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.