8.9 Heating a room
A simulation of heating a room demonstrates natural convection driven by buoyancy forces. An idealised, ground floor room is presented below, with external glass doors and sloping roof, and internal walls and ceiling.
A heater is located along one side wall, below
the point where the roof and ceiling meet. The aim of the
simulation was to calculate the room temperature with the heater
running at 1kW, when the ambient external temperature 
.
The thermal boundary conditions were specified as
follows: floor temperature 
; ceiling 
, representing the first
floor temperature; insulated walls, with 
, see
Sec. 4.17
; glass doors and
roof with a heat flux according to Eq. (4.30
) using 
and 
,
respectively.
The mesh contained 350,000 hexahedral cells with
grading that gave a cell height of approximately 
along the walls.
Transport properties for air, 
and 
, were used. Turbulence
was modelled using the 
SST model described in Sec. 7.11
, with initial levels
of 
and 
. The near-wall cell centres corresponded to 
, so the continuous
wall function from Sec. 7.6
and thermal
wall function from Sec. 7.14
were applied at
the boundaries.
The simulation used the transient solution
algorithm in Sec. 5.19
, including the buoyancy force
in
Eq. (2.67
), with
.
The condition 
was applied at all boundaries, combined with the flux
calculation in Eq. (5.20
).
The variations in 
within 
were calculated
using the ideal gas Eq. (2.55
) using 
.
The simulation ran with a time step
.
The flow is highly unsteady, but at 
the heat losses
through the boundaries oscillate about the mean levels indicated
above.
Between the ground and 2m, occupants experience a
variation in 
. In the space adjacent to the roof and ceiling, the
higher 
generates significant heat losses, especially to the outside
through the roof.
