Characterization of natural convection in a circular cavity with flexible fin subjected to sinusoidal thermal loading

This problem simulates engineering problems that humans face in practical life such as circulating fluid in indoor novel enclosure and dry (or steam) thermal sterilization of medical equipment. The investigation focuses on a circular cavity heated and cooled by arched walls and incorporating a flexible fin fixed at the bottom point of the enclosure. The new concept explores the impact of the oscillatory variation of a heat source attached to the free end of the fin, following a sinusoidal pattern. We utilize the Galerkin finite element method to solve this dimensionless nonlinear problem. To ensure the reliability of the numerical results, validation against experimental data is conducted. The various parameters considered are: the angular frequency F (1–4), the amplitude of hot spot of the fin tip A (0.1–0.25), the width of the oscillating fin B (0.01–0.025) and the length of the oscillating fin L (0.01–0.1). The left wall heat source is investigated with three arced lengths: θ (π/3, 2π/3, π). These parameters are studied concerning the average Nusselt number, isotherms, and streamline patterns. The results indicate that the average Nusselt number elevates when the left heat source expands to occupy a larger segment of the left part of the circular cavity, where for an angle equal to π, the heat transfer increases by 81% compared to a heat source occupying only π/3. However, it dwindles when the amplitude of the tip source increases. Furthermore, higher angular frequencies stimulate stronger convection flows. It is also found that the length of the oscillating fin should not go be excessive.