Fractional derivatives have been proven to showcase a spectrum of solutions that is useful in the fields of engineering, medical, and manufacturing sciences. Studies on the application of fractional derivatives on fluid flow are relatively new, especially in analytical studies. Thus, geometrical representations for fractional derivatives in the mechanics of fluid flows are yet to be discovered. Nonetheless, theoretical studies will be useful in facilitating future experimental studies. Therefore, the aim of this study is to showcase an analytical solution on the impact of the Caputo-Fabrizio fractional derivative for a magnethohydrodynamic (MHD) Casson fluid flow with thermal radiation and chemical reaction. Analytical solutions are obtained via Laplace transform through compound functions. The obtained solutions are first verified, then analysed. It is observed from the study that variations in the fractional derivative parameter, α, exhibits a transitional behaviour of fluid between unsteady state and steady state. Numerical analyses on skin friction, Nusselt number, and Sherwood number were also analysed. Behaviour of these three properties were in agreement of that from past literature.
With the advancement of nuclear energy as one of the top clean energy sources, studies on radiation effects are becoming more popular. Radiation absorption is an exothermic phenomenon where radiative energy is released to the surrounding environment. This occurrence can be seen widely in the field of manufacturing, biology, medicine and fluid mechanics. In this study, the impact of radiation absorption of fluid flow over a vertical plate that is exponentially accelerating will be investigated. Heat and mass transfer flowing vertically over the
Driven by technological advancement, the Riga plate can be seen as a key feature in developing the engineering world. As such, this study aims to investigate the effects of an accelerating semi-infinite Riga plate over a convective flow of MHD Casson fluid incorporated with the Caputo fractional derivative. The obtained governing PDEs are converted in dimensionless form and reduced to systems of ODEs via Laplace transform. Zakian's method of inverse Laplace transform is then utilised to generate graphical results in the time domain. Variations of parameter such as Casson, modified Hartmann number, Grashof number, magnetic parameter and fractional parameters are investigated for velocity profiles. Skin friction coefficient is also calculated and presented numerically. Study shows that Riga plate aids in fluid flow, hence increasing its velocity.
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
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