 5, no. 9 (2019): e02432. https://doi.org/10.1016/j.heliyon.2019.e02432
Waini, Iskandar, Anuar Ishak, and Ioan Pop. "Mixed convection flow over an exponentially stretching/shrinking vertical surface in a hybrid nanofluid." Alexandria Engineering Journal 59, no. 3 (2020): 1881-1891. https://doi.org/10.1016/j.aej.2020.05.030
Prasad, Ajay K., and Jeffrey R. Koseff. "Combined forced and natural convection heat transfer in a deep lid-driven cavity flow." International Journal of Heat and Fluid Flow 17, no. 5 (1996): 460-467. https://doi.org/10.1016/0142-727X(96)00054-9
Merkin, J. H. "Mixed convection boundary layer flow on a vertical surface in a saturated porous medium." Journal of Engineering Mathematics 14, no. 4 (1980): 301-313. https://doi.org/10.1007/BF00052913
Merkin, J. H. "On dual solutions occurring in mixed convection in a porous medium." Journal of Engineering Mathematics 20, no. 2 (1986): 171-179. https://doi.org/10.1007/BF00042775
Ghalambaz, Mohammad, Natalia C. Roşca, Alin V. Roşca, and Ioan Pop. "Mixed convection and stability analysis of stagnation-point boundary layer flow and heat transfer of hybrid nanofluids over a vertical plate." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 7 (2020): 3737-3754. https://doi.org/10.1108/HFF-08-2019-0661
Waini, Iskandar, Anuar Ishak, Teodor Groşan, and Ioan Pop. "Mixed convection of a hybrid nanofluid flow along a vertical surface embedded in a porous medium." International Communications in Heat and Mass Transfer 114 (2020): 104565. https://doi.org/10.1016/j.icheatmasstransfer.2020.104565
Yashkun, Ubaidullah, Khairy Zaimi, Anuar Ishak, Ioan Pop, and Rabeb Sidaoui. "Hybrid nanofluid flow through an exponentially stretching/shrinking sheet with mixed convection and Joule heating." International Journal of Numerical Methods for Heat & Fluid Flow 31, no. 6 (2021): 1930-1950. https://doi.org/10.1108/HFF-07-2020-0423
Zainal, Nurul Amira, Roslinda Nazar, Kohilavani Naganthran, and Ioan Pop. "MHD mixed convection stagnation point flow of a hybrid nanofluid past a vertical flat plate with convective boundary condition." Chinese Journal of Physics 66 (2020): 630-644. https://doi.org/10.1016/j.cjph.2020.03.022
Khan, M. Riaz, Kejia Pan, Arif Ullah Khan, and S. Nadeem. "Dual solutions for mixed convection flow of SiO2−Al2O3/water hybrid nanofluid near the stagnation point over a curved surface." Physica A: Statistical Mechanics and Its Applications 547 (2020): 123959. https://doi.org/10.1016/j.physa.2019.123959
Jamil, Muhammad, and Najeeb Alam Khan. "Slip effects on fractional viscoelastic fluids." International Journal of Differential Equations 2011 (2011): 193813. https://doi.org/10.1155/2011/193813
Andersson, Helge I. "Slip flow past a stretching surface." Acta Mechanica 158, no. 1 (2002): 121-125. https://doi.org/10.1007/BF01463174
Hayat, Tanzila, S. Nadeem, and A. U. Khan. "Rotating flow of Ag-CuO/H2O hybrid nanofluid with radiation and partial slip boundary effects." The European Physical Journal E 41, no. 6 (2018): 75. https://doi.org/10.1140/epje/i2018-11682-y
Aly, Emad H., and I. Pop. "MHD flow and heat transfer near stagnation point over a stretching/shrinking surface with partial slip and viscous dissipation: Hybrid nanofluid versus nanofluid." Powder Technology 367 (2020): 192-205. https://doi.org/10.1016/j.powtec.2020.03.030
Zainal, Nurul Amira, Roslinda Nazar, Kohilavani Naganthran, and Ioan Pop. "Unsteady stagnation point flow of hybrid nanofluid past a convectively heated stretching/shrinking sheet with velocity slip." Mathematics 8, no. 10 (2020): 1649. https://doi.org/10.3390/math8101649
Swain, K., Fateh Mebarek-Oudina, and S. M. Abo-Dahab. "Influence of MWCNT/Fe3O4 hybrid nanoparticles on an exponentially porous shrinking sheet with chemical reaction and slip boundary conditions." Journal of Thermal Analysis and Calorimetry 147 (2021): 1561-1570. https://doi.org/10.1007/s10973-020-10432-4
Abbas, Nadeem, S. Nadeem, and M. Y. Malik. "Theoretical study of micropolar hybrid nanofluid over Riga channel with slip conditions." Physica A: Statistical Mechanics and Its Applications 551 (2020): 124083. https://doi.org/10.1016/j.physa.2019.124083
Khan, Umair, Anum Shafiq, A. Zaib, and Dumitru Baleanu. "Hybrid nanofluid on mixed convective radiative flow from an irregular variably thick moving surface with convex and concave effects." Case Studies in Thermal Engineering 21 (2020): 100660. https://doi.org/10.1016/j.csite.2020.100660
Hayat, Tanzila, and S. Nadeem. "Heat transfer enhancement with Ag-CuO/water hybrid nanofluid." Results in Physics 7 (2017): 2317-2324. https://doi.org/10.1016/j.rinp.2017.06.034
Waini, Iskandar, Anuar Ishak, and Ioan Pop. "Hybrid nanofluid flow induced by an exponentially shrinking sheet." Chinese Journal of Physics 68 (2020): 468-482. https://doi.org/10.1016/j.cjph.2019.12.015
Lund, Liaquat Ali, Zurni Omar, Ilyas Khan, and El-Sayed M. Sherif. "Dual solutions and stability analysis of a hybrid nanofluid over a stretching/shrinking sheet executing MHD flow." Symmetry 12, no. 2 (2020): 276. https://doi.org/10.3390/sym12020276
Anuar, Nur Syazana, Norfifah Bachok, and Ioan Pop. "Radiative hybrid nanofluid flow past a rotating permeable stretching/shrinking sheet." International Journal of Numerical Methods for Heat & Fluid Flow 31, no. 3 (2021): 914-932. https://doi.org/10.1108/HFF-03-2020-0149
Shoaib, Muhammad, Muhammad Asif Zahoor Raja, Muhammad Touseef Sabir, Saeed Islam, Zahir Shah, Poom Kumam, and Hussam Alrabaiah. "Numerical investigation for rotating flow of MHD hybrid nanofluid with thermal radiation over a stretching sheet." Scientific Reports 10, no. 1 (2020): 18533. https://doi.org/10.1038/s41598-020-75254-8
Zainal, Nurul Amira, Roslinda Nazar, Kohilavani Naganthran, and Ioan Pop. "MHD flow and heat transfer of hybrid nanofluid over a permeable moving surface in the presence of thermal radiation." International Journal of Numerical Methods for Heat & Fluid Flow 31, no. 3 (2021): 858-879. https://doi.org/10.1108/HFF-03-2020-0126
Yan, Liang, Sumera Dero, Ilyas Khan, Irshad Ali Mari, Dumitru Baleanu, Kottakkaran Sooppy Nisar, El-Sayed M. Sherif, and Hany S. Abdo. "Dual solutions and stability analysis of magnetized hybrid nanofluid with Joule heating and multiple slip conditions." Processes 8, no. 3 (2020): 332. https://doi.org/10.3390/pr8030332
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
Hale, N. P. "A sixth-order extension to the MATLAB bvp4c software of J. Kierzenka and l. Shampine." Department of Mathematics, Imperial College London (2006).