The influence of surrounding fluid on a large array of oscillators is important to study for applications in fields such as medicine, biology, and atomic force microscopy. In the present study, we investigate a large array of cantilever beams oscillating in an unbounded fluid to better understand the fluid dynamic behavior. The two-dimensional boundary integral method is applied to analyze a large array of cantilever oscillators using an analytical solution approach for the unsteady Stokes and continuity equations. We analyze array sizes from 5 to 50 beams by comparing hydrodynamic transverse force and velocity profiles for two different velocity configurations. Including the interactions of neighbor and non-neighbor members leads to distinct array effects. With an increase in the number of oscillators in an array, the array effect influences the overall dynamics. Furthermore, to justify the influence of an array effect, the hydrodynamic loading is compared to the same and varying array surface area of different array sizes. Our analysis and new findings strengthen our hypothesis that the predictions of existing knowledge obtained from small-size arrays and coupled oscillators cannot readily inform dynamic predictions of large-size arrays. The underlying reason being the additional array effect(s) which are not present in a small-size array. The novelty of this paper is the ability to model such large arrays and investigate the array effect in an unbounded fluid.

A new design of immersion heater is proposed for common household use and is checked for stress induced due to heating and the corresponding factor of safety (FOS). Temperature distribution with time is obtained by building a finite element model of the simplified heater geometry (body) while considering conduction and convection due to buoyancy effect. For realistic results, a two-step analysis is done. Firstly, the temperature distribution with time, is calculated in Solidworks® Flow Simulation software by considering the conduction in heater body and convection in the surrounding water. Secondly, the calculated temperatures are exported into Solidworks structural simulation and thermal stresses are calculated. An effort is made to study the effect of purely thermal stresses on the heater body as it is heated under 3000 W power and visualize the flow trajectory of fluid particles as it is heated. The results are used to assess the stress, strain, and FOS of the design and to finalize its geometry. It is concluded in the study that buoyancy effects and flow trajectory of fluid particles is paramount in determining the thermal stresses in a heater design.

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