This paper examines the process of instability of natural convection in an inclined cavity based on numerical simulations. The energy gradient method is employed to analyze the physics of the flow instability in natural convection. It is found that the maximum value of the energy gradient function in the flow field correlates well with the location where flow instability occurs. Meanwhile, the effects of the flow time, the plate length, and the inclination angle on the instability have also been discussed. It is observed that the locations of instabilities migrate right as the flow time increased. With the increase of plate length, the onset time of the instability on the top wall of the cavity decreases gradually and the locations of instabilities move to the right side. Furthermore, the locations of instability move left with the increase of the inclination angle in a certain range. However, these positions move right as the accumulation of the heat flux is restrained in the lower left corner of the cavity once the inclination angle exceeds a certain range.

This paper numerically investigates the physical mechanism of flow instability and heat transfer of natural convection in a cavity with thin fin(s). The left and the right walls of the cavity are differentially heated. The cavity is given an initial temperature, and the thin fin(s) is fixed on the hot wall in order to control the heat transfer. The finite volume method and the SIMPLE algorithm are used to simulate the flow. Distributions of the temperature, the pressure, the velocity and the total pressure are obtained. Then, the energy gradient theory is employed to study the physical mechanism of flow instability and the effect of the thin fin(s) on heat transfer. Based on the energy gradient theory, the energy gradient function K represents the characteristic of flow instability. It is observed from the simulation results that the positions where instabilities take place in the temperature contours accord well with those of higher K value, which demonstrates that the energy gradient theory reveals the physical mechanism of flow instability. Furthermore, the effects of the fin length, the fin position, the fin number, and Ra on heat transfer are investigated. It is found that the effect of the fin length on heat transfer is negligible when Ra is relatively high. When there is only one fin, the most efficient heat transfer rate is achieved as the fin is fixed at the middle height of the cavity. The fin blocks heat transfer with a relatively small Ra, but the fin enhances heat transfer with a relatively large Ra. The fin(s) enhances heat transfer gradually with the increase of Ra under the influence of the thin fin(s). Finally, a linear correlation of Kmax with Ra is obtained which reveals the physical mechanism of natural convection from different approaches. Thin fin(s) K h T temperature of the hot wall K u, v velocity components in x, y directions respectively m s -1  m v amplitude of the disturbance of velocity in transverse direction m s -1 x, y coordinates m Greek symbols  coefficient of thermal expansion (10 -6 )K -1  thermal conductivity W m -1 K -1  dynamic viscosity Nm -2 s  kinematic viscosity m² s -1 3  density of fluid kg m -3 d  frequency of the disturbance rad s -1 E  energy difference along transverse direction J m -3 H  energy difference along streamwise direction J m -3 T  temperature difference K x  grid mesh sizes m

This paper numerically investigates the thermal flow and heat transfer by natural convection in a cavity fixed with a fin array. The computational domain consists of both solid (copper) and fluid (air) areas. The finite volume method and the SIMPLE scheme are used to simulate the steady flow in the domain. Based on the numerical results, the energy gradient function of the energy gradient theory is calculated. It is observed from contours of the temperature and energy gradient function that the position where thermal instability takes place correlates well with the region of large values, which demonstrates that the energy gradient method reveals the physical mechanism of the flow instability. Furthermore, the effects of the fin height, the fin number, and the fin shape on the heat transfer rate are also investigated. It is found that the thermal performance of the fin array is determined by the combined effect of the fin space and fin height. It is also observed that the effect of fin shape on heat transfer is insignificant.

The periodically fully developed laminar heat transfer and pressure drop of arrays with nonuniform plate length aligned at an angle (25 deg) to air direction have been investigated by numerical analysis in the Reynolds number range of 50-1700. The body-fitted coordinate system generated by the multisurface method was adopted to retain the corresponding periodic relation of the lines in physical and computational domains. The computations were carried out just in one cycle. Numerical results show that both the heat transfer and pressure drop increase with the increase in the length ratio of the long plate to the short plate, and decrease with the decrease in the ratio of transverse pitch to the longitudinal pitch. The numerical results exhibit good agreement with available experimental data.

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