Heat transfer engineering is significant in many applications, especially in buoyancy natural convection in concentric and eccentric cavities. The biggest practical challenges, in this context, are capturing the self-natural flow, estimating the mixing performance, and determining what parameters affect the temperature distribution in the cavity. In this paper, we focus on the improvement of a mathematical model, in order to enhance the accuracy of the solution, by investigating a new source term in the SST k−ω turbulence model based on the finite volume technique. The commercial numerical simulation software ANSYS Fluent 2021R1 is implemented to validate the accuracy. A concentric cavity was chosen for validation, the obtained temperature profiles at θ=0∘, θ=30∘, θ=60∘, θ=90∘, θ=120∘, θ=150∘, and θ=180∘ were compared with previous experimental data. We applied this model to four eccentric rotating scenarios, including inner counterclockwise rotation, outer counterclockwise rotation, inner–outer clockwise rotation, and inner clockwise–outer counterclockwise rotation. The numerical simulation results reveal that the new source term in the momentum equation can produce superior results in the concentric test-case. The proposed mathematical model can describe the heat transfer under the eccentric co-rotation scenario well. Furthermore, the results for eccentric cases confirm that the rotational direction affects the mixing temperature by generating a large vortex in the cavity, which increases the temperature mixing performance.

In the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

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