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The energy storage features on natural convection in Casson fluids are investigated in this work using the finite element method. By measuring cylinders and wavy surfaces, we may examine flow patterns and the effectiveness of heat transmission systems. We study the variation of the mass and heat transfer rates as a function of the cylinder geometry. To approximately determine velocities and temperatures, the Ladyzhenskaya-Babuška—Brezzi (LBB)-stable element is employed. Following this discretization, the resulting discrete nonlinear system is linearized using Newton's method and subsequently solved using PARDISO. Fractional applications in Casson fluid analysis reveal insights into energy storage effects, employing finite element methods to explore flow patterns, heat transmission efficiency, and geometric variations while observing the impact of parameters such as Rayleigh, Hartmann, and Lewis numbers on fluid behavior and thermal properties. The preceding research has verified the accuracy of the numerical results. According to the results, concentration gradients and other modifications to liquids become more noticeable as the Rayleigh number grows. Convective heat transmission is reduced as the Ha is raised. When the Le grows, the deformation Nu avg and S h avg also increase. Reducing the beta makes the isotherms more stable and less affected by the motion of the fluid.
Majeed et al. (Fri,) studied this question.