Three-dimensional continuation study of convection in a tilted rectangular enclosure.

Area of Science:

• Fluid Dynamics and Heat Transfer
• Computational Physics

Background:

• Natural convection in enclosed cavities is fundamental to heat transfer phenomena.
• Understanding fluid behavior under varying geometric and thermal conditions is crucial for engineering applications.

Purpose of the Study:

• To investigate the impact of inclination on natural convection in a 3D rectangular cavity.
• To identify and characterize stable convective flow solutions as a function of Rayleigh number and inclination angle.

Main Methods:

• A continuation method based on a 3D spectral finite element code was employed.
• Bifurcation analysis was performed to map solution branches and stability.
• The study focused on a fluid with Prandtl number (Pr) of 1.

Main Results:

• Three distinct stable solutions were identified in the inclined cavity: longitudinal roll L- (aligned with inclination), longitudinal roll L+ (opposite to inclination), and oblique roll O± (perturbed transverse rolls).
• The domain of existence for these solutions was mapped in the Rayleigh number-inclination parameter space.
• The Nusselt number, a measure of heat transfer, was found to be maximized at a 49.55° inclination for the L- solution.

Conclusions:

• Cavity inclination introduces complex changes to natural convection, leading to multiple stable flow regimes.
• The L- longitudinal roll solution exhibits optimal heat transfer performance at a specific inclination angle.
• The study provides a comprehensive understanding of flow stability and heat transfer in tilted rectangular cavities.