Question 2 of 8: Interior office heating load; net-zero energy buildings

Problem 2: Interior office heating load; net-zero energy buildings (10 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. A single office cell, 5 m (external wall) × 4 m deep × 3 m high. Only two of its six surfaces lose heat — the external wall with its window, and the wall onto the corridor — because the offices above, below and to either side are at the same temperature.

Find. (a) The steady-state heat input the room needs at design conditions; (b) an explanation of the net-zero-energy building concept.

Approach. Sum $UA\,\Delta t$ over the two exposed surfaces, add the sensible load of one air change per hour of outdoor air, and take the total as the design heat input.

1. Part (a) — opaque external wall. The window occupies 4 m² of the $5\times3 = 15\ \text{m}^2$ external wall, leaving 11 m² of opaque construction: $$q_{w}=U A\,\Delta t = 1.0(11)(21)=231\ \text{W}$$
2. Window. The glazing is more than five times as conductive as the wall it sits in, and on only 4 m² it is the single largest fabric term: $$q_{g}=5.6(4)(21)=470\ \text{W}$$
3. Wall onto the corridor. The corridor is heated, but only to 16 °C, so a 4 K difference drives heat out of the office across the full 15 m²: $$q_{c}=2.7(15)(4)=162\ \text{W}$$
4. Ventilation air. One air change per hour of the 60 m³ room is $60/3600 = 0.01667\ \text{m}^3/\text{s}$ of outdoor air, entering at −1 °C where $\rho = p/RT = 101.325/(0.287\times272.15)=1.297\ \text{kg/m}^3$: $$q_{v}=\rho\dot V c_p \Delta t = 1.297(0.01667)(1005)(21)=456\ \text{W}$$ Evaluating the density at the outdoor state is the correct choice, because the mass that has to be heated is the mass that comes in.
5. Total design heat input. $$q=231+470+162+456=\boxed{1{,}320\ \text{W}\;\approx\;1.32\ \text{kW}}$$ That is 66 W/m² of floor area — high for an office, and the breakdown shows why: the window and the air change together account for 70 % of it.
6. Part (b) — what a net-zero energy building is. A net-zero energy building (NZEB, or zero net energy building) is one whose on-site renewable generation over a representative year equals or exceeds the delivered energy it consumes over that same year, assessed at an agreed boundary and with an agreed metric. The three metrics in common use give different answers for the same building: net-zero site energy counts kilowatt-hours at the meter; net-zero source (primary) energy multiplies each carrier by its generation and delivery efficiency, which penalises electricity on a fossil grid and rewards it on a hydro grid such as British Columbia's or Quebec's; and net-zero carbon counts emissions, which is the metric the Canada Green Building Council's Zero Carbon Building standard and most Canadian municipal policies now use. The qualifier “net” matters: the building still draws from the grid at night and in December and exports at noon in June, so it is annually balanced rather than autonomous. A building that is also autonomous hour by hour is called net-zero off-grid and needs storage of a wholly different order.
7. The design sequence that makes it achievable. Because generation area on a building is limited by roof and facade, the only way to reach balance is to drive demand down first, and the accepted order is (i) reduce loads, (ii) recover what is left, (iii) supply the remainder efficiently, (iv) generate on site. Load reduction is architectural before it is mechanical: orientation and massing, a window-to-wall ratio around 0.3 to 0.4 rather than the fully-glazed curtain wall, continuous exterior insulation with thermal bridges detailed out, an airtightness target near 0.6 air changes per hour at 50 Pa, triple glazing with a low-emissivity coating and a warm-edge spacer, and external shading sized so that summer sun is excluded while winter sun is admitted. Daylight harvesting with photoelectric dimming, and LED lighting at under 6 W/m², attack both the lighting energy and the cooling load it creates. The office cell in part (a) is a good illustration: replacing its $U = 5.6$ single glazing with a triple-glazed unit at $U = 0.9$ would cut the window term from 470 W to 76 W and the whole room load by 30 %.
8. Recovery, efficient supply, and harvesting. What load remains is met with heat recovery and high-efficiency plant: sensible or enthalpy recovery on the ventilation air at 70 to 85 % effectiveness (a Canadian code requirement in most climate zones), demand-controlled ventilation on CO₂, decoupled ventilation and thermal delivery through displacement supply or radiant panels so that fan energy falls, variable-speed drives on every pump and fan, and heat pumps in place of combustion — ground-source or water-source where the site allows, because as Problem 4 of this paper shows a ground loop keeps the source temperature near 5 °C when the air is at −25 °C. Waste-heat recovery from refrigeration, servers and drain water closes further gaps. Only then does generation make sense: roof-mounted or facade-integrated photovoltaics, a solar-thermal array for domestic hot water, and occasionally small wind or a biomass boiler. In Canadian practice the binding constraint is roof area against a winter-peaked heating demand and a summer-peaked solar resource, which is why net-zero is far easier on a two-storey school than on a twenty-storey tower, and why seasonal balance — net metering, borehole thermal storage, or district connection — is normally part of the answer. The National Energy Code of Canada for Buildings 2020 tiered pathway and the CaGBC Zero Carbon Building standard are the two frameworks a Canadian designer would work within.