Comparison of hyperbolic and parabolic equations modelling buoyancy driven flow in a square cavity

Abstract

The effects of a hyperbolic and parabolic heat transfer equation on buoyancy-driven flow in a square cavity are studied. Boundary conditions where the bottom wall is hot and the side and top walls are cold are investigated. The case when the bottom and sidewalls are warm and the top wall is cold is also examined. Simulation of the flow is done using the finite element approach. An equation for the heat function is determined. The finite difference method is used to determine solutions to the heat transfer equation. We find that a hyperbolic heat transfer equation increases the magnitude of vorticity, stream function, and heat function. This suggests that hyperbolic heat transfer equations have stronger circulation and achieve a stable state sooner than parabolic heat transfer equations.

Keywords

• Buoyancy-driven flow
• Square cavity
• Hyperbolic heat transfer equation
• Parabolic heat transfer equation
• Finite elements