22-Mec-B2 Environmental Control in Buildings · December 2016

Question 8 of 8: Hourly cooling load by the CLTD / SCL / CLF method

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. Professional Engineers of Ontario / Engineers Canada annual examination 07-Mec-B2 Environmental Control in Buildings, December 2016, three hours, open book. Eight problems of 20 points each; candidates are required to solve five, and all questions carry the same value. Psychrometric charts and an R-22 p-h diagram are appended to the paper. All eight problems are solved here.

Reference texts for this subject.

W. P. Jones, Air Conditioning Engineering, 5th ed., Butterworth-Heinemann — the standard reference for this examination code; Ch. 2–3 (psychrometry), Ch. 5–6 (heating and cooling loads), Ch. 15 (fans and duct design).
McQuiston, Parker & Spitler, Heating, Ventilating and Air Conditioning: Analysis and Design, 6th ed., Wiley — Ch. 3 (moist air), Ch. 5 (heat transmission in building structures), Ch. 8 (energy estimating and the degree-day method), Ch. 12–13 (fluid flow, fans and duct design).
ASHRAE Handbook — Fundamentals (2021) — Ch. 1 (psychrometrics), Ch. 14 (climatic design information), Ch. 18 (non-residential cooling and heating load calculations), Ch. 21 (duct design), Ch. 26 (heat, air and moisture control), Ch. 30 (thermophysical properties of refrigerants).
Moran, Shapiro, Boettner & Bailey, Fundamentals of Engineering Thermodynamics, 9th ed., Wiley — Ch. 10 (vapour-compression refrigeration and heat pumps).
ANSI/ASHRAE Standard 62.1, Ventilation for Acceptable Indoor Air Quality; ANSI/ASHRAE Standard 55, Thermal Environmental Conditions for Human Occupancy.
Canadian frame: National Building Code of Canada 2020 and its Appendix C design temperatures; National Energy Code of Canada for Buildings 2020; Environment and Climate Change Canada degree-day normals for Toronto and Ottawa; CSA B52 Mechanical Refrigeration Code; Canada Green Building Council LEED Canada and the CaGBC Zero Carbon Building Standard for Problem 5.

Check: assumptions carried through this paper. Cover-page instruction 1 invites a clear statement of any assumption. Standard barometric pressure of 101.325 kPa is used throughout; moist-air properties follow the ASHRAE Handbook — Fundamentals Ch. 1 formulation (Hyland–Wexler saturation pressure, so results agree with the appended chart to chart-reading accuracy rather than being read off it); R-22 properties are on the IIR datum and agree with the appended p-h diagram. Problem-specific assumptions — the coil bypass factor, climate and degree-day data, fuel prices and equipment efficiencies, duct roughness, and the CLTD / SCL / CLF table entries — are stated where they are first used.

Question 8: Hourly cooling load by the CLTD / SCL / CLF method (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. A single interior office room whose only exterior surface is an east-facing glazed wall of 160 ft², with the occupancy and lighting schedule below, evaluated at 15:00 in July.

Given data and assumed table entries, Problem 8
Quantity	Symbol	Value
Glass area, east facing, unshaded	A	8 ft × 20 ft = 160 ft²
Room dry bulb	t_R	75 °F
Occupants, 8:00–18:00	—	6, at 250 Btu/h sensible + 200 Btu/h latent each
Lighting, 8:00–18:00	—	6 fixtures × 2 × 40 W, ballast factor 1.20
Glazing overall coefficient	U	0.55 Btu/h·ft²·°F (assumed)
Shading coefficient, heat-absorbing / clear pair	SC	0.53 (assumed)
Glass CLTD at hour 15	CLTD	13 °F (assumed)
Solar cooling load factor, east, July, hour 15	SCL	55 Btu/h·ft² (assumed)
Cooling load factors at hour 15	CLF_p, CLF_l	0.92 people, 0.89 lights (assumed)

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

Check: stated assumptions. The question explicitly asks for them. Room and construction: medium-weight construction with carpeted floor and suspended ceiling, so zone type B for the load-factor tables; the other three walls, floor and ceiling adjoin conditioned space at the same temperature and are therefore adiabatic, and the middle-floor location means no roof or ground contact. Wind and infiltration: the building is mechanically pressurised, so infiltration through the curtain wall is neglected and wind affects only the outside film coefficient already embedded in the glazing U-value. Climate: Ottawa July design conditions of 87 °F dry bulb with a 20 F° daily range, giving a mean outdoor temperature of 77 °F; latitude taken as the 40°N tables, the nearest tabulated set. Solar geometry: no external shading, no adjacent building obstruction, and no internal blinds as the question states. Occupancy: "light physical work" is taken as moderately active office work, 250 Btu/h sensible and 200 Btu/h latent per person, adjusted for a normal mixture of men, women and children. Ventilation air is excluded, because it is a coil load rather than a room load and the question asks only for people, lights and glass.

The room and the component cooling loads at 15:00. By mid-afternoon the direct beam has long left an east facade, yet transmitted solar is still the largest single component because the diffuse and reflected components persist and the morning gain is still being re-released by the room mass.

Approach. Each gain is converted to a cooling load at the hour of interest by its own transfer factor: sensible gains from people and lights through a cooling load factor, glass conduction through a corrected cooling load temperature difference, and transmitted solar through a solar cooling load factor and the shading coefficient. Latent gain becomes load instantaneously.

People. Six occupants at 250 Btu/h sensible each, entering at 08:00 and evaluated seven hours later within a ten-hour occupancy, take a cooling load factor of 0.92:$$q_{p,s}=N\,q_{s}\,\mathrm{CLF}=6\times250\times0.92=1,380\ \text{Btu/h}$$The latent portion appears as load the instant it is released, with no storage and no factor:$$q_{p,l}=6\times200=1,200\ \text{Btu/h}$$
Lights. Fluorescent tubes draw more than their nominal rating because of the ballast, so a special allowance factor of 1.20 is applied to the installed wattage:$$W=6\times2\times40\times1.20=576\ \text{W}\ \Rightarrow\ q_{l,\text{input}}=1,965.4\ \text{Btu/h}$$With a cooling load factor of 0.89 for ten hours of operation seen at the seventh hour,$$q_{l}=1,965.4\times0.89=1,749.2\ \text{Btu/h}$$A suspended ceiling plenum would in practice remove some of this to the return air; that refinement is neglected here.
Glass conduction. The cooling load temperature difference for glass is tabulated for a 78 °F room and an 85 °F mean outdoor temperature, and both must be corrected:$$\mathrm{CLTD}_{\text{corr}}=\mathrm{CLTD}+(78-t_{R})+(t_{o,\text{mean}}-85)=13+3-8=8.0\ \text{F}^\circ$$$$q_{\text{cond}}=U\,A\,\mathrm{CLTD}_{\text{corr}}=0.55\times160\times8.0=704\ \text{Btu/h}$$Ottawa's mean July temperature is well below the tabulated basis, which is why the correction removes more than half the conduction term.
Transmitted solar. This is the dominant component, and it is charged through the solar cooling load factor for the orientation, month and hour, scaled by the shading coefficient of the glazing:$$q_{\text{solar}}=A\,\mathrm{SC}\,\mathrm{SCL}=160\times0.53\times55=4,664\ \text{Btu/h}$$The heat-absorbing outer pane is doing real work here: clear double glazing at SC = 0.88 would put this term above 7,700 Btu/h.
Assemble the room load. The glass wall contributes $704+4,664=5,368$ Btu/h in total, so$$q_{\text{sensible}}=1,380+1,749.2+5,368=8,497\ \text{Btu/h}$$$$\boxed{\ q_{\text{total}}=8,497+1,200=9,697\ \text{Btu/h}\ }$$That is 2.84 kW, or 0.81 tons of refrigeration, at a room sensible heat ratio of 0.876. Transmitted solar alone is 48.1 % of the total, which is the engineering message of the question: on a fully glazed facade the glazing specification governs the plant size far more than the occupancy or the lighting does.

One further observation is worth recording. Fifteen hundred hours is not the peak hour for this room — an east facade peaks between 08:00 and 09:00, when the solar cooling load factor is roughly three times the value used here, so the room design load would be found in the morning. The hour 15:00 was chosen by the examiner precisely because it forces the candidate to use the tables rather than a peak-hour rule of thumb, and because it exposes how much of an east room's afternoon load is stored morning sun coming back out of the structure.

Problem 8 — results at hour 15:00, July
Component	Cooling load, Btu/h
People, sensible (6 × 250 × 0.92)	1,380
Lights (576 W × 3.412 × 0.89)	1,749.2
Glass conduction (U A CLTD)	704
Glass transmitted solar (A SC SCL)	4,664
Room sensible load	8,497
People, latent (6 × 200)	1,200
Room total cooling load	9,697 Btu/h = 2.84 kW = 0.81 tons
Room sensible heat ratio	0.876
Load per unit of glass area	60.6 Btu/h·ft²

Topic. The CLTD / SCL / CLF method: converting instantaneous heat gain into the cooling load the plant actually sees.

Key relations. People $q=N q_{s}\mathrm{CLF}+N q_{l}$; lights $q=W F_{ul} F_{sa}\times3.412\times\mathrm{CLF}$; glass conduction $q=UA\,\mathrm{CLTD}_{\text{corr}}$ with $\mathrm{CLTD}_{\text{corr}}=\mathrm{CLTD}+(78-t_{R})+(t_{o,m}-85)$; transmitted solar $q=A\,\mathrm{SC}\,\mathrm{SCL}$.

Why this works. Heat gain and cooling load are not the same thing. Radiant energy — sunlight through glass, radiation from lamps and from people — does not warm the air directly; it first strikes the floor, walls and furniture, is stored there, and is released to the air by convection over the following hours. The cooling load factors and the solar cooling load are pre-computed transfer functions that carry out that delay and attenuation for standard room constructions, so a designer can obtain an hourly load without running a transfer-function calculation. The convective and latent portions have no such lag, which is exactly why latent gain takes no factor at all. The whole scheme depends on the room mass being correctly classified: a heavy structure delays and flattens the peak, a light one follows the gain almost immediately.

Common pitfall. Applying a cooling load factor to the latent gain, or omitting the ballast allowance on fluorescent lighting, both of which are small. The large errors are using the uncorrected CLTD — worth 5 F° here, more than half the conduction term — and reading the solar cooling load for the wrong orientation or hour, since an east facade's SCL falls by a factor of three between 09:00 and 15:00.

Source. ASHRAE Handbook — Fundamentals, Ch. 18 (non-residential cooling and heating load calculations); McQuiston, Parker & Spitler, HVAC: Analysis and Design, 6th ed., Ch. 7 and its CLTD/SCL/CLF tables; ASHRAE Handbook — Fundamentals (2021), Ch. 15 (fenestration) for shading coefficients and glazing U-factors.

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