Free Convection Caputo-Fabrizio Casson Blood Flow in the Cylinder with Slip Velocity

Authors

  • Wan Faezah Wan Azmi Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Ahmad Qushairi Mohamad Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Lim Yeou Jiann Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Sharidan Shafie Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

DOI:

https://doi.org/10.37934/cfdl.15.3.3547

Keywords:

Casson Fluid, Caputo-Fabrizio, Slip Velocity, Free Convection, Finite Hankel Transform

Abstract

Recently, fluid with fractional-order derivative model attracted many researchers to further study compared with the classical fluid mode since it is more precise and realistic. To imitate the applications of blood flow in narrow arteries, researchers focused on the fractional Casson fluid flow in the cylinder. However, most researchers solved the problems numerically and without considering the slip effect at the boundary. Thus, obtaining solutions analytically to the unsteady fractional Casson fluid flow in the slip cylinder with free convection is the goal of this study. The Caputo-Fabrizio fractional derivative approach is utilized to model this problem. By joining the approach of the Laplace transform and finite Hankel transform, the fractional governing equations are solved, and analytical solutions to the velocity and temperature profiles are gained. The fluid velocity rises as the slip velocity and Grashof number increase and it declines with the increment of the Casson parameter and Prandtl number. Increasing the fractional parameter will result in an increase in fluid velocity and temperature for a large time interval. The slip velocity effect influenced fluid flow, especially at the cylinder’s wall. These findings are beneficial to explore the more fractional-order derivative model and for studying the problems in biomedical engineering.

Downloads

Download data is not yet available.

Author Biographies

Wan Faezah Wan Azmi, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

ahmadqushairi@utm.my

Ahmad Qushairi Mohamad, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

ahmadqushairi@utm.my

Lim Yeou Jiann, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

ahmadqushairi@utm.my

Sharidan Shafie, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

ahmadqushairi@utm.my

References

Zokri, Syazwani Mohd, Nur Syamilah Arifin, Abdul Rahman Mohd Kasim, and Mohd Zuki Salleh. "Free convection boundary layer flow of Jeffrey nanofluid on a horizontal circular cylinder with viscous dissipation effect." Journal of Advanced Research in Micro and Nano Engineering 1, no. 1 (2020): 1-14.

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

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

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.2020.09.032

Abdelhameed, Tarek N. "Entropy generation analysis for MHD flow of water past an accelerated plate." Scientific Reports 11, no. 1 (2021): 1-11. https://doi.org/10.1038/s41598-021-89744-w

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.

Alderman, N. J. "Non-Newtonian fluids: guide to classification and characteristics." London: ESDU (1997).

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

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

Mohamed, Muhammad Khairul Anuar, Siti Hanani Mat Yasin, and Mohd Zuki Salleh. "Slip Effects on MHD Boundary Layer Flow over a Flat Plate in Casson Ferrofluid." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 88, no. 1 (2021): 49-57. https://doi.org/10.37934/arfmts.88.1.4957

Qushairi, Mohamad Ahmad, Jiann Lim Yeou, Sharidan Shafie, Ilyas Khan, and Zulkhibri Ismail. "Exact solution for unsteady free convection flow of Casson fluid in vertical channel." In MATEC Web of Conferences, vol. 189, p. 01007. EDP Sciences, 2018. https://doi.org/10.1051/matecconf/201818901007

Azmi, Wan Faezah Wan, Ahmad Qushairi Mohamad, Yeak Su Hoe, Zaiton Mat Isa, and Sharidan Shafie. "Effects of Magnetohydrodynamics and Heat Transfer in Casson Fluid Through a Channel." Malaysian Journal of Fundamental and Applied Sciences 17, no. 4 (2021): 416-429. https://doi.org/10.11113/mjfas.v17n4.2068

Rao, S. Ramalingeswara, G. Vidyasagar, and G. V. S. R. Deekshitulu. "Unsteady MHD free convection Casson fluid flow past an exponentially accelerated infinite vertical porous plate through porous medium in the presence of radiation absorption with heat generation/absorption." Materials Today: Proceedings 42 (2021): 1608-1616. https://doi.org/10.1016/j.matpr.2020.07.554

Ali, Farhad, Salman Yousaf, Ilyas Khan, and Nadeem Ahmad Sheikh. "A new idea of Atangana-Baleanu time fractional derivatives to blood flow with magnetics particles in a circular cylinder: two phase flow model." Journal of Magnetism and Magnetic Materials 486 (2019): 165282. https://doi.org/10.1016/j.jmmm.2019.165282

Kumar, Gaurav, and S. M. K. Rizvi. "Casson fluid flow past on vertical cylinder in the presence of chemical reaction and magnetic field." Applications and Applied Mathematics: An International Journal (AAM) 16, no. 1 (2021): 28.

Shaikh, Amjad, Asifa Tassaddiq, Kottakkaran Sooppy Nisar, and Dumitru Baleanu. "Analysis of differential equations involving Caputo–Fabrizio fractional operator and its applications to reaction–diffusion equations." Advances in Difference Equations 2019, no. 1 (2019): 1-14. https://doi.org/10.1186/s13662-019-2115-3

Ross, Bertram. "A brief history and exposition of the fundamental theory of fractional calculus." Fractional calculus and its applications (1975): 1-36. https://doi.org/10.1007/BFb0067096

Ramzan, Muhammad, Zaib Un Nisa, Ahmad Shafique, and Mudassar Nazar. "Slip and Thermo Diffusion Effects on the Flow Over an Inclined Plate." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 94, no. 2 (2022): 13-28. https://doi.org/10.37934/arfmts.94.2.1328

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

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.

Jamil, Dzuliana Fatin, Salman Saleem, Rozaini Roslan, Fahad S. Al-Mubaddel, Mohammad Rahimi-Gorji, Alibek Issakhov, and Salah Ud Din. "Analysis of non-Newtonian magnetic Casson blood flow in an inclined stenosed artery using Caputo-Fabrizio fractional derivatives." Computer Methods and Programs in Biomedicine 203 (2021): 106044. https://doi.org/10.1016/j.cmpb.2021.106044

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

Rao, I. J., and K. R. Rajagopal. "The effect of the slip boundary condition on the flow of fluids in a channel." Acta Mechanica 135, no. 3 (1999): 113-126. https://doi.org/10.1007/BF01305747

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

Rozeli, Nurliyana Syamira, Ahmad Nazri Mohd Som, Norihan Md Arifin, Fadzilah Md Ali, and Aniza Abd Ghani. "Double Stratified MHD Stagnation Point Slip Flow Over a Permeable Shrinking/Stretching Surface in A Porous Medium." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 90, no. 2 (2022): 64-72. https://doi.org/10.37934/arfmts.90.2.6472

Noor, Nur Azlina Mat, Mohd Ariff Admon, and Sharidan Shafie. "Unsteady MHD Squeezing Flow of Casson Fluid Over Horizontal Channel in Presence of Chemical Reaction." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 92, no. 2 (2022): 49-60. https://doi.org/10.37934/arfmts.92.2.4960

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

Jalil, M., and W. Iqbal. "Numerical analysis of suction and blowing effect on boundary layer slip flow of Casson fluid along with permeable exponentially stretching cylinder." AIP Advances 11, no. 3 (2021): 035304. https://doi.org/10.1063/5.0042314

Azmi, Wan Faezah Wan, Ahmad Qushairi Mohamad, Lim Yeou Jiann, and Sharidan Shafie. "Analytical Solution of Unsteady Casson Fluid Flow Through a Vertical Cylinder with Slip Velocity Effect." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 87, no. 1 (2021): 68-75. https://doi.org/10.37934/arfmts.87.1.6875

Azmi, Wan Faezah Wan, Ahmad Qushairi Mohamad, Lim Yeou Jiann, and Sharidan Shafie. "UNSTEADY MHD CASSON FLUID FLOW IN A VERTICAL CYLINDER WITH POROSITY AND SLIP VELOCITY EFFECTS." In e-Proceedings of the 5 th International Conference on Computing, Mathematics and Statistics (iCMS 2021), p. 60. 2021. https://doi.org/10.37934/arfmts.87.1.6875

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, 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

Downloads

Published

2023-02-03

Issue

Section

Articles

Most read articles by the same author(s)