Convection patterns in end-heated inclined enclosures

Area of Science:

• Fluid Dynamics
• Heat Transfer
• Conjugate Heat Transfer

Background:

• Natural convection in enclosed cavities is crucial for various engineering applications.
• Understanding flow stability in inclined systems is complex due to combined effects of buoyancy and inclination.

Purpose of the Study:

• To theoretically and numerically investigate natural convection patterns in inclined, side-heated rectangular boxes.
• To characterize convection patterns, focusing on flow instabilities across a wide range of Prandtl numbers and inclinations.
• To analyze the influence of inclination and confinement on flow stability and heat transfer mechanisms.

Main Methods:

• Linear stability analysis of the basic steady unicellular flow.
• Theoretical determination of the boundary layer regime (BLR) frontier.
• Numerical calculations in two- and three-dimensional enclosures.

Main Results:

• Onset of flow instabilities depends on the core Rayleigh number and is influenced by Prandtl number and inclination angle.
• Core-flow instabilities are observed for Prandtl numbers less than or equal to 1; boundary layer instabilities dominate at higher Prandtl numbers.
• Inclination suppresses stationary thermal modes and alters oscillatory longitudinal instability properties, with an analytical frequency relationship derived.

Conclusions:

• Confinement effects can stabilize the core flow, especially when the boundary layer regime is reached.
• Inclination introduces complex couplings between momentum and temperature fields, leading to unique instability mechanisms.
• The study provides a comprehensive stability diagram and theoretical criteria for predicting flow behavior in inclined cavities.