Thermal Radiation in Nanofluid Penetrable Flow Bounded with Partial Slip Condition
DOI:
https://doi.org/10.37934/cfdl.13.8.3244Keywords:
Dual solutions, nanofluid, thermal radiation, boundary layer flow, suctionAbstract
Thermal radiation enhances heat transfer, and it is used widely in manufacturing and materials processing applications. Thus, steady two-dimensional boundary layer flow over an exponentially porous shrinking sheet of nanofluids was considered in the influence of thermal radiation related to partial slip boundary conditions and suction. This paper aims to study the nanofluid penetrable flow over an exponentially shrinking sheet with thermal radiation and partial slip. The effects of silver (Ag) nanoparticles with two different types of base fluids named water and kerosene oil are investigated in this study. First, the governing equations and boundary conditions are transformed to a non-linear ordinary differential equation and then solved using bvp4c solver. Using Matlab software, it is found that the dual solution exists in some values from the suction parameter. Furthermore, we identified both nanoparticle volume fraction and suction parameter increase, leading to the rise in velocity profile. Moreover, the suction parameter increases both skin friction coefficient and Nusselt number increase.
References
Sheikholeslami, Mohsen, Davood Domiri Ganji, M. Younus Javed, and R. Ellahi. "Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model." Journal of Magnetism and Magnetic Materials 374 (2015): 36-43. https://doi.org/10.1016/j.jmmm.2014.08.021
Sakiadis, B. C. "Boundary layer behaviour on continuous solid surfaces. 1." Boundary layer equations for two-dimensional and axisymmetric flow 2 (1960): 26-28. https://doi.org/10.1002/aic.690070108
Rajagopal, Kumbakonam R., T. Y. Na, and A. S. Gupta. "Flow of a viscoelastic fluid over a stretching sheet." Rheologica Acta 23, no. 2 (1984): 213-215. https://doi.org/10.1007/BF01332078
Vajravelu, K. "Viscous flow over a nonlinearly stretching sheet." Applied mathematics and computation 124, no. 3 (2001): 281-288. https://doi.org/10.1016/S0096-3003(00)00062-X
Khan, W. A., and I. Pop. "Boundary-layer flow of a nanofluid past a stretching sheet." International journal of heat and mass transfer 53, no. 11-12 (2010): 2477-2483. https://doi.org/10.1016/j.ijheatmasstransfer.2010.01.032
Mahapatra, T. Ray, and A. S. Gupta. "Heat transfer in stagnation-point flow towards a stretching sheet." Heat and Mass transfer 38, no. 6 (2002): 517-521. https://doi.org/10.1007/s002310100215
Kafoussias, N. G., and E. W. Williams. "The effect of temperature-dependent viscosity on free-forced convective laminar boundary layer flow past a vertical isothermal flat plate." Acta Mechanica 110, no. 1 (1995): 123-137. https://doi.org/10.1007/BF01215420
Hussain, Azad, Sana Afzal, Rizwana Rizwana, and M. Y. Malik. "MHD stagnation point flow of a Casson fluid with variable viscosity flowing past an extending/shrinking sheet with slip effects." Physica A: Statistical Mechanics and Its Applications 553 (2020): 124080. https://doi.org/10.1016/j.physa.2019.124080
Abbas, Tariq, Sajid Rehman, Rehan Ali Shah, Muhammad Idrees, and Mubashir Qayyum. "Analysis of MHD Carreau fluid flow over a stretching permeable sheet with variable viscosity and thermal conductivity." Physica A: Statistical Mechanics and its Applications 551 (2020): 124225. https://doi.org/10.1016/j.physa.2020.124225
Zulkifli, Siti Norfatihah, Norhafizah Md Sarif, and Mohd Zuki Salleh. "Numerical solution of boundary layer flow over a moving plate in a nanofluid with viscous dissipation: A revised model." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 56, no. 2 (2019): 287-295.
Hayat, T., Z. Abbas, I. Pop, and S. Asghar. "Effects of radiation and magnetic field on the mixed convection stagnation-point flow over a vertical stretching sheet in a porous medium." International Journal of Heat and Mass Transfer 53, no. 1-3 (2010): 466-474. https://doi.org/10.1016/j.ijheatmasstransfer.2009.09.010
Ali, F. M., R. Nazar, N. M. Arifin, and I. Pop. "MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field." Applied Mathematics and Mechanics 32, no. 4 (2011): 409-418. https://doi.org/10.1007/s10483-011-1426-6
Reddy, P. Bala Anki. "Magnetohydrodynamic flow of a Casson fluid over an exponentially inclined permeable stretching surface with thermal radiation and chemical reaction." Ain Shams Engineering Journal 7, no. 2 (2016): 593-602.https://doi.org/10.1016/j.asej.2015.12.010
Lund, Liaquat Ali, Zurni Omar, Jawad Raza, and Ilyas Khan. "Magnetohydrodynamic flow of Cu-Fe 3 O 4/H 2 O hybrid nanofluid with effect of viscous dissipation: Dual similarity solutions." Journal of Thermal Analysis and Calorimetry (2020): 1-13.https://doi.org/10.1007/s10973-020-09602-1
Sohail, Muhammad, and Rahila Naz. "Modified heat and mass transmission models in the magnetohydrodynamic flow of Sutterby nanofluid in stretching cylinder." Physica A: Statistical Mechanics and its Applications 549 (2020): 124088.https://doi.org/10.1016/j.physa.2019.124088
Mahanthesh, B. "Magnetohydrodynamic flow of Carreau liquid over a stretchable sheet with a variable thickness." Multidiscipline Modeling in Materials and Structures (2020). https://doi.org/10.1108/MMMS-11-2019-0205
Buongiorno, Jacopo. "Convective transport in nanofluids." (2006): 240-250. https://doi.org/10.1115/1.2150834
Xuan, Yimin, and Qiang Li. "Heat transfer enhancement of nanofluids." International Journal of heat and fluid flow 21, no. 1 (2000): 58-64.https://doi.org/10.1016/S0142-727X(99)00067-3
Khan, W. A., and I. Pop. "Boundary-layer flow of a nanofluid past a stretching sheet." International journal of heat and mass transfer 53, no. 11-12 (2010): 2477-2483.https://doi.org/10.1016/j.ijheatmasstransfer.2010.01.032
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
Zainal, Nurul Amira, Roslinda Nazar, Kohilavani Naganthran, and Ioan Pop. "Stability analysis of MHD hybrid nanofluid flow over a stretching/shrinking sheet with quadratic velocity." Alexandria Engineering Journal 60, no. 1 (2021): 915-926. https://doi.org/10.1016/j.aej.2020.10.020
Junoh, Mohamad Mustaqim, Fadzilah Md Ali, Norihan Md Arifin, Norfifah Bachok, and Ioan Pop. "MHD stagnation-point flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid with induced magnetic field." International Journal of Numerical Methods for Heat & Fluid Flow (2019). https://doi.org/10.1108/HFF-06-2019-0500
Waini, I., A. Ishak, and I. Pop. "MHD flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge." Applied Mathematics and Mechanics 41, no. 3 (2020): 507-520. https://doi.org/10.1007/s10483-020-2584-7
Uddin, M. S., A. Zaib, and K. Bhattacharyya. "Effect of thermal radiation on heat transfer in an unsteady copper-water nanofluid flow over an exponentially shrinking porous sheet." Journal of Applied Mechanics and Technical Physics 58, no. 4 (2017): 670-678. https://doi.org/10.1134/S0021894417040113
Sheikholeslami, M., T. Hayat, and A. Alsaedi. "MHD free convection of Al2O3-water nanofluid considering thermal radiation: a numerical study." International Journal of Heat and Mass Transfer 96 (2016): 513-524. https://doi.org/10.1016/j.ijheatmasstransfer.2016.01.059
Sharma, Rajesh, Anuar Ishak, Roslinda Nazar, and Ioan Pop. "Boundary layer flow and heat transfer over a permeable exponentially shrinking sheet in the presence of thermal radiation and partial slip." Journal of Applied Fluid Mechanics 7, no. 1 (2014): 125-134. https://doi.org/10.36884/jafm.7.01.19489
Adnan, Nurul Shahirah Mohd, Norihan Md Arifin, Norfifah Bachok, and Fadzilah Md Ali. "Stability analysis of MHD flow and heat transfer passing a permeable exponentially shrinking sheet with partial slip and thermal radiation." CFD Letters 11, no. 12 (2019): 34-42.
Ahmad, Saeed, Muhammad Yousaf, Amir Khan, and Gul Zaman. "Magnetohydrodynamic fluid flow and heat transfer over a shrinking sheet under the influence of thermal slip." Heliyon 4, no. 10 (2018): e00828. https://doi.org/10.1016/j.heliyon.2018.e00828
Bilal, M. "Micropolar flow of EMHD nanofluid with non-linear thermal radiation and slip effects." Alexandria Engineering Journal 59, no. 2 (2020): 965-976. https://doi.org/10.1016/j.aej.2020.03.023
Ghosh, Sudipta, and Swati Mukhopadhyay. "Stability analysis for model-based study of nanofluid flow over an exponentially shrinking permeable sheet in presence of slip." Neural Computing and Applications (2019): 1-11.https://doi.org/10.1007/s00521-019-04221-w
Yang, Weidong, Xuehui Chen, Zeyi Jiang, Xinru Zhang, and Liancun Zheng. "Effect of slip boundary condition on flow and heat transfer of a double fractional Maxwell fluid." Chinese Journal of Physics 68 (2020): 214-223.https://doi.org/10.1016/j.cjph.2020.09.003
Mohamadi, S., M. H. Yazdi, E. Solomin, A. Fudholi, K. Sopian, and Perk Lin Chong. "Heat transfer and entropy generation analysis of internal flow of nanorefrigerant with slip condition at wall." Thermal Science and Engineering Progress 22 (2021): 100829. https://doi.org/10.1016/j.tsep.2020.100829
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
Pal, Dulal, and Hiranmoy Mondal. "Influence of temperature-dependent viscosity and thermal radiation on MHD forced convection over a non-isothermal wedge." Applied Mathematics and Computation 212, no. 1 (2009): 194-208. https://doi.org/10.1016/j.amc.2009.02.013
Das, Kalidas. "Cu-water nanofluid flow and heat transfer over a shrinking sheet." Journal of Mechanical Science and Technology 28, no. 12 (2014): 5089-5094. https://doi.org/10.1007/s12206-014-1130-2
Hussain, S. T., Sohail Nadeem, and Rizwan Ul Haq. "Model-based analysis of micropolar nanofluid flow over a stretching surface." The European Physical Journal Plus 129, no. 8 (2014): 1-10. https://doi.org/10.1140/epjp/i2014-14161-8
Naganthran, Kohilavani, Roslinda Nazar, and Ioan Pop. "Stability analysis of impinging oblique stagnation-point flow over a permeable shrinking surface in a viscoelastic fluid." International Journal of Mechanical Sciences 131 (2017): 663-671. https://doi.org/10.1016/j.ijmecsci.2017.07.029
Jamaludin, Anuar, Roslinda Nazar, and Ioan Pop. "Mixed convection stagnation-point flow of a nanofluid past a permeable stretching/shrinking sheet in the presence of thermal radiation and heat source/sink." Energies 12, no. 5 (2019): 788. https://doi.org/10.3390/en12050788