Question

A building facade has 48 m² of glazing area. The properties of glass used in the glazing are as follows:
U-value: 5.2 W/m² °C
Light to Solar Gain (LSG) Ratio: 1.5
Visual Light Transmittance (VLT): 0.6
The average solar radiation on the glazing is 400 W/m². If the outdoor and indoor set point temperatures are 35 °C and 20 °C, respectively, then the total heat gain (in kW) through the glazing by conduction and radiation is (rounded off to two decimal places).

Hint:

Add the conduction heat gain (U times area times temperature difference) to the solar heat gain (SHGC times radiation times area), using SHGC = VLT divided by LSG.

Answer 1

Correct Answer: 11.5

Instead of finding the two heat gain paths for the whole 48 square metre facade straight away, it helps to work out the heat flux for one square metre of glazing first, then scale up at the end. This keeps the two physical mechanisms, conduction and solar radiation, clearly separate.

Conduction, per square metre: the temperature difference across the glass is $\Delta T = 35 - 20 = 15^{\circ}C$. With a U-value of $5.2\ \text{W/m}^2{}^{\circ}C$, each square metre of glass conducts

\[ 5.2 \times 15 = 78\ \text{W/m}^2 \]

Solar radiation, per square metre: the fraction of incoming sunlight that actually becomes heat inside is the Solar Heat Gain Coefficient (SHGC), and this is linked to the given Light-to-Solar-Gain ratio by $LSG = VLT/SHGC$. Plugging in the numbers,

\[ SHGC = 0.6 / 1.5 = 0.4 \]

So for every square metre receiving $400\ \text{W/m}^2$ of solar radiation, the heat that actually gets in is

\[ 0.4 \times 400 = 160\ \text{W/m}^2 \]

Combine per unit area, then scale by area: adding the two contributions per square metre gives

\[ 78 + 160 = 238\ \text{W/m}^2 \]

Multiplying by the total glazed area of 48 square metres,

\[ 238 \times 48 = 11424\ \text{W} = 11.424\ \text{kW} \]

Rounded to two decimal places, the total heat gain through the glazing by conduction and radiation works out to about 11.42 kW, matching the officially accepted answer of roughly 11.5 kW for this range question.