### Journals Information

Mathematics and Statistics Vol. 9(6), pp. 867 - 881
DOI: 10.13189/ms.2021.090602
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## An Analytical Study for Caputo Fractional Derivative on Unsteady Casson Fluid with Thermal Radiation Effect

Ridhwan Reyaz , Ahmad Qushairi Mohamad *, Yeaou Jiann Lim , Muhammad Saqib , Zaiton Mat Isa , Sharidan Shafie
Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia

ABSTRACT

Studies on Casson fluid are essential in the development of the manufacturing and engineering fields since it is widely used there. Meanwhile, fractional derivative has been known to be a constructive paradox that can be beneficial in the future. In this study, the development fractional derivative on Casson fluid flow is investigated. A fractional Casson fluid model with effect of thermal radiation is derived together with momentum and energy equations. The Caputo definition of fractional derivative is used in the mathematical formulation. Casson fluid with constant wall temperature over an oscillating plate in the presence of thermal radiation is considered. Solutions were obtained by using Laplace transform and are presented in the form of Wright function. Graphical analysis on velocity and temperature profiles was conducted with variations in parametric values such as fractional parameter, Grashof number, Prandtl number and radiation parameter. Numerical computations were carried out to investigate behaviours of skin friction and Nusselt number. It is found that when the fractional parameter is increased, the velocity and temperature profiles will also increase. Existence of fractional parameter in both velocity and temperature profiles shows the transitional phenomenon of both profiles from an unsteady state to steady state, providing a new perspective on Casson fluid flow. An increment in both profiles is also observed when the thermal radiation parameter is increased. The present results are also validated with published results, and it is found that they are in agreement with each other.

KEYWORDS
Casson Fluid, Caputo Derivative, Thermal Radiation, Wright Function

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ridhwan Reyaz , Ahmad Qushairi Mohamad , Yeaou Jiann Lim , Muhammad Saqib , Zaiton Mat Isa , Sharidan Shafie , "An Analytical Study for Caputo Fractional Derivative on Unsteady Casson Fluid with Thermal Radiation Effect," Mathematics and Statistics, Vol. 9, No. 6, pp. 867 - 881, 2021. DOI: 10.13189/ms.2021.090602.

(b). APA Format:
Ridhwan Reyaz , Ahmad Qushairi Mohamad , Yeaou Jiann Lim , Muhammad Saqib , Zaiton Mat Isa , Sharidan Shafie (2021). An Analytical Study for Caputo Fractional Derivative on Unsteady Casson Fluid with Thermal Radiation Effect. Mathematics and Statistics, 9(6), 867 - 881. DOI: 10.13189/ms.2021.090602.