The Investigation of the Riemann-Liouville Fractional Operator on Natural Convective Fluid Flow in a Vertical Cylindrical Material with Variable Viscosity
DOI:
https://doi.org/10.62054/ijdm/0302.10Abstract
This research analyzes the effect of the Riemann-Liouville fractional operator on the natural convective fluid motion through a vertical cylindrical body of a material with temperature-dependent fluid viscosity. The conventional momentum and energy equations get revised using fractional derivatives of $\alpha$ order ($0<\alpha\le 1$), implemented in the Riemann-Liouville context. Solutions for the equations of momentum and energy will be derived using the Laplace transform in addition to the generalized Mittag-Leffler function. The different distributions of velocity and temperature, caused by $\alpha$, the fractional order viscosity parameter, and $\gamma$, the variable viscosity parameter, is considered by this study in terms of the various solved equations. Graphically, the results are displayed and compared with the classical integer order case ($\alpha=1$). The study finds that the fractional derivative implement memory effects, causing a delay in the development of flow, while variable viscosity influenced the velocity magnitude. The analytical and numerical solutions agree with each.
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