Analytical Treatment for Accelerated Riga Plate on Fractional Caputo-Fabrizio Casson Fluid
DOI:
https://doi.org/10.37934/cfdl.15.4.114131Keywords:
Caputo-Fabrizio fractional derivative, unsteady Casson fluid flow, Riga plate, Laplace transformAbstract
The Riga plate is a substantial alteration in the world of engineering. Mainly used in submarines to regulate water flow, studying the behaviour of fluid flowing over a Riga plate is very advantageous. Although there are ample studies on fluid flowing over a Riga plate, the introduction of fractional derivatives, coupled with a non-Newtonian fluid, has yet to be done. Within the field of fluid mechanics, specifically boundary layer flow, fractional derivatives do not have a proven geometrical representation. However, analytical solutions would be useful in aiding experimental researches in the future. Thus, this study aims to present an analytical function for a Caputo-Fabrizio fractional derivative on an unsteady Casson fluid flowing over an accelerating vertical Riga plate by using the Laplace transform method. The parametric effects considered in this study is elucidated. Through observation of obtained graphical results generated via the obtained analytical solutions, it is found that amplification of the fractional parameter and modified Hartmann number increases the fluid velocity with an average increment of 42.05% and 1.56%, respectively. While amplification of the Casson parameter and Prandtl number dampens the fluid velocity by an average of 45.09% and 43.56%, respectively
Downloads
References
Khashi’ie, Najiyah Safwa, Norihan Md Arifin, and Ioan Pop. "Mixed convective stagnation point flow towards a vertical Riga plate in hybrid Cu-Al2O3/water nanofluid." Mathematics 8, no. 6 (2020): 912. https://doi.org/10.3390/math8060912
Ganesh, N. Vishnu, Qasem M. Al-Mdallal, Sara Al Fahel, and Shymaa Dadoa. "Riga–Plate flow of γ Al2O3-water/ethylene glycol with effective Prandtl number impacts." Heliyon 5, no. 5 (2019): e01651. https://doi.org/10.1016/j.heliyon.2019.e01651
Bilal, S., Kanayo K. Asogwa, Hammad Alotaibi, M. Y. Malik, and Ilyas Khan. "Analytical treatment of radiative Casson fluid over an isothermal inclined Riga surface with aspects of chemically reactive species." Alexandria Engineering Journal 60, no. 5 (2021): 4243-4253. https://doi.org/10.1016/j.aej.2021.03.015
Loganathan, Parasuraman, and Krishnamurthy Deepa. "Electromagnetic and radiative Casson fluid flow over a permeable vertical Riga-plate." Journal of Theoretical and Applied Mechanics 57 (2019). https://doi.org/10.15632/jtam-pl/112421
Loganathan, P., and K. Deepa. "Stratified Casson Fluid Flow Past a Riga-plate with Generative/Destructive Heat Energy." International Journal of Applied and Computational Mathematics 6, no. 4 (2020): 1-20. https://doi.org/10.1007/s40819-020-00863-w
Parasuraman, Loganathan, and Deepa Krishnamurthy. "Heat and mass transfer analysis of casson fluid flow on a permeable riga-plate." Indian Journal of Pure & Applied Physics (IJPAP) 58, no. 2 (2020): 79-86. https://doi.org/10.1615/InterJFluidMechRes.2020027371
Nasrin, Sonia, Rabindra Nath Mondal, and Md Mahmud Alam. "Impulsively Started Horizontal Riga Plate Embedded in Unsteady Casson Fluid Flow with Rotation." Journal of Applied Mathematics and Physics 8, no. 9 (2020): 1861-1876. https://doi.org/10.4236/jamp.2020.89140
Loganathan, Parasuraman, and Krishnamurthy Deepa. "Computational exploration of Casson fluid flow over a Riga-plate with variable chemical reaction and linear stratification." Nonlinear Analysis: Modelling and Control 25, no. 3 (2020): 443-460. https://doi.org/10.15388/namc.2020.25.16659
Shah, Faisal, M. Ijaz Khan, Tasawar Hayat, Shaher Momani, and M. Imran Khan. "Cattaneo-Christov heat flux (CC model) in mixed convective stagnation point flow towards a Riga plate." Computer Methods and Programs in Biomedicine 196 (2020): 105564. https://doi.org/10.1016/j.cmpb.2020.105564
Rizwana, Rizwana, and S. Nadeem. "Series solution of unsteady MHD oblique stagnation point flow of copper-water nanofluid flow towards Riga plate." Heliyon 6, no. 10 (2020): e04689. https://doi.org/10.1016/j.heliyon.2020.e04689
Mallawi, F. O. M., M. Bhuvaneswari, S. Sivasankaran, and S. Eswaramoorthi. "Impact of double-stratification on convective flow of a non-Newtonian liquid in a Riga plate with Cattaneo-Christov double-flux and thermal radiation." Ain Shams Engineering Journal 12, no. 1 (2021): 969-981. https://doi.org/10.1016/j.asej.2020.04.010
Khatun, Sheela, Muhammad Minarul Islam, Md Mollah, Saykat Poddar, and Md Alam. "EMHD radiating fluid flow along a vertical Riga plate with suction in a rotating system." SN Applied Sciences 3, no. 4 (2021): 1-14. https://doi.org/10.1007/s42452-021-04444-4
Bhatti, M. M., and Efstathios E. Michaelides. "Study of Arrhenius activation energy on the thermo-bioconvection nanofluid flow over a Riga plate." Journal of Thermal Analysis and Calorimetry 143, no. 3 (2021): 2029-2038. https://doi.org/10.1007/s10973-020-09492-3
Bhatti, M. M., and Efstathios E. Michaelides. "Study of Arrhenius activation energy on the thermo-bioconvection nanofluid flow over a Riga plate." Journal of Thermal Analysis and Calorimetry 143, no. 3 (2021): 2029-2038. https://doi.org/10.1177/0954408917719791
Prasad, Kerehalli Vinayaka, Hanumesh Vaidya, Gudekote Manjunatha, Kuppalapalle Vajravelu, Choudhari Rajashekhar, and V. Ramanjini. "Influence of Variable Transport Properties on Casson Nanofluid Flow over a Slender Riga Plate: Keller Box Scheme." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 64, no. 1 (2019): 19-42.
Waini, Iskandar, Anuar Ishak, and Ioan Pop. "Symmetrical solutions of hybrid nanofluid stagnation-point flow in a porous medium." International Communications in Heat and Mass Transfer 130 (2022): 105804. https://doi.org/10.1016/j.icheatmasstransfer.2021.105804
Waini, Iskandar, Umair Khan, Aurang Zaib, Anuar Ishak, and Ioan Pop. "Inspection of TiO2-CoFe2O4 nanoparticles on MHD flow toward a shrinking cylinder with radiative heat transfer." Journal of Molecular Liquids 361 (2022): 119615. https://doi.org/10.1016/j.molliq.2022.119615
Khashi’ie, Najiyah Safwa, Iskandar Waini, Nurul Amira Zainal, Khairum Hamzah, and Abdul Rahman Mohd Kasim. "Hybrid nanofluid flow past a shrinking cylinder with prescribed surface heat flux." Symmetry 12, no. 9 (2020): 1493. https://doi.org/10.3390/sym12091493
Khan, Ilyas, Nehad Ali Shah, and Dumitru Vieru. "Unsteady flow of generalized Casson fluid with fractional derivative due to an infinite plate." The European physical journal plus 131, no. 6 (2016): 1-12. https://doi.org/10.1140/epjp/i2016-16181-8
Ali, Farhad, Nadeem Ahmad Sheikh, Ilyas Khan, and Muhammad Saqib. "Solutions with Wright function for time fractional free convection flow of Casson fluid." Arabian Journal for Science and Engineering 42, no. 6 (2017): 2565-2572. https://doi.org/10.1007/s13369-017-2521-3
Khan, Ilyas, Muhammad Saqib, and Farhad Ali. "Application of time-fractional derivatives with non-singular kernel to the generalized convective flow of Casson fluid in a microchannel with constant walls temperature." The European Physical Journal Special Topics 226, no. 16 (2017): 3791-3802. https://doi.org/10.1140/epjst/e2018-00097-5
Yépez-Martínez, Huitzilin, and José Francisco Gómez-Aguilar. "A new modified definition of Caputo–Fabrizio fractional-order derivative and their applications to the multi step homotopy analysis method (MHAM)." Journal of Computational and Applied Mathematics 346 (2019): 247-260. https://doi.org/10.1016/j.cam.2018.07.023
Sheikh, Nadeem Ahmad, Farhad Ali, Muhammad Saqib, Ilyas Khan, and Syed Aftab Alam Jan. "A comparative study of Atangana-Baleanu and Caputo-Fabrizio fractional derivatives to the convective flow of a generalized Casson fluid." The European Physical Journal Plus 132, no. 1 (2017): 1-14. https://doi.org/10.1140/epjp/i2017-11326-y
Sheikh, Nadeem Ahmad, Farhad Ali, Muhammad Saqib, Ilyas Khan, Syed Aftab Alam Jan, Ali Saleh Alshomrani, and Metib Said Alghamdi. "Comparison and analysis of the Atangana–Baleanu and Caputo–Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction." Results in physics 7 (2017): 789-800. https://doi.org/10.1016/j.rinp.2017.01.025
Jamil, Dzuliana Fatin, Salah Uddin, M. Ghazali Kamardan, and Rozaini Roslan. "The effects of magnetic blood flow in an inclined cylindrical tube using caputo-fabrizio fractional derivatives." CFD Letters 12, no. 1 (2020): 111-122.
Maiti, S., S. Shaw, and G. C. Shit. "Caputo–Fabrizio fractional order model on MHD blood flow with heat and mass transfer through a porous vessel in the presence of thermal radiation." Physica A: Statistical Mechanics and its Applications 540 (2020): 123149. https://doi.org/10.1016/j.physa.2019.123149
Asogwa, Kanayo K., Sardar M. Bilal, Isaac L. Animasaun, and Fateh M. Mebarek-Oudina. "Insight into the significance of ramped wall temperature and ramped surface concentration: The case of Casson fluid flow on an inclined Riga plate with heat absorption and chemical reaction." Nonlinear Engineering 10, no. 1 (2021): 213-230. https://doi.org/10.1515/nleng-2021-0016
Shahrim, Muhammad Nazirul, Ahmad Qushairi Mohamad, Lim Yeou Jiann, Muhamad Najib Zakaria, Sharidan Shafie, Zulkhibri Ismail, and Abdul Rahman Mohd Kasim. "Exact solution of fractional convective Casson fluid through an accelerated plate." CFD Letters 13, no. 6 (2021): 15-25. https://doi.org/10.37934/cfdl.13.6.1525
Hussanan, Abid, Mohd Zuki Salleh, Ilyas Khan, and Razman Mat Tahar. "Heat transfer in magnetohydrodynamic flow of a Casson fluid with porous medium and Newtonian heating." Journal of nanofluids 6, no. 4 (2017): 784-793. https://doi.org/10.1166/jon.2017.1359
Reyaz, Ridhwan, Ahmad Qushairi Mohamad, Lim Yeou Jiann, Muhammad Saqib, and Sharidan Shafie. "Presence of Riga Plate on MHD Caputo Casson Fluid: An Analytical Study." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 93, no. 2 (2022): 86-99. https://doi.org/10.37934/arfmts.93.2.8699
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.
Zakaria, Muhamad Najib, Abid Hussanan, Ilyas Khan, and Sharidan Shafie. "The effects of radiation on free convection flow with ramped wall temperature in Brinkman type fluid." Jurnal Teknologi 62, no. 3 (2013). https://doi.org/10.11113/jt.v62.1886
Anantha Kumar, K., V. Sugunamma, and N. Sandeep. "Effect of thermal radiation on MHD Casson fluid flow over an exponentially stretching curved sheet." Journal of Thermal Analysis and Calorimetry 140, no. 5 (2020): 2377-2385. https://doi.org/10.1007/s10973-019-08977-0
Yusof, Nur Syamila, Siti Khuzaimah Soid, Mohd Rijal Illias, Ahmad Sukri Abd Aziz, and Nor Ain Azeany Mohd Nasir. "Radiative Boundary Layer Flow of Casson Fluid Over an Exponentially Permeable Slippery Riga Plate with Viscous Dissipation." Journal of Advanced Research in Applied Sciences and Engineering Technology 21, no. 1 (2020): 41-51. https://doi.org/10.37934/araset.21.1.4151
Hussanan, Abid, Mohd Zuki Salleh, Ilyas Khan, and Zhi-Min Chen. "Unsteady water functionalized oxide and non-oxide nanofluids flow over an infinite accelerated plate." Chinese Journal of Physics 62 (2019): 115-131. https://doi.org/10.1016/j.cjph.2019.09.020
Khan, Masood, S. Hyder Ali, and Constantin Fetecau. "Exact solutions of accelerated flows for a Burgers’ fluid. I. The case γ< λ2/4." Applied Mathematics and Computation 203, no. 2 (2008): 881-894. https://doi.org/10.1007/s00033-008-7155-6
Khan, M., S. Hyder Ali, and Haitao Qi. "Some accelerated flows for a generalized Oldroyd-B fluid." Nonlinear analysis: real world applications 10, no. 2 (2009): 980-991. https://doi.org/10.1016/j.nonrwa.2007.11.017
Atangana, Abdon, and Dumitru Baleanu. "Caputo-Fabrizio derivative applied to groundwater flow within confined aquifer." Journal of Engineering Mechanics 143, no. 5 (2017): D4016005. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001091
Raza, Nauman, and Muhammad Asad Ullah. "A comparative study of heat transfer analysis of fractional Maxwell fluid by using Caputo and Caputo–Fabrizio derivatives." Canadian Journal of Physics 98, no. 1 (2020): 89-101. https://doi.org/10.1139/cjp-2018-0602
Asjad, Muhammad Imran, Nehad Ali Shah, Maryam Aleem, and Ilyas Khan. "Heat transfer analysis of fractional second-grade fluid subject to Newtonian heating with Caputo and Caputo-Fabrizio fractional derivatives: A comparison." The European physical journal plus 132, no. 8 (2017): 1-19. https://doi.org/10.1140/epjp/i2017-11606-6
Hussanan, Abid, Mohd Zuki Salleh, Ilyas Khan, and Razman Mat Tahar. "Unsteady heat transfer flow of a Casson fluid with Newtonian heating and thermal radiation." Jurnal Teknologi 78, no. 4-4 (2016). https://doi.org/10.11113/jt.v78.8264
Hussanan, Abid, Mohd Zuki Salleh, Razman Mat Tahar, and Ilyas Khan. "Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating." PloS one 9, no. 10 (2014): e108763. https://doi.org/10.1371/journal.pone.0108763
Mohamad, Ahmad Qushairi, Ilyas Khan, Lim Yeou Jiann, Sharidan Shafie, Zaiton Mat Isa, and Zulkhibri Ismail. "Heat transfer on rotating second grade fluid through an accelerated plate." Malaysian Journal of Fundamental and Applied Sciences 13, no. 3 (2017): 219-223. https://doi.org/10.11113/mjfas.v13n3.645
Reyaz, Ridhwan, Ahmad Qushairi Mohamad, Yeou Jiann Lim, Muhammad Saqib, and Sharidan Shafie. "Analytical solution for impact of Caputo-Fabrizio fractional derivative on MHD casson fluid with thermal radiation and chemical reaction effects." Fractal and Fractional 6, no. 1 (2022): 38. https://doi.org/10.3390/fractalfract6010038
Downloads
Published
How to Cite
Issue
Section
