Tutorials

How To Calculate Building Heating Energy

In order to maintain a constant internal environment in a building located in a cold climate, a heating system must be implemented to balance lost heat with added indoor heat. Therefore, the average rate of heat transfer through the building must equal zero. The rate of incoming heat required to ensure this stability is calculated with the equation:

Qheat = Qcond + Qair

(Eq 1)

where Qheat is the rate at which heat is added to the indoor air by the heater, Qcond refers to the rate of conductive heat loss through the building, and Qair represents the rate of heat loss as a result of the cold incoming air from openings. The SI unit of heat exchange rate is the Watt (W), which is equivalent to one joule per second (J/s).

The conductive heat loss through the area of a building envelope is quantified by the relationship:

Qcond = UA(Ti - To)

(Eq 2)

where Qcond is the rate of heat loss by conduction, U denotes the conductance, or thermal transmittance, of the materials that compose the envelope in W/m^{2 O}C or W/m²K, A is the surface area of the envelope in m², and Ti - To is the temperature difference between the conditioned indoor and the unconditioned outdoor environments in ^OC or K.

For a given building site and size, the temperature difference, Ti - To, between the indoor and outdoor environments usually cannot be altered. The product UA can be represented by the variable Kcond. Therefore, eq 3 can be rewritten as follows:

Qcond = Kcond(Ti - To)

(Eq 3)

Layers of air form barriers on the sides of exposed surfaces. Because air is an insulator, we considered these barriers when calculating the insulating capacities offered by each building assembly. 

In order to account for the varying properties of the envelope assemblies highlighted above, Kcond is the sum of the individual UA products for each assembly, as shown below:

Kcond = UAwindow + UAwall +UAroof

(Eq 4)

The overall U-value of an envelope assembly is dependent on the sum of the thermal resistance, R, of the materials it consists of. Thermal resistance is a measure of a material’s capacity to resist heat flow. It is inversely related to thermal capacitance. Consequently, high R-value envelope materials have low conductivity and, in turn, allow little quantities of heat to be lost through them. This is captured in the equation below:

Uk = 1/(R1 + R2 + R3 + ....)

(Eq 5)

 where R is in the units of m^{2 O}C/W or m²K/W.