# Exact Solution of Fractional Convective Casson Fluid Through an Accelerated Plate

## Authors

• Muhammad Nazirul Shahrim Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia
• Ahmad Qushairi Mohamad Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia
• Lim Yeou Jiann Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia
• Muhamad Najib Zakaria Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia
• Sharidan Shafie Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia
• Zulkhibri Ismail Centre for Mathematical Sciences, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Kuantan Pahang, Malaysia
• Abdul Rahman Mohd Kasim Centre for Mathematical Sciences, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Kuantan Pahang, Malaysia

## Keywords:

Casson fluid, Caputo derivative, Laplace transform, Wright function, Heat transfer

## Abstract

Fractional derivative has perfectly adopted to model few physical phenomena such as viscoelasticity of coiling polymers, traffic construction, fluid dynamics and electrical networks. However, the application of the fractional derivatives for describing the physical characteristics of non-Newtonian fluid over a moving plate is still rare. In the present study, the effect of the Caputo fractional derivative on the Casson fluid flow which is induced by an accelerated plate is analytically analysed. The governing equations are initially transformed into dimensionless expressions by using suitable dimensionless variables. Then the Laplace transform method is utilized to calculate the exact solutions for the fractional governing partial differential equations. The obtained solutions are validated by comparing the results for specific case with the existing solutions in the literature. The impact of fractional parameter, Prandtl number, and time on the velocity and temperature profiles are graphically showed and discussed. The results depict that the temperature and velocity increase with the increment of fractional parameter and time. Interestingly, the velocity decreases at region near the plate but is enhanced at the area far away from the plate when the Casson fluid parameter is increased. This study is essential in understanding the factional non-Newtonian fluid flows which is more realistic in nature.

## References

Imran, M. A., Shakila Sarwar, M. Abdullah, and I. Khan. "An analysis of the semi-analytic solutions of a viscous fluid with old and new definitions of fractional derivatives." Chinese journal of physics 56, no. 5 (2018): 1853-1871. https://doi.org/10.1016/j.cjph.2018.08.017.

Imran, M. A., Nehad Ali Shah, Ilyas Khan, and Maryam Aleem. "Applications of non-integer Caputo time fractional derivatives to natural convection flow subject to arbitrary velocity and Newtonian heating." Neural Computing and Applications 30, no. 5 (2018): 1589-1599. https://doi.org/10.1007/s00521-016-2741-6.

Imran, M. A., Maryam Aleem, M. B. Riaz, Rizwan Ali, and Ilyas Khan. "A comprehensive report on convective flow of fractional (ABC) and (CF) MHD viscous fluid subject to generalized boundary conditions." Chaos, Solitons & Fractals 118 (2019): 274-289. https://doi.org/10.1016/j.chaos.2018.12.001.

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.

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/https://doi.org/10.1140/epjp/i2016-16181-8.

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.

Wahid, Nur Syahirah, Mohd Ezad Hafidz Hafidzuddin, Norihan Md Arifin, Mustafa Turkyilmazoglu, and Nor Aliza Abd Rahmin. "Magnetohydrodynamic (MHD) Slip Darcy Flow of Viscoelastic Fluid Over A Stretching Sheet and Heat Transfer with Thermal Radiation and Viscous Dissipation." CFD Letters 12, no. 1 (2020): 1-12.

Ewis, Karem Mahmoud. “Analytical Solution of Modified Bingham Fluid Flow through Parallel Plates Channel Subjected to Forchheimer Medium and Hall Current Using Linearized Differential Transformation Method.” Journal of Advanced Research in Numerical Heat Transfer 4, no. 1 (2021): 14–31.

Ghiasi, Emran Khoshrouye, and Reza Saleh. “Analytical and Numerical Solutions to the 2D Sakiadis Flow of Casson Fluid with Cross Diffusion, Inclined Magnetic Force, Viscous Dissipation and Thermal Radiation Based on Buongiorno’s Mathematical Model.” CFD Letters 11, no. 1 (2019): 40–54.

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.

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.

Mahanthesh, B, T Brizlyn, SabirAli Shehzad, and B J Gireesha. “Nonlinear Thermo-Solutal Convective Flow of Casson Fluid over an Oscillating Plate Due to Non-Coaxial Rotation with Quadratic Density Fluctuation Exact Solutions.” Multidiscipline Modeling in Materials and Structures 15, no. 4 (2018): 818–842. https://doi.org/10.1108/MMMS-06-2018-0124.

Nadeem, S., Rizwan Ul Haq, and C. Lee. “MHD Flow of a Casson Fluid over an Exponentially Shrinking Sheet.” Scientia Iranica 19, no. 6 (2012): 1550–1553. https://doi.org/10.1016/j.scient.2012.10.021.

Nadeem, S., Rizwan Ul Haq, Noreen Sher Akbar, and Z. H. Khan. “MHD Three-Dimensional Casson Fluid Flow Past a Porous Linearly Stretching Sheet.” Alexandria Engineering Journal 52, no. 4 (2013): 577–882. https://doi.org/10.1016/j.aej.2013.08.005.

Khan, Dolat, Arshad Khan, Ilyas Khan, Farhad Ali, Faizan ul Karim, and I. Tlili. “Effects of Relative Magnetic Field, Chemical Reaction, Heat Generation and Newtonian Heating on Convection Flow of Casson Fluid over a Moving Vertical Plate Embedded in a Porous Medium.” Scientific Reports 9, no. 1 (2019): 1–18. https://doi.org/10.1038/s41598-018-36243-0.

Mohamad, Ahmad Qushairi, Nurul Aini Jaafar, Sharidan Shafie, Zulkhibri Ismail, and Muhammad Qasim. "Theoretical study on rotating casson fluid in moving channel disk." In Journal of Physics: Conference Series, vol. 1366, no. 1, p. 012039. IOP Publishing, 2019. https://doi.org/10.1088/1742-6596/1366/1/012039.

Alwawi, Firas A., Hamzeh T. Alkasasbeh, A. M. Rashad, and Ruwaidiah Idris. "MHD natural convection of Sodium Alginate Casson nanofluid over a solid sphere." Results in physics 16 (2020): 102818. https://doi.org/10.1016/j.rinp.2019.102818.

Kumar, K Anantha, 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.

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.

2021-07-02

## How to Cite

Muhammad Nazirul Shahrim, Ahmad Qushairi Mohamad, Lim Yeou Jiann, Muhamad Najib Zakaria, Sharidan Shafie, Zulkhibri Ismail, & Abdul Rahman Mohd Kasim. (2021). Exact Solution of Fractional Convective Casson Fluid Through an Accelerated Plate. CFD Letters, 13(6), 15–25. https://doi.org/10.37934/cfdl.13.6.1525

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