Internal heat gains and a degree-day fuel estimate: 22-Mec-B2 Environmental Control in Buildings, December 2014, Q4

Question 4: Internal heat gains and a degree-day fuel estimate (20 points)

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. Part (a): an office of 4,000 ft² with a stated occupancy, lighting density and equipment density, each on its own schedule, evaluated at 16:00. Part (b): an Ottawa building with a design heating load and a furnace of stated efficiency burning natural gas.

Given data — Problem 4
Quantity	Value
Floor area	4,000 ft²
Occupancy	20 people, 08:00–17:00
Lighting	2.5 W/ft², recessed unvented fluorescent, 08:00–18:00
Equipment	1.8 W/ft²
Design conditions (b)	$70^\circ\text{F}$ inside, $-12^\circ\text{F}$ outside
Design heating load (b)	350,000 Btu/hr
Furnace efficiency / heating value (b)	80 % / 1,000 Btu/ft³

Find. (a) The sensible and latent heat gains in the space at 16:00; (b) the annual quantity of natural gas required, by the degree-day method.

Approach. For (a), evaluate each gain component against its schedule at 16:00, applying the ASHRAE special-allowance factor to the fluorescent lighting and the standard office sensible/latent split to the occupants. For (b), scale the design load by the ratio of annual degree-days to the design temperature difference, divide by the furnace efficiency and the fuel heating value, and apply the empirical correction factor.

(a) People. At 16:00 the space is occupied, so all 20 people are present. For moderately active office work ASHRAE gives 250 Btu/hr sensible and 200 Btu/hr latent per person (450 Btu/hr total), so $q_{s,\mathrm{people}} = 20(250) = 5{,}000\ \text{Btu}/\text{hr}$ and $q_{l,\mathrm{people}} = 20(200) = 4{,}000\ \text{Btu}/\text{hr}$. People are the only latent source in the space.
(a) Lighting. The lights are on from 08:00 to 18:00, so at 16:00 they are running. The connected load is $2.5(4{,}000) = 10{,}000\ \text{W}$, and fluorescent fixtures need the special allowance factor $F_{sa} = 1.20$ to account for ballast losses: $$q_{\mathrm{light}} = 3.412\,(10{,}000)(1.20) = 40{,}944\ \text{Btu}/\text{hr}$$ Because the fixtures are recessed but unvented, all of that heat enters the conditioned space rather than being carried away in a return-air plenum, so the use factor is 1.0.
(a) Equipment. Office equipment is treated as entirely sensible, $q_{\mathrm{equip}} = 3.412\,(1.8)(4{,}000) = 24{,}566\ \text{Btu}/\text{hr}$.
(a) Cooling load factors. A cooling load factor of 1.0 is taken for all three components. This is the correct choice here, not a shortcut: the system operates only during occupied hours, and CLF tables are built on the assumption of continuous operation — ASHRAE directs that CLF = 1.0 be used whenever the plant is shut down at night, because the heat stored in the structure during the day must be removed during the same operating period. At 16:00, eight hours into a schedule that began at 08:00, the stored-heat effect would in any case be small.
(a) Totals. Adding the three sensible contributions, $$q_s = 5{,}000+40{,}944+24{,}566 = \boxed{70{,}510\ \text{Btu}/\text{hr}}\qquad q_l = \boxed{4{,}000\ \text{Btu}/\text{hr}}$$ a total instantaneous gain of 74,510 Btu/hr, or 21.8 kW — about 18.6 Btu/hr per square foot, which is typical of a densely equipped office floor.
(b) Degree-days and the design temperature difference. Ottawa has approximately 8,100 °F·days of heating below the 65°F base (4,500 °C·days below 18°C in Environment and Climate Change Canada's tables). The design temperature difference is $\Delta t = 70-(-12) = 82\ ^\circ\text{F}$.
(b) Uncorrected fuel quantity. The degree-day method scales the design load by the ratio of the season's degree-days to the design difference: $$V = \frac{q_{\mathrm{design}}\times 24 \times \mathrm{DD}}{\Delta t \times \eta \times \mathrm{HV}} = \frac{350{,}000(24)(8{,}100)}{82(0.80)(1{,}000)} = 1{,}037{,}000\ \text{ft}^{3}/\text{yr}$$
(b) Apply the empirical correction factor. The raw degree-day method overstates consumption, because it credits nothing to internal gains, solar gain, or the part-load efficiency of the plant. ASHRAE gives an empirical correction $C_D$ that for a 70°F indoor design and 8,100 degree-days is 0.65, so $$V_{\mathrm{corrected}} = 0.65\,(1{,}037{,}000) = \boxed{674{,}000\ \text{ft}^{3}/\text{yr}}$$ which is 19,100 m³/yr, or about 711 GJ/yr of gas purchased.

Check: degree-days and the correction factor must both be stated. DD₃₅ = 8,100 °F·days for Ottawa and $C_D = 0.65$ are read from published tables, not derived from the question. A candidate quoting a different Ottawa degree-day figure (published values range from about 8,000 to 8,300) or omitting $C_D$ altogether should say so explicitly, as cover-page instruction 1 invites; the uncorrected figure is 1,037,000 ft³/yr.

The two halves of this problem sit at opposite ends of the design process, and that contrast is the lesson. Part (a) is an instantaneous, deterministic calculation used to size equipment, where being wrong by 20 % means a coil that cannot hold the space. Part (b) is a seasonal estimate used for budgeting and for comparing alternatives, where a 20 % error is ordinary and the correction factor is itself an admission that the model is crude. Bin methods or an hourly simulation would be used where the energy estimate actually mattered — for instance in a Canadian energy-code compliance path under NECB.

Problem 4 — answers
Quantity	Result
(a) People — sensible / latent	5,000 / 4,000 Btu/hr
(a) Lighting (with $F_{sa}=1.20$)	40,944 Btu/hr
(a) Equipment	24,566 Btu/hr
(a) Total sensible gain at 16:00	70,510 Btu/hr
(a) Total latent gain at 16:00	4,000 Btu/hr
(a) Total gain	74,510 Btu/hr (21.8 kW)
(b) Design temperature difference	$82\ ^\circ\text{F}$
(b) Gas before correction	1,037,000 ft³/yr
(b) Gas after correction ($C_D = 0.65$)	674,000 ft³/yr (19,100 m³/yr; 711 GJ/yr)

Topic. Internal heat gain components with schedules and special-allowance factors, and seasonal fuel estimation by the corrected degree-day method.

Key relations. $q_{\mathrm{light}} = 3.412\,W_{\mathrm{conn}}\,F_{sa}\,F_{ul}\,\mathrm{CLF}$; $q_{\mathrm{people}} = N(q_s + q_l)\,\mathrm{CLF}$; $1\ \text{W} = 3.412\ \text{Btu}/\text{hr}$; $V = q_{\mathrm{design}}\,(24)\,\mathrm{DD}\,C_D/(\Delta t\,\eta\,\mathrm{HV})$.

Why this works. Both calculations rest on proportionality to a temperature difference. The gain calculation asks what is happening now, so each component is evaluated against its own schedule and multiplied by the factors that describe how much of the nominal power actually becomes heat in the space — the ballast allowance for fluorescent lamps, the vented/unvented distinction for recessed fixtures, the sensible/latent split for people. The degree-day calculation asks what happens over a season, and assumes the building's heat loss is linear in the indoor-outdoor difference, so the ratio of seasonal degree-days to the design difference scales the design load directly into a seasonal energy.

Common pitfall. Forgetting the 1.20 ballast factor (a 6,800 Btu/hr error here, nearly 10 % of the sensible gain), or assigning latent heat to office equipment. On part (b), the most common error is omitting the factor of 24 when the load is quoted per hour and degree-days are per day.

Source. ASHRAE Handbook — Fundamentals Ch. 18 (internal loads, special-allowance and use factors, CLF) and Ch. 19 (degree-day and bin methods, correction factor $C_D$); McQuiston, Parker & Spitler, Ch. 8 and Ch. 15.

Question 4 of 8: Internal heat gains and a degree-day fuel estimate

Question 4: Internal heat gains and a degree-day fuel estimate (20 points)