MHD Stagnation Point Flow of Micropolar Fluid over a Stretching/ Shrinking Sheet
DOI:
https://doi.org/10.37934/cfdl.16.12.113127Keywords:
Stretching/shrinking sheet, MHD, Micropolar Fluid, Adams Bash fourth MethodAbstract
In this article, the stagnation point flow of a micropolar fluid on a stretching/shrinking sheet has been discussed subject to the assumption of velocity slip. Similarity transformation is used to transform the modelled Partial Differential Equations (PDEs) into a system of Ordinary Differential Equations (ODEs). The numerical results have been found by the shooting technique along with Adams Moulton method of order four. The obtained numerical results are compared with the help of Fortran Language program and compared with the earlier published results and excellent validation of the present numerical results has been achieved for the local Nusselt number. Finally, the numerical results are presented with discussion of the effects of different physical parameters.
References
Ishak, A., R. Nazar, and I. Pop. "Mixed convection stagnation point flow of a micropolar fluid towards a stretching sheet." Meccanica 43 (2008): 411-418. https://doi.org/10.1007/s11012-007-9103-5
Ishak, Anuar, Roslinda Nazar, and Ioan Pop. "Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet." Meccanica 41 (2006): 509-518. https://doi.org/10.1007/s11012-006-0009-4
Bakar, Shahirah Abu, Norihan Md Arifin, and Ioan Pop. "Stability Analysis on Mixed Convection Nanofluid Flow in a Permeable Porous Medium with Radiation and Internal Heat Generation." Journal of Advanced Research in Micro and Nano Engineering 13, no. 1 (2023): 1-17. https://doi.org/10.37934/armne.13.1.117
Akram, Javaria, and Noreen Sher Akbar. "Mathematical modeling of Aphron drilling nanofluid driven by electroosmotically modulated peristalsis through a pipe." Mathematical Modelling of Natural Phenomena 17 (2022): 19. https://doi.org/10.1051/mmnp/2022012
Srisailam, Batcha, Katkoori Sreeram Reddy, Ganji Narender, and Bala Siddhulu Malga. "The Effect of Viscous Dissipation and Chemical reaction on the flow of MHD Nanofluid." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 107, no. 2 (2023): 150-170. https://doi.org/10.37934/arfmts.107.2.150170
Wang, C. Y., and Chiu-On Ng. "Stagnation flow on a heated vertical plate with surface slip." Journal of heat transfer 135, no. 7 (2013): 074505. https://doi.org/10.1115/1.4023750
Deissler, R. G. "An analysis of second-order slip flow and temperature-jump boundary conditions for rarefied gases." International Journal of Heat and Mass Transfer 7, no. 6 (1964): 681-694. https://doi.org/10.1016/0017-9310(64)90161-9
Fang, Tiegang, Shanshan Yao, Ji Zhang, and Abdul Aziz. "Viscous flow over a shrinking sheet with a second order slip flow model." Communications in Nonlinear Science and Numerical Simulation 15, no. 7 (2010): 1831-1842. https://doi.org/10.1016/j.cnsns.2009.07.017
Maraj, E. N., Iffat Zehra, and Noreen SherAkbar. "Rotatory flow of MHD (MoS2-SiO2)/H2O hybrid nanofluid in a vertical channel owing to velocity slip and thermal periodic conditions." Colloids and Surfaces A: Physicochemical and Engineering Aspects 639 (2022): 128383. https://doi.org/10.1016/j.colsurfa.2022.128383
Maraj, E. N., Noreen Sher Akbar, I. Zehra, A. W. Butt, and Huda Ahmed Alghamdi. "Electro-osmotically modulated magneto hydrodynamic peristaltic flow of menthol based nanofluid in a uniform channel with shape factor." Journal of Magnetism and Magnetic Materials 576 (2023): 170774. https://doi.org/10.1016/j.jmmm.2023.170774
Eckert, Ernest Rudolf Georg. "Die Berechnung des Warmeuberganges in der laminaren Grenzschicht umstromter Korper." VDI Forschungsheft 416 (1942): 1-24.
Eringen, A. Cemal. "Theory of micropolar fluids." Journal of mathematics and Mechanics (1966): 1-18. https://doi.org/10.1512/iumj.1967.16.16001
Duraihem, Faisal Z., E. N. Maraj, Noreen Sher Akbar, and R. Mehmood. "Thermal stratification effect on gravity driven transport of hybrid CNTs down a stretched surface through porous medium." Heliyon 9, no. 5 (2023). https://doi.org/10.1016/j.heliyon.2023.e15699
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
Hiemenz, Karl. "Die Grenzschicht an einem in den gleichformigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder." Dinglers Polytech. J. 326 (1911): 321-324.
J Akram, Javaria, Noreen Sher Akbar, Monairah Alansari, and Dharmendra Tripathi. "Electroosmotically modulated peristaltic propulsion of TiO2/10W40 nanofluid in curved microchannel." International Communications in Heat and Mass Transfer 136 (2022): 106208. https://doi.org/10.1016/j.icheatmasstransfer.2022.106208
Ghailan, Khalid Y., Noreen Sher Akbar, Ashwag Albakri, and Mohammed M. Alshehri. "Biological analysis of emerging nanoparticles with blood through propagating flow along a plumb porous canal in the occurrence of energy and heat transfer." Surfaces and Interfaces 40 (2023): 103013. https://doi.org/10.1016/j.surfin.2023.103013
Jiann, Lim Yeou, Sharena Mohamad Isa, Noraihan Afiqah Rawi, Ahmad Qushairi Bin Mohamad, and Sharidan Shafie. "Investigating the Effects of Wu's Slip and Smoluchowski's Slip on Hybrid TiO2/Ag Nanofluid Performance." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 107, no. 2 (2023): 236-252. https://doi.org/10.37934/arfmts.107.2.236252
Nandeppanavar, Mahantesh M., K. Vajravelu, M. Subhas Abel, and M. N. Siddalingappa. "Second order slip flow and heat transfer over a stretching sheet with non-linear Navier boundary condition." International Journal of Thermal Sciences 58 (2012): 143-150. https://doi.org/10.1016/j.ijthermalsci.2012.02.019
Bachok, Norfifah, Anuar Ishak, and Ioan Pop. "Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet." Physics letters A 374, no. 40 (2010): 4075-4079. https://doi.org/10.1016/j.physleta.2010.08.032
Akbar, Noreen Sher, A. Al-Zubaidi, S. Saleem, and Shami AM Alsallami. "Variable fluid properties analysis for thermally laminated 3-dimensional magnetohydrodynamic non-Newtonian nanofluid over a stretching sheet." Scientific Reports 13, no. 1 (2023): 3231. https://doi.org/10.1038/s41598-023-30233-7
Roşca, Alin V., and Ioan Pop. "Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip." International Journal of Heat and Mass Transfer 60 (2013): 355-364. https://doi.org/10.1016/j.ijheatmasstransfer.2012.12.028
Rees, D. Andrew S., and I. Pop. "Free convection boundary-layer flow of a micropolar fluid from a vertical flat plate." IMA Journal of Applied Mathematics 61, no. 2 (1998): 179-197. https://doi.org/10.1093/imamat/61.2.179
Bhargava, Rama, S. Sharma, H. S. S. Takhar, O. A. A. Bég, and Pradeep Bhargava. "Numerical solutions for micropolar transport phenomena over a nonlinear stretching sheet." Nonlinear analysis: modelling and control 12, no. 1 (2007): 45-63. https://doi.org/10.15388/NA.2007.12.1.14721
Nazar, Roslinda, Norsarahaida Amin, Diana Filip, and Ioan Pop. "Stagnation point flow of a micropolar fluid towards a stretching sheet." International Journal of Non-Linear Mechanics 39, no. 7 (2004): 1227-1235. https://doi.org/10.1016/j.ijnonlinmec.2003.08.007
Sharma, Rajesh, Anuar Ishak, and Ioan Pop. "Stagnation point flow of a micropolar fluid over a stretching/shrinking sheet with second-order velocity slip." Journal of Aerospace Engineering 29, no. 5 (2016): 04016025. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000616
Sharma, Rajesh, Anuar Ishak, and Ioan Pop. "Partial slip flow and heat transfer over a stretching sheet in a nanofluid." Mathematical Problems in Engineering 2013 (2013). https://doi.org/10.1155/2013/724547
Sajid, M., N. Ali, Z. Abbas, and T. Javed. "Stretching flows with general slip boundary condition." International Journal of Modern Physics B 24, no. 30 (2010): 5939-5947. https://doi.org/10.1142/S0217979210055512
Hayat, T., M. Mustafa, S. A. Shehzad, and S. Obaidat. "Melting heat transfer in the stagnation‐point flow of an upper‐convected Maxwell (UCM) fluid past a stretching sheet." International journal for numerical methods in fluids 68, no. 2 (2012): 233-243. https://doi.org/10.1002/fld.2503
Ariman, T. T. N. D., M. A. Turk, and N. D. Sylvester. "Applications of microcontinuum fluid mechanics." International Journal of Engineering Science 12, no. 4 (1974): 273-293. https://doi.org/10.1016/0020-7225(74)90059-7
Thirupathi, Gurrala, Kamatam Govardhan, and Ganji Narender. "Radiative magnetohydrodynamics Casson nanofluid flow and heat and mass transfer past on nonlinear stretching surface." Journal of Advanced Research in Numerical Heat Transfer 6, no. 1 (2021): 1-21. https://doi.org/10.3762/bxiv.2021.65.v1
Turkyilmazoglu, M. "Heat and mass transfer of MHD second order slip flow." Computers & Fluids 71 (2013): 426-434. https://doi.org/10.1016/j.compfluid.2012.11.011
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
Wu, Lin. "A slip model for rarefied gas flows at arbitrary Knudsen number." Applied Physics Letters 93, no. 25 (2008). https://doi.org/10.1063/1.3052923
