Shyam Sunder Nishad
Natural convection (laminar) in water filled in a long rectangular enclosure

Physical problem:
The side-walls of the enclosure are thermally insulated, while the top and the bottom ones are maintained at constant temperature, as shown in the figure below. The walls are stationary and impermeable. At time t=0, the bottom wall is heated uniformly and instantly to temperature T_hot. We need to simulate, what happens next, till steady state is achieved.
Task
To compute the velocity, temperature and vorticity fields for 2-D, laminar natural convection in the enclosure.

Assumptions
● Bottom and top walls remain at constant temperature.
● Side walls are insulated, and impermeable.
● Flow is incompressible, two-dimensional and laminar (newtonian).
The videos below can be downloaded from links below.
Ra = 1000, Pr = 7 ( 0.2 MB )
Ra = 3000, Pr = 7 ( 0.7 MB )

Notations:
Ra: Rayleigh number
Pr: Prandtl number


Problem Statement: Natural convection (laminar) in water filled in a long rectangular enclosure

Method used
● Non-dimensionalization of the equations,
● Stream function-vorticity approach,
● Gauss Seidel algorithm as the numerical solver

Results and discussion