Numerical Investigation on Mode-Transition of Laminar Natural Convection in Inclined Enclosures with the Higher-Order Compact FDM

摘要

Using the technique described by first author [1], a fourth-order compact finite difference algorithm for the solution of two-dimensional incompressible laminar thermal flows using the vorticity-stream function formulation was developed in [2]. In the present work, this algorithm is applied to report a numerical study of natural convection and the associated mode-transition in a two-dimensional differentially heated inclined enclosure. To check the validity of the present high-order algorithm, buoyancy-driven flows in a square cavity with the benchmark solutions [3] were solved. The angle of inclination of cavity was varied from 0° to 90°. Enclosure is assumed to fill with a Boussinesq fluid with a Prandtl number of 0.71. For Rayleigh numbers from 10~3 to 10~5, a detailed numerical analysis is made for enclosures with overall aspect ratios 4. Air-filled (Pr = 0.71) enclosures with aspect ratios As = 4 is chosen as the flow model to examine the influences of the inclination at various Rayleigh numbers. The present numerical results on coarser mesh size are compared with ones reported on finer mesh size [4]. The comparison shows quite good agreement in either maximum velocities or mean Nusselt numbers.