Slip Velocity Effect on Unsteady Free Convection Flow of Casson Fluid in a Vertical Cylinder
DOI:
https://doi.org/10.37934/cfdl.15.5.2941Keywords:
Casson Fluid, Slip Velocity, Free Convection, Laplace transform, Finite Hankel TransformAbstract
Many researchers study the Casson fluid flow in the cylinder since it imitates human blood flow in the small arteries. However, only a few researchers considered slip velocity at the boundary. The slip velocity is crucial in blood flow study due to naturally occurs during stretchable movement of the arteries. Hence, the study aims to obtain analytical solutions and understand the fluid flow behaviour with the slip velocity effect for the unsteady free convection flow of Casson fluid in a cylinder. The analytical solutions are obtained by using the joint methods of the finite Hankel transform and the Laplace transform. All initial and boundary conditions are satisfied by the analytical solutions that were obtained. The behaviour of velocity and temperature profiles are plotted and discussed graphically. It is evident from the results that increasing the slip velocity, Grashof number and time will enhance blood velocity while increasing the Casson parameter causes a decrement of blood velocity. Besides, the Prandtl number increases resulting in blood velocity and the blood temperature falling. Lastly, the obtained analytical solution is validated by comparing it with the previous study and found to be in good mutual agreement. The obtained analytical solution is significant to check the accuracy of the numerical solutions
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Tulu, Ayele, and Wubshet Ibrahim. "Spectral relaxation method analysis of Casson nanofluid flow over stretching cylinder with variable thermal conductivity and Cattaneo–Christov heat flux model." Heat Transfer 49, no. 6 (2020): 3433-3455. https://doi.org/10.1002/htj.21781
Chhabra, Rajendra P. "Non-Newtonian fluids: an introduction." In Rheology of complex fluids, pp. 3-34. Springer, New York, NY, 2010. https://doi.org/10.1007/978-1-4419-6494-6_1
Casson, N. "A flow equation for pigment-oil suspensions of the printing ink type." Rheology of disperse systems (1959).
Walelign, Tadesse, Eshetu Haile, Tesfaye Kebede, and Assaye Walelgn. "Analytical study of heat and mass transfer in MHD flow of chemically reactive and thermally radiative Casson nanofluid over an inclined stretching cylinder." Journal of Physics Communications 4, no. 12 (2020): 125003. https://doi.org/10.1088/2399-6528/abcdba
Rehman, Khalil Ur, Aqeela Qaiser, M. Y. Malik, and U. Ali. "Numerical communication for MHD thermally stratified dual convection flow of Casson fluid yields by stretching cylinder." Chinese Journal of Physics 55, no. 4 (2017): 1605-1614. https://doi.org/10.1016/j.cjph.2017.05.002
Bejawada, Shankar Goud, Yanala Dharmendar Reddy, Wasim Jamshed, Kottakkaran Sooppy Nisar, Abdulaziz N. Alharbi, and Ridha Chouikh. "Radiation effect on MHD Casson fluid flow over an inclined non-linear surface with chemical reaction in a Forchheimer porous medium." Alexandria Engineering Journal 61, no. 10 (2022): 8207-8220. https://doi.org/10.1016/j.aej.2022.01.043
Dash, R. K., K. N. Mehta, and G. Jayaraman. "Casson fluid flow in a pipe filled with a homogeneous porous medium." International Journal of Engineering Science 34, no. 10 (1996): 1145-1156. https://doi.org/10.1016/0020-7225(96)00012-2
Goud, B. Shankar, P. Pramod Kumar, and Bala Siddulu Malga. "Effect of Heat source on an unsteady MHD free convection flow of Casson fluid past a vertical oscillating plate in porous medium using finite element analysis." Partial Differential Equations in Applied Mathematics 2 (2020): 100015. https://doi.org/10.1016/j.padiff.2020.100015
Das, M., R. Mahato, and R. Nandkeolyar. "Newtonian heating effect on unsteady hydromagnetic Casson fluid flow past a flat plate with heat and mass transfer." Alexandria Engineering Journal 54, no. 4 (2015): 871-879. https://doi.org/10.1016/j.aej.2015.07.007
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
Kataria, Hari R., and Harshad R. Patel. "Soret and heat generation effects on MHD Casson fluid flow past an oscillating vertical plate embedded through porous medium." Alexandria Engineering Journal 55, no. 3 (2016): 2125-2137. https://doi.org/10.1016/j.aej.2016.06.024
Kataria, Hari R., and Harshad R. Patel. "Effects of chemical reaction and heat generation/absorption on magnetohydrodynamic (MHD) Casson fluid flow over an exponentially accelerated vertical plate embedded in porous medium with ramped wall temperature and ramped surface concentration." propulsion and power research 8, no. 1 (2019): 35-46. https://doi.org/10.1016/j.jppr.2018.12.001
Kataria, Hari R., and Harshad R. Patel. "Effects of chemical reaction and heat generation/absorption on magnetohydrodynamic (MHD) Casson fluid flow over an exponentially accelerated vertical plate embedded in porous medium with ramped wall temperature and ramped surface concentration." propulsion and power research 8, no. 1 (2019): 35-46. https://doi.org/10.1016/j.jppr.2018.12.001
Ali, Farhad, Nadeem Ahmad Sheikh, Ilyas Khan, and Muhammad Saqib. "Magnetic field effect on blood flow of Casson fluid in axisymmetric cylindrical tube: A fractional model." Journal of Magnetism and Magnetic Materials 423 (2017): 327-336. https://doi.org/10.1016/j.jmmm.2016.09.125
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
Khalid, Asma, Ilyas Khan, Arshad Khan, and Sharidan Shafie. "Unsteady MHD free convection flow of Casson fluid past over an oscillating vertical plate embedded in a porous medium." Engineering Science and Technology, an International Journal 18, no. 3 (2015): 309-317. https://doi.org/10.1016/j.jestch.2014.12.006
Khalid, Asma, Ilyas Khan, and Sharidan Shafie. "Exact solutions for unsteady free convection flow of Casson fluid over an oscillating vertical plate with constant wall temperature." In Abstract and Applied Analysis, vol. 2015. Hindawi, 2015. https://doi.org/10.1155/2015/946350
Khalid, Asma, Ilyas Khan, and Sharidan Shafie. "Unsteady boundary layer flow of a Casson fluid past an oscillating vertical plate with constant wall temperature." Malaysian Journal of Fundamental and Applied Sciences 11, no. 1 (2015). https://doi.org/10.11113/mjfas.v11n1.360
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, Arshad, Ilyas Khan, Asma Khalid, and Sharidan Shafie. "Effects of arbitrary shear stress on unsteady free convection flow of Casson fluid past a vertical plate." Results in physics 7 (2017): 3301-3306. https://doi.org/10.1016/j.rinp.2017.08.022
Kataria, HariR, and HarshadR Patel. "Heat and mass transfer in magnetohydrodynamic (MHD) Casson fluid flow past over an oscillating vertical plate embedded in porous medium with ramped wall temperature." Propulsion and Power Research 7, no. 3 (2018): 257-267. https://doi.org/10.1016/j.jppr.2018.07.003
Khalid, Asma, Ilyas Khan, and Sharidan Shafie. "Exact solutions for unsteady free convection flow of Casson fluid over an oscillating vertical plate with constant wall temperature." In Abstract and Applied Analysis, vol. 2015. Hindawi, 2015. https://doi.org/10.1155/2015/946350
Ewis, Karem Mahmoud. "Effects of Variable Thermal Conductivity and Grashof Number on Non-Darcian Natural Convection Flow of Viscoelastic Fluids with Non Linear Radiation and Dissipations." Journal of Advanced Research in Applied Sciences and Engineering Technology 22, no. 1 (2021): 69-80. https://doi.org/10.37934/araset.22.1.6980
Khan, Ilyas, Nehad Ali Shah, Asifa Tassaddiq, Norzieha Mustapha, and Seripah Awang Kechil. "Natural convection heat transfer in an oscillating vertical cylinder." PloS one 13, no. 1 (2018): e0188656. https://doi.org/10.1371/journal.pone.0188656
Ahmed, Najma, Nehad Ali Shah, and Dumitru Vieru. "Natural convection with damped thermal flux in a vertical circular cylinder." Chinese journal of physics 56, no. 2 (2018): 630-644. https://doi.org/10.1016/j.cjph.2018.02.007
Shah, Nehad Ali, Aziz Ullah Awan, Rabia Khan, Iskander Tlili, M. Umar Farooq, Bashir Salah, and Jae Dong Chung. "Free convection Hartmann flow of a viscous fluid with damped thermal transport through a cylindrical tube." Chinese Journal of Physics (2022). https://doi.org/10.1016/j.cjph.2021.09.019
Javaid, Maria, M. Imran, M. A. Imran, I. Khan, and K. S. Nisar. "Natural convection flow of a second grade fluid in an infinite vertical cylinder." Scientific Reports 10, no. 1 (2020): 1-11. https://doi.org/10.1038/s41598-020-64533-z
Ali, Farhad, Anees Imtiaz, Ilyas Khan, and Nadeem Ahmad Sheikh. "Flow of magnetic particles in blood with isothermal heating: A fractional model for two-phase flow." Journal of Magnetism and Magnetic Materials 456 (2018): 413-422. https://doi.org/10.1016/j.jmmm.2018.02.063
Ali, Farhad, Anees Imtiaz, Ilyas Khan, Nadeem Ahmad Sheikh, and Dennis Ling Chuan Ching. "Hemodynamic flow in a vertical cylinder with heat transfer: two-phase Caputo Fabrizio fractional model." Journal of Magnetics 23, no. 2 (2018): 179-191. https://doi.org/10.4283/JMAG.2018.23.2.179
Ali, Farhad, Nabeel Khan, Anees Imtiaz, Ilyas Khan, and Nadeem Ahmad Sheikh. "The impact of magnetohydrodynamics and heat transfer on the unsteady flow of Casson fluid in an oscillating cylinder via integral transform: A Caputo–Fabrizio fractional model." Pramana 93, no. 3 (2019): 1-12. https://doi.org/10.1007/s12043-019-1805-4
Imtiaz, Anees, Oi-Mean Foong, Aamina Aamina, Nabeel Khan, Farhad Ali, and Ilyas Khan. "Generalized model of blood flow in a vertical tube with suspension of gold nanomaterials: applications in the cancer therapy." Computers, Materials & Continua 65, no. 1 (2020): 171-192. https://doi.org/10.32604/cmc.2020.011397
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
Maiti, Subrata, Sachin Shaw, and G. C. Shit. "Fractional order model for thermochemical flow of blood with Dufour and Soret effects under magnetic and vibration environment." Colloids and Surfaces B: Biointerfaces 197 (2021): 111395. https://doi.org/10.1016/j.colsurfb.2020.111395
Maiti, Subrata, Sachin Shaw, and G. C. Shit. "Fractional order model of thermo-solutal and magnetic nanoparticles transport for drug delivery applications." Colloids and Surfaces B: Biointerfaces 203 (2021): 111754. https://doi.org/10.1016/j.colsurfb.2021.111754
Nubar, Yves. "Blood flow, slip, and viscometry." Biophysical Journal 11, no. 3 (1971): 252-264. https://doi.org/10.1016/S0006-3495(71)86212-4
Bhat, Ashwini, and Nagaraj N. Katagi. "Influence of Slip Velocity on Micropolar Fluid Through a Porous Channel: Using Keller-Box Method." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 66, no. 2 (2020): 49-64.
Reddy, Y. Dharmendar, Fateh Mebarek-Oudina, B. Shankar Goud, and A. I. Ismail. "Radiation, Velocity and Thermal Slips Effect Toward MHD Boundary Layer Flow Through Heat and Mass Transport of Williamson Nanofluid with Porous Medium." Arabian Journal for Science and Engineering (2022): 1-15. https://doi.org/10.1007/s13369-022-06825-2
Reddy, Nalivela Nagi, Yanala Dharmendar Reddy, Vempati Srinivasa Rao, B. Shankar Goud, and Kottakkaran Sooppy Nisar. "Multiple slip effects on steady MHD flow past a non-isothermal stretching surface in presence of Soret, Dufour with suction/injection." International Communications in Heat and Mass Transfer 134 (2022): 106024. https://doi.org/10.1016/j.icheatmasstransfer.2022.106024
Goud, B. Shankar. "Thermal radiation influences on MHD stagnation point stream over a stretching sheet with slip boundary conditions." International Journal of Thermofluid Science and Technology 7, no. 2 (2020). https://doi.org/10.36963/IJTST.2020070201
Yanala, Dharmendar Reddy, Anil Kumar Mella, Srinivasa Rao Vempati, and B. Shankar Goud. "Influence of slip condition on transient laminar flow over an infinite vertical plate with ramped temperature in the presence of chemical reaction and thermal radiation." Heat Transfer 50, no. 8 (2021): 7654-7671. https://doi.org/10.1002/htj.22247
Gudekote, Manjunatha, Rajashekhar Choudhari, Hanumesh Vaidya, and Kerehalli Vinayaka Prasad. "Peristaltic flow of Herschel-Bulkley fluid in an elastic tube with slip at porous walls." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 52, no. 1 (2018): 63-75.
Baliga, Divya, Manjunatha Gudekote, Rajashekhar Choudhari, Hanumesh Vaidya, and Kerehalli Vinayaka Prasad. "Influence of velocity and thermal slip on the peristaltic transport of a herschel-bulkley fluid through an inclined porous tube." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 56, no. 2 (2019): 195-210.
Ullah, Imran, Sharidan Shafie, and Ilyas Khan. "Effects of slip condition and Newtonian heating on MHD flow of Casson fluid over a nonlinearly stretching sheet saturated in a porous medium." Journal of King Saud University-Science 29, no. 2 (2017): 250-259. https://doi.org/10.1016/j.jksus.2016.05.003
Imran, Muhammad A., Shakila Sarwar, and Muhammad Imran. "Effects of slip on free convection flow of Casson fluid over an oscillating vertical plate." Boundary Value Problems 2016, no. 1 (2016): 1-11. https://doi.org/10.1186/s13661-016-0538-2
Saqib, Muhammad, Farhad Ali, Ilyas Khan, and Nadeem Ahmad Sheikh. "Heat and mass transfer phenomena in the flow of Casson fluid over an infinite oscillating plate in the presence of first-order chemical reaction and slip effect." Neural Computing and Applications 30, no. 7 (2018): 2159-2172. https://doi.org/10.1007/s00521-016-2810-x
Hayat, Tasawar, Muhammad Farooq, and A. Alsaedi. "Thermally stratified stagnation point flow of Casson fluid with slip conditions." International Journal of Numerical Methods for Heat & Fluid Flow (2015). https://doi.org/10.1108/HFF-05-2014-0145
El-Aziz, Abd, and Ahmed A. Afify. "Influences of slip velocity and induced magnetic field on MHD stagnation-point flow and heat transfer of Casson fluid over a stretching sheet." Mathematical Problems in Engineering 2018 (2018). https://doi.org/10.1155/2018/9402836
Jiang, Yuting, Haitao Qi, Huanying Xu, and Xiaoyun Jiang. "Transient electroosmotic slip flow of fractional Oldroyd-B fluids." Microfluidics and Nanofluidics 21, no. 1 (2017): 1-10. https://doi.org/10.1007/s10404-016-1843-x
Shah, Nehad Ali, Xiaoping Wang, Haitao Qi, Shaowei Wang, and Ahmad Hajizadeh. "Transient electro-osmotic slip flow of an oldroyd-B fluid with time-fractional Caputo-Fabrizio derivative." Journal of Applied and Computational Mechanics 5, no. 4 (2019): 779-790.
Padma, R., R. Tamil Selvi, and R. Ponalagusamy. "Effects of slip and magnetic field on the pulsatile flow of a Jeffrey fluid with magnetic nanoparticles in a stenosed artery." The European Physical Journal Plus 134, no. 5 (2019): 221. https://doi.org/10.1140/epjp/i2019-12538-9
Padma, R., R. Ponalagusamy, and R. Tamil Selvi. "Mathematical modeling of electro hydrodynamic non-Newtonian fluid flow through tapered arterial stenosis with periodic body acceleration and applied magnetic field." Applied Mathematics and Computation 362 (2019): 124453. https://doi.org/10.1016/j.amc.2019.05.024
