Pasa Analytics | Heat Transfer - Advanced Numerical Simulation

The video sequence below shows the daily temperature evolution in a room bounded by two concrete walls.

The room is filled with air, initially at 0°C. The external surfaces of the walls are subjected to daily temperature variations simulating solar exposure. The left wall is directly exposed to sunlight, while the right wall is in the shade, resulting in lower temperature fluctuations and a lower average temperature (20°C vs 30°C for the sun-exposed side).

Although simplified (single spatial dimension, conduction only through concrete and air), this model provides valuable insights. It shows progressive temperature stabilization in the room toward distance-weighted average external temperatures.

For a more complete modeling, a 2D model was implemented with the same physics as before (pure conduction).

The visualization shows temperature evolution with a color scale (blue for cold, red for hot). Daily variations in the walls and progressive thermal wave penetration into the room are clearly visible.

This modeling remains limited as it doesn't account for natural convection: warm air, being less dense, should rise, creating convective movements that significantly alter heat transfer.

The goal of this advanced modeling is to simulate complete thermal transfers through room walls, including natural convection phenomena in the air.

Geometric Configuration

• Two-dimensional room: 5 m × 3 m
• Lateral walls and slab: concrete
• Ceiling: wood
• Boundary conditions: variable temperatures simulating daily solar exposure

Modeled Physics

The model combines:

• Conduction in solid materials (Fourier's law)
• Natural convection in air (Navier-Stokes equations for incompressible fluid)
• Thermal coupling at air/solid interfaces

The logarithmic scale allows simultaneous visualization of temperatures in walls (higher) and in air (lower).