# Numerical Study of Mixed Convection and Heat Transfer in Arc-Shaped Cavity with Inner Heat Sources
###### Abstract  
The mixed convection and heat transfer in enclosures with inner heat sources widely exist in building ventilation, cooling of nuclear reactors and cooling of electronic components. In this study, the heat transfer characteristics of mixed convection in an open arc-shaped cavity with double heat sources under the condition of bottom heating and top wall cooling are studied by two-dimensional numerical simulation using ANSYS FLUENT. The influence of the Reynolds number on flow structures, transient characteristics and heat transfer characteristics in the arc cavity was studied by changing inlet wind speed. As the Reynolds number changes from 2.19 \(\times\) 10\({}^{5}\) to 4.38 \(\times\) 10\({}^{7}\), the flow in the fully developed stage will evolve from turbulent flow to periodic flow and then to steady state flow. In this study, the critical Reynolds number intervals for three different flow states are given. The increase in the Reynolds number enhances the heat convection in the cavity. The difference between heat convection and heat conduction is increased, which has a linear relationship with the Reynolds number. As the Reynolds number increases, the heat removal capacity in the middle region of the double heat sources is not always enhanced, which is due to the sudden change in flow structure and flow state around Re = 1.18 \(\times\) 10\({}^{7}\). arc-shaped cavity; mixed convection; Re; flow transition; heat transfer +
Footnote †: journal: Applied Sciences
shapes [2; 3; 4; 5]. As a relatively economical and convenient means, numerical simulation has been widely used in recent years. [PERSON] [6] studied natural convection in an isosceles triangle cavity by combining numerical simulation with flow visualization experiment and obtained the influence rule of aspect ratio and Grashof number on flow bifurcation. [PERSON] et al. [7] conducted a three-dimensional numerical simulation for a closed square cavity with external cooling and internal heat source, and they found that the heat transfer increased significantly with the increase in Rayleigh number. When the Rayleigh number was \(10^{7}\), the optimal heat transfer effect was achieved. With the expansion of application fields, some scholars have extended the types and states of fluids in recent years [8; 9]. Although the method of the model test has operational limitations and equipment requirements, as the most authentic and intuitive method, it has been applied in a large number of studies, including the smoke flow method, schlieren experiment and interference imaging. [PERSON] [10] first used the interference imaging method to display the flow and temperature distribution in the cavity in 1960, and the schlieren experiment is relatively simple and easy to operate. It has been widely used in subsequent studies with the development of PIV technology [11; 12; 13]. The study of mixed convection in a cavity is not as significant as that of natural convection, and its development started late. The research either focuses on the discussion of the wind environment and thermal comfort inside the long-span structure, which focuses on the evaluation scheme for the actual project, or the theoretical analysis of the flow structure and heat transfer characteristics in the micro-scale model. The first part of the study mainly used a combination of numerical simulation and field measurement. For example, [PERSON] et al. [14] used wind tunnel tests and computational fluid dynamics (CFDs) simulation to study the active chimney effect to enhance natural ventilation, considering the design factors including the size and location of the chimney. [PERSON] et al. [15] used the wind tunnel test and CFDs to study the natural ventilation and dust suppression effect of coal sheds with porous wind walls under the action of wind. By estimating the ventilation volume and dust suppression rate, the dust suppression effect of coal sheds with different gable walls was quantified. The latter part is mainly analyzed by numerical simulation [16; 17; 18; 19; 20].