MHD Stagnation-Point Flow and Heat Transfer in a Micropolar Fluid over an Exponentially Vertical Sheet
DOI:
https://doi.org/10.37934/cfdl.15.3.8196Keywords:
Micropolar fluid, MHD, stagnation point flow, heat transfer, exponentially stretching/shrinking sheet, mixed convectionAbstract
This paper examines the magneto hydrodynamic (MHD), stagnation-point flow and heat transfer caused by an exponentially stretching/shrinking vertical sheet and the presence of mixed convection (buoyancy effect) in a micropolar fluid. A set of variables is employed to transform the system of partial differential equations (PDEs) to ordinary differential equations (ODEs). The ODEs are then numerically solved in MATLAB software using BVP4c. There are a lot of agreements when compared to previous findings. The impacts of different parameters, such as micropolar, magnetic, mixed convection, radiation, temperature, and stretching/shrinking parameters are displayed graphically. It is found that contradictory phenomena between Micropolar and mixed convection for fluid velocity, angular velocity and temperature distribution profiles. The velocity profile at the vertical plate increases due to the increasing buoyancy, magnetic and radiation parameters. The particle rotation occurs in two phenomena for buoyancy and magnetic parameters and it is reversible for micropolar. The temperature of the fluid decreases with buoyancy and magnetic parameters.
Downloads
References
Lund, Liaquat Ali, Zurni Omar, Ilyas Khan, Dumitru Baleanu, and Kottakkaran Sooppy Nisar. "Convective effect on magnetohydrodynamic (MHD) stagnation point flow of Casson fluid over a vertical exponentially stretching/shrinking surface: Triple solutions." Symmetry 12, no. 8 (2020): 1238. https://doi.org/10.3390/sym12081238
Dash, G. C., R. S. Tripathy, M. M. Rashidi, and S. R. Mishra. "Numerical approach to boundary layer stagnation-point flow past a stretching/shrinking sheet." Journal of Molecular Liquids 221 (2016): 860-866. https://doi.org/10.1016/j.molliq.2016.06.072
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
Soid, Siti Khuzaimah, Anuar Ishak, and Ioan Pop. "MHD stagnation-point flow over a stretching/shrinking sheet in a micropolar fluid with a slip boundary." Sains Malaysiana 47, no. 11 (2018): 2907-2916. https://doi.org/10.17576/jsm-2018-4711-34
Shu, Jian-Jun, and Jenn Shiun Lee. "Fundamental solutions for micropolar fluids." Journal of Engineering Mathematics 61, no. 1 (2008): 69-79. https://doi.org/10.1007/s10665-007-9160-8
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
Ishak, Anuar, Yian Yian Lok, and Ioan Pop. "Stagnation-point flow over a shrinking sheet in a micropolar fluid." Chemical Engineering Communications 197, no. 11 (2010): 1417-1427. https://doi.org/10.1080/00986441003626169
Borrelli, Alessandra, Giulia Giantesio, and Maria Cristina Patria. "Numerical simulations of three-dimensional MHD stagnation-point flow of a micropolar fluid." Computers & Mathematics with Applications 66, no. 4 (2013): 472-489. https://doi.org/10.1016/j.camwa.2013.05.023
Attia, Hazem Ali. "Stagnation point flow and heat transfer of a micropolar fluid with uniform suction or blowing." Journal of the Brazilian Society of Mechanical Sciences and Engineering 30 (2008): 51-55. https://doi.org/10.1590/S1678-58782008000100008
Mishra, S. R., I. Khan, Q. M. Al-Mdallal, and T. Asifa. "Free convective micropolar fluid flow and heat transfer over a shrinking sheet with heat source." Case Studies in Thermal Engineering 11 (2018): 113-119. https://doi.org/10.1016/j.csite.2018.01.005
Nisar, Kottakkaran Sooppy, Aftab Ahmed Faridi, Sohail Ahmad, Nargis Khan, Kashif Ali, Wasim Jamshed, Abdel-Haleem Abdel-Aty, and I. S. Yahia. "Cumulative impact of micropolar fluid and porosity on MHD channel flow: a numerical study." Coatings 12, no. 1 (2022): 93. https://doi.org/10.3390/coatings12010093
Abbas, Nadeem, S. Nadeem, and M. N. Khan. "Numerical analysis of unsteady magnetized micropolar fluid flow over a curved surface." Journal of Thermal Analysis and Calorimetry 147, no. 11 (2022): 6449-6459. https://doi.org/10.1007/s10973-021-10913-0
Reddy, S. R. R., and P. Bala Anki Reddy. "Thermal radiation effect on unsteady three-dimensional MHD flow of micropolar fluid over a horizontal surface of a parabola of revolution." Propulsion and Power Research 11, no. 1 (2022): 129-142. https://doi.org/10.1016/j.jppr.2022.01.001
Qian, Wei-Mao, M. Ijaz Khan, Faisal Shah, Mair Khan, Yu-Ming Chu, Waqar A. Khan, and Mubbashar Nazeer. "Mathematical modeling and MHD flow of micropolar fluid toward an exponential curved surface: heat analysis via ohmic heating and heat source/sink." Arabian Journal for Science and Engineering 47, no. 1 (2022): 867-878. https://doi.org/10.1007/s13369-021-05673-w
Goud, B. Shankar, Yanala Dharmendar Reddy, Nawal A. Alshehri, Wasim Jamshed, Rabia Safdar, Mohamed R. Eid, and Mohamed Lamjed Bouazizi. "Numerical Case Study of Chemical Reaction Impact on MHD Micropolar Fluid Flow Past over a Vertical Riga Plate." Materials 15, no. 12 (2022): 4060. https://doi.org/10.3390/ma15124060
Lakshmi Devi, G., H. Niranjan, and S. Sivasankaran. "Effects of chemical reactions, radiation, and activation energy on MHD buoyancy induced nano fluidflow past a vertical surface." Scientia Iranica 29, no. 1 (2022): 90-100.
Song, Ying-Qing, Hassan Waqas, Shan Ali Khan, Sami Ullah Khan, M. Ijaz Khan, Yu-Ming Chu, and Sumaira Qayyum. "Nonlinear thermally radiative heat transport for brinkman type micropolar nano-material over an inclined surface with motile microorganisms and exponential heat source." International Communications in Heat and Mass Transfer 126 (2021): 105351. https://doi.org/10.1016/j.icheatmasstransfer.2021.105351
Asghar, Adnan, Teh Yuan Ying, and Khairy Zaimi. "Two-Dimensional Magnetized Mixed Convection Hybrid Nanofluid Over a Vertical Exponentially Shrinking Sheet by Thermal Radiation, Joule Heating, Velocity and Thermal Slip Conditions." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 95, no. 2 (2022): 159-179. https://doi.org/10.37934/arfmts.95.2.159179
Jahan, Sultana, M. Ferdows, Md Shamshuddin, and Khairy Zaimi. "Radiative Mixed Convection Flow Over a Moving Needle Saturated with Non-Isothermal Hybrid Nanofluid." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 88, no. 1 (2021): 81-93. https://doi.org/10.37934/arfmts.88.1.8193
Widodo, Basuki, Adhi Surya Nugraha, and Tri Rahayuningsih. "Numerical Solution of Mixed Convection MHD Viscous Fluid Flow on Lower Stagnation Point of a Sliced Magnetic Sphere." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 95, no. 1 (2022): 110-120. https://doi.org/10.37934/arfmts.95.1.110120
Mahdy, A., Taghreed H. Al-Arabi, Ahmed M. Rashad, and Wafaa Saad. "Influence Of Thermal Radiation on Unsteady Mixed Convection Flow of Hybrid Nanoliquid Past an Elongated Sheet." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 94, no. 2 (2022): 110-122. https://doi.org/10.37934/arfmts.94.2.110122
Ali, I. R., Ammar I. Alsabery, Norhaliza Abu Bakar, and Rozaini Roslan. "Mixed Convection in a Lid-Driven Horizontal Rectangular Cavity Filled with Hybrid Nanofluid by Finite Volume Method." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 93, no. 1 (2022): 110-122. https://doi.org/10.37934/arfmts.93.1.110122
Yasin, Siti Hanani Mat, Muhammad Khairul Anuar Mohamed, Zulkhibri Ismail, Basuki Widodo, and Mohd Zuki Salleh. "Numerical Investigation of Ferrofluid Flow at Lower Stagnation Point over a Solid Sphere using Keller-Box Method." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 94, no. 2 (2022): 200-214. https://doi.org/10.37934/arfmts.94.2.200214
Mopuri, Obulesu, Charankumar Ganteda, Bhagyashree Mahanta, and Giulio Lorenzini. "MHD heat and mass transfer steady flow of a convective fluid through a porous plate in the presence of multiple parameters." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 89, no. 2 (2022): 56-75. https://doi.org/10.37934/arfmts.89.2.5675
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
Raju, Chakravarthula SK, and Naramgari Sandeep. "Dual solutions for unsteady heat and mass transfer in bio-convection flow towards a rotating cone/plate in a rotating fluid." In International Journal of Engineering Research in Africa, vol. 20, pp. 161-176. Trans Tech Publications Ltd, 2016. https://doi.org/10.4028/www.scientific.net/JERA.20.161
Zohra, Fatema T., Mohammed J. Uddin, and Ahamd I. M. Ismail. "Magnetohydrodynamic bio‐nanoconvective Naiver slip flow of micropolar fluid in a stretchable horizontal channel." Heat Transfer-Asian Research 48, no. 8 (2019): 3636-3656. https://doi.org/10.1002/htj.21560
Soid, Siti Khuzaimah, Anuar Ishak, and Ioan Pop. "Unsteady MHD flow and heat transfer over a shrinking sheet with ohmic heating." Chinese Journal of Physics 55, no. 4 (2017): 1626-1636. https://doi.org/10.1016/j.cjph.2017.05.001
Lund, Liaquat Ali, Zurni Omar, Ilyas Khan, Dumitru Baleanu, and Kottakkaran Sooppy Nisar. "Dual similarity solutions of MHD stagnation point flow of Casson fluid with effect of thermal radiation and viscous dissipation: stability analysis." Scientific Reports 10, no. 1 (2020): 1-13. https://doi.org/10.1038/s41598-020-72266-2
Waini, Iskandar, Anuar Ishak, and Ioan Pop. "Hybrid nanofluid flow towards a stagnation point on an exponentially stretching/shrinking vertical sheet with buoyancy effects." International Journal of Numerical Methods for Heat & Fluid Flow 31, no. 1 (2020): 216-235. https://doi.org/10.1108/HFF-02-2020-0086
Uddin, Md Sharif, Krishnendu Bhattacharyya, and Sharidan Shafie. "Micropolar fluid flow and heat transfer over an exponentially permeable shrinking sheet." Propulsion and Power Research 5, no. 4 (2016): 310-317. https://doi.org/10.1016/j.jppr.2016.11.005
Siddiqa, Sadia, Naheed Begum, Md Anwar Hossain, Muhammad Nasir Abrar, Rama Subba Reddy Gorla, and Qasem Al-Mdallal. "Effect of thermal radiation on conjugate natural convection flow of a micropolar fluid along a vertical surface." Computers & Mathematics with Applications 83 (2021): 74-83. https://doi.org/10.1016/j.camwa.2020.01.011
Rehman, Fiaz Ur, Sohail Nadeem, Hafeez Ur Rehman, and Rizwan Ul Haq. "Thermophysical analysis for three-dimensional MHD stagnation-point flow of nano-material influenced by an exponential stretching surface." Results in Physics 8 (2018): 316-323. https://doi.org/10.1016/j.rinp.2017.12.026
Reddy, G. Janardhana, Bhaskerreddy Kethireddy, and H. P. Rani. "Bejan's heat flow visualization for unsteady micropolar fluid past a vertical slender hollow cylinder with large Grashof number." International Journal of Applied and Computational Mathematics 4, no. 1 (2018): 1-25. https://doi.org/10.1007/s40819-017-0468-4
Mutegi, R. A., John Achola Okello, and M. Kimathi. "Analysis of Effect of Inclined Magnetic Field on MHD Boundary Layer Flow over a Porous Exponentially Stretching Sheet Subject to Thermal Radiation." Asian Research Journal of Mathematics 17, no. 9 (2021): 20-33. https://doi.org/10.9734/arjom/2021/v17i930328
Abdul Halim, Nadhirah, and Noor Fadiya Mohd Noor. "Mixed convection flow of Powell-Eyring nanofluid near a stagnation point along a vertical stretching sheet." Mathematics 9, no. 4 (2021): 364. https://doi.org/10.3390/math9040364