Question 5 of 8: Cooling load of an east-facing office at 15:00 in July

Question 5: Cooling load of an east-facing office at 15:00 in July (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Find. The room cooling load at 15:00 in July from the glass wall, the lights and the occupants, with the assumptions stated.

Approach. Use the ASHRAE CLTD/SCL/CLF method. The glass contributes two separate terms — transmitted solar radiation as $A\cdot SC\cdot SCL$ and conduction as $A\cdot U\cdot CLTD_{\text{corr}}$ — while the lights and the sensible part of the occupant gain are multiplied by cooling load factors that account for the room's thermal storage. Latent gain becomes load immediately and takes no factor.

1. Establish the design conditions and check the sun. Ottawa's 2.5% summer design condition is $86\,{}^{\circ}\text{F}$ dry bulb with a mean daily range of $20\,{}^{\circ}\text{F}$. At 15:00 solar time in July ($\delta = 20.6\,{}^{\circ}$, hour angle $45\,{}^{\circ}$) the solar altitude is $\beta = 45.7\,{}^{\circ}$ and the azimuth is $71.4\,{}^{\circ}$ west of south. For a wall facing east the wall-solar azimuth is therefore $161\,{}^{\circ}$: greater than $90\,{}^{\circ}$, so the glass receives no direct beam at 15:00. Its instantaneous solar gain is diffuse and ground-reflected only, $E_t = 39.7$ Btu h$^{-1}$ft$^{-2}$, which would transmit just $240\times 0.55\times 0.87\times 39.7 = 4560$ Btu/hr. The load at 15:00 will be larger than that, because the mass of the room is still re-releasing energy stored during the intense morning sun — and capturing exactly that lag is what the SCL table is for.
2. Glass solar cooling load. For east glass at $40\,{}^{\circ}$N in July, hour 15, in a medium-weight (zone type B) space with no interior shade, the solar cooling load factor is $SCL = 56$ Btu h$^{-1}$ft$^{-2}$, and heat-absorbing outer pane with clear inner pane in a double unit gives a shading coefficient $SC = 0.55$: $$q_{\text{solar}}=A\cdot SC\cdot SCL = 240\times 0.55\times 56 = \boxed{\;7392\ \text{Btu}\,\text{h}^{-1}\;}$$ As anticipated in step 1 this exceeds the instantaneous transmitted gain by 62%, the difference being stored morning energy re-emerging — the dominant term in this room by a wide margin.
3. Glass conduction load. A double-glazed unit with a 1/2 in air space has $U = 0.55$ Btu h$^{-1}$ft$^{-2}$°F$^{-1}$ in summer conditions, and the tabulated glass cooling load temperature difference at hour 15 is $CLTD = 13\,{}^{\circ}\text{F}$. The table is published for a $78\,{}^{\circ}\text{F}$ room and an $85\,{}^{\circ}\text{F}$ mean outdoor temperature, so it must be corrected: $$CLTD_{\text{corr}} = CLTD + (78-t_{\text{in}}) + (t_{o,\text{mean}}-85)$$ with $t_{o,\text{mean}} = 86-20/2 = 76\,{}^{\circ}\text{F}$, giving $CLTD_{\text{corr}} = 13+3-9 = 7\,{}^{\circ}\text{F}$. Hence $$q_{\text{cond}}=A\,U\,CLTD_{\text{corr}} = 240\times 0.55\times 7 = 924\ \text{Btu}\,\text{h}^{-1}$$ a small term: at 15:00 the outdoor air is barely warmer than the room, so conduction through the glass is almost irrelevant compared with the radiation passing through it.
4. Lighting load. Fluorescent tubes need a ballast allowance, conventionally 1.20 for a two-lamp magnetic ballast, and the lights have been on for 7 of their 10 hours, giving a cooling load factor $CLF = 0.90$ for a zone-B room: $$q_{\text{lights}}=W\times 3.412\times F_{\text{ballast}}\times CLF = 400\times 3.412\times 1.20\times 0.90$$ $$q_{\text{lights}}=1474\ \text{Btu}\,\text{h}^{-1}$$
5. Occupant load. "Light physical work" in an office corresponds to the ASHRAE moderately-active office entry, 250 Btu/hr sensible and 200 Btu/hr latent per person. The sensible part is partly radiant and so is delayed; 7 hours into a 10-hour occupancy the factor is $CLF = 0.92$. The latent part becomes load at once and takes no factor: $$q_{\text{people,s}}=6\times 250\times 0.92 = 1380\ \text{Btu}\,\text{h}^{-1},\qquad q_{\text{people,l}}=6\times 200 = 1200\ \text{Btu}\,\text{h}^{-1}$$
6. Sum the components. The five terms add to $$q_{\text{sens}}=7392+924+1474+1380 = 11\,170\ \text{Btu}\,\text{h}^{-1}$$ $$\boxed{\;q_{\text{total}}=11\,170+1200 = 12\,370\ \text{Btu}\,\text{h}^{-1}= 1.03\ \text{tons}\;}$$ with a room sensible heat factor of $11\,170/12\,370 = 0.903$. Per unit of glass that is 51.5 Btu h$^{-1}$ft$^{-2}$ of facade — a high but entirely typical figure for unshaded all-glass curtain wall, and the reason such rooms are normally given internal blinds or a lower shading coefficient at the design stage.