Building Model

We can perform a good approximation of a building’s energy using a simplified model.

• Walls
• Windows
• Doors
• Ceiling
• Floor
• Infiltration and Air Exchange

For simplicity, imagine a simple box-shaped building with a flat roof and with dimensions l for length, w for width, and h for the height.

Then the total area of the walls is 2 (lh + wh), the area of the floor and the ceiling is lw, and the volume is lwh. (Let’s assume that the thickness of the walls is unimportant in calculating these areas and volumes.)

We subtract the area of the doors and windows from the wall area to get the area to use for a q=UA \Delta T computation.

Combined Convective-Radiative R-Value

Surfaces have heat loss contributions from convection and from radiation. It is customary to combine these into a single effective R-value.

We’ll use these values for a non-reflective surfaces.

• Ceiling 0.61 ht-ft2-F/BTU
• Inside wall 0.68
• Floor 0.92
• Outdoor air 0.17

Floor Heat Loss

For simple concrete on earth buildings the loss is mostly at the perimeter of the building. Since the temperature difference between the building interior and the ground is fairly small this heat loss is small compared to the perimeter.

q_{floor} = F P \Delta T

Where F is the heat loss factor (BTU/hr-ft-F) and P is the perimeter of the building. We’ll use a value of 0.75 BTU/hr-ft-F.

Building Infiltration

We’ve seen the formula

q_{inf} = \rho c n V \Delta T

• density of air 0.075 lb/ft3
• specific heat of air 0.24 BTU/lb-F

Newer homes are about 0.5 air changes per hour.

We use our volume above V = lwh.