ME 452: HVAC Load Analysis and Design Fundamentals
Estimated study time: 17 minutes
Table of contents
Sources and References
- McQuiston, Parker, and Spitler, Heating, Ventilating, and Air Conditioning: Analysis and Design, 6th ed., Wiley.
- ASHRAE Handbook—Fundamentals (current edition), ASHRAE, Atlanta.
- ASHRAE Handbook—HVAC Systems and Equipment, ASHRAE.
- Kreider, Curtiss, and Rabl, Heating and Cooling of Buildings: Principles and Practice of Energy Efficient Design, 3rd ed., CRC Press.
- Mitchell and Braun, Principles of Heating, Ventilation, and Air Conditioning in Buildings, Wiley.
- ASHRAE Standard 55 (Thermal Environmental Conditions) and Standard 62.1 (Ventilation for Acceptable IAQ).
Chapter 1: Moist Air and Psychrometric Analysis
Heating, ventilating, and air-conditioning design is an exercise in controlling simultaneously the temperature, humidity, cleanliness, and motion of air delivered to occupied spaces. Because every one of these quantities is coupled to the thermodynamic state of moist air, the discipline begins with a careful treatment of psychrometrics: the thermodynamics of mixtures of dry air and water vapour at the pressures and temperatures encountered in buildings.
1.1 Moist Air as a Two-Component Mixture
At ordinary building pressures (near one atmosphere) and temperatures (roughly -40 to 50 °C), dry air behaves as an ideal gas and water vapour at its low partial pressure is also very nearly ideal. The total pressure is the sum of the dry-air and water-vapour partial pressures,
\[ p = p_a + p_w. \]The humidity ratio \( W \) is defined as the mass of water vapour per unit mass of dry air in the same volume,
\[ W = \frac{m_w}{m_a} = 0.622 \frac{p_w}{p - p_w}. \]Relative humidity \( \phi \) is the ratio of the actual water-vapour mole fraction to the saturation value at the same temperature,
\[ \phi = \frac{p_w}{p_{ws}(T)}. \]The saturation pressure \( p_{ws}(T) \) is tabulated and is well approximated by correlations such as the Hyland–Wexler formulation used in the ASHRAE Handbook.
1.2 Enthalpy and the Psychrometric Chart
Taking the enthalpy of dry air at 0 °C as zero and that of liquid water at 0 °C as zero, the specific enthalpy per unit mass of dry air is
\[ h = c_{pa} T + W\,(h_{fg0} + c_{pv} T), \]with \( c_{pa} \approx 1.006 \) kJ/(kg·K), \( c_{pv} \approx 1.86 \) kJ/(kg·K), and \( h_{fg0} \approx 2501 \) kJ/kg. The psychrometric chart plots \( W \) against dry-bulb temperature with lines of constant enthalpy, wet-bulb temperature, and relative humidity overlaid. Every HVAC process—heating, cooling, humidification, dehumidification, mixing—is represented by a line or sequence of lines on this chart.
1.3 Elementary Processes
Sensible heating and cooling occur at constant humidity ratio: horizontal lines on the chart. The rate of sensible heat transfer is
\[ \dot{Q}_s = \dot{m}_a c_p (T_2 - T_1), \]where \( c_p = c_{pa} + W c_{pv} \). Cooling below the dew point condenses moisture; the coil process combines a sensible and a latent component and is represented by a sloped line between the entering state and the apparatus dew point, with bypass factor
\[ BF = \frac{T_{out} - T_{adp}}{T_{in} - T_{adp}}. \]Adiabatic mixing of two moist-air streams yields
\[ W_3 = \frac{\dot{m}_1 W_1 + \dot{m}_2 W_2}{\dot{m}_1 + \dot{m}_2}, \qquad h_3 = \frac{\dot{m}_1 h_1 + \dot{m}_2 h_2}{\dot{m}_1 + \dot{m}_2}. \]Chapter 2: Heating and Cooling Load Calculations
Load calculations translate weather, occupancy, construction, and internal-gain data into peak and hourly thermal demands on the conditioning equipment. The distinction between instantaneous heat gain and cooling load is central: thermal mass stores and re-releases energy, so the coil must often be sized for a load that peaks hours after the gain that caused it.
2.1 Design Conditions
Outdoor design conditions are specified as percentiles of the long-term weather record. For cooling, 0.4, 1, and 2 percent dry-bulb values are typical, together with mean coincident wet-bulb temperature. For heating, 99.6 and 99 percent design dry-bulb temperatures are used, generally without solar credit. Indoor conditions follow ASHRAE Standard 55: typically 21–23 °C and 30–60 percent RH in winter, 23–26 °C and similar humidity in summer.
2.2 Heat Flow Through the Envelope
Steady conductive gain through an opaque element of area \( A \) and overall coefficient \( U \) is
\[ \dot{Q} = U A (T_{o} - T_{i}). \]For transient behaviour, the conduction transfer function (CTF) or radiant time series (RTS) methods are standard. RTS expresses the hourly cooling load as a convolution of the sensible gain history with a set of tabulated radiant time factors that represent the building’s thermal mass response.
2.3 Solar Gains Through Fenestration
Solar transmission through a window is characterized by the solar heat gain coefficient (SHGC), which is the ratio of transmitted plus absorbed-then-reinward-emitted radiation to incident radiation. The instantaneous fenestration gain is
\[ \dot{Q}_{sol} = A\,\mathrm{SHGC}\,E_t, \]where \( E_t \) is the total incident irradiance on the tilted surface, computed from direct, diffuse, and ground-reflected components using solar geometry and, for sloped surfaces, anisotropic sky models. Interior shading devices modify SHGC through a shading coefficient or more sophisticated layer-by-layer calculation.
2.4 Infiltration and Ventilation
Air leakage through the envelope is driven by stack, wind, and mechanical pressure differences. Stack pressure is
\[ \Delta p_s = \rho_o g h \frac{T_o - T_i}{T_i}, \]and the crack flow follows a power law,
\[ \dot{V} = C (\Delta p)^{n}, \]with \( n \) typically 0.6–0.7. Required ventilation rates follow ASHRAE Standard 62.1 and depend on occupancy and floor area. Sensible and latent ventilation loads are
\[ \dot{Q}_s = \dot{m}_a c_p (T_o - T_i), \qquad \dot{Q}_l = \dot{m}_a h_{fg} (W_o - W_i). \]2.5 Internal Gains
Occupants, lights, and equipment all contribute. Each occupant at light activity emits about 75 W sensible and 55 W latent. Lighting gain equals installed watts modified by a usage factor and a radiative/convective split that interacts with mass. Plug loads are estimated from installed equipment or from ASHRAE defaults per unit area.
Chapter 3: Air Distribution, Duct Design, and Fans
3.1 Fan and Duct Fundamentals
Airflow in ducts is incompressible at HVAC velocities. The extended Bernoulli equation with friction and fitting losses is
\[ p_{t1} = p_{t2} + \sum \Delta p_{f} + \sum \Delta p_{m}, \]where \( p_t \) is total (stagnation) pressure. Straight-duct friction is given by the Darcy–Weisbach form,
\[ \Delta p_f = f \frac{L}{D_h} \frac{\rho V^2}{2}, \]with \( f \) from the Colebrook equation or equivalent charts. Minor (fitting) losses are expressed through loss coefficients \( C \) tabulated by geometry,
\[ \Delta p_m = C \frac{\rho V^2}{2}. \]3.2 Duct Sizing Methods
Three common strategies are equal-friction, static-regain, and constant-velocity. The equal-friction method fixes a pressure gradient (commonly 0.8–1.0 Pa/m) and selects duct sizes so each run develops that gradient. Static-regain sets successive velocity reductions so that regained static pressure offsets downstream friction, producing balanced branches without dampers. Constant-velocity methods are used for high-velocity or dust-laden service.
3.3 Fan Selection and Operating Point
A fan’s pressure–flow characteristic intersects the system curve, \( \Delta p = R \dot{V}^2 \), at the operating point. The fan power is
\[ \dot{W}_{fan} = \frac{\dot{V}\,\Delta p_{t}}{\eta_{fan}}. \]Fan-law scaling with speed \( N \) and density \( \rho \) gives
\[ \frac{\dot{V}_2}{\dot{V}_1} = \frac{N_2}{N_1}, \qquad \frac{\Delta p_2}{\Delta p_1} = \left(\frac{N_2}{N_1}\right)^2 \frac{\rho_2}{\rho_1}, \qquad \frac{\dot{W}_2}{\dot{W}_1} = \left(\frac{N_2}{N_1}\right)^3 \frac{\rho_2}{\rho_1}. \]Variable-speed drives exploit the cubic power law for large energy savings at part load.
Chapter 4: Indoor Air Quality and Thermal Comfort
4.1 Thermal Comfort
Fanger’s predicted mean vote (PMV) model combines six variables—air temperature, mean radiant temperature, relative humidity, air speed, metabolic rate, and clothing insulation—into a single index ranging from -3 (cold) to +3 (hot). The predicted percentage dissatisfied (PPD) follows
\[ \mathrm{PPD} = 100 - 95 \exp\!\left(-0.03353\,\mathrm{PMV}^4 - 0.2179\,\mathrm{PMV}^2\right). \]Standard 55 defines comfort zones on the psychrometric chart in terms of operative temperature and humidity.
4.2 Ventilation for Acceptable IAQ
Standard 62.1 prescribes breathing-zone outdoor airflow
\[ \dot{V}_{bz} = R_p N_p + R_a A, \]where \( R_p \) is per-person airflow, \( N_p \) is occupancy, \( R_a \) is per-area airflow, and \( A \) is floor area. Zone and system corrections account for distribution effectiveness and multiple-zone diversity. Demand-controlled ventilation modulates outdoor air against measured CO₂ concentration to reduce energy while preserving IAQ.
4.3 Contaminant Removal
A well-mixed zone with generation \( \dot{G} \), volume flow \( \dot{V} \), and inlet concentration \( C_0 \) reaches steady-state concentration
\[ C = C_0 + \frac{\dot{G}}{\dot{V}}. \]Transient response is first order with time constant \( V/\dot{V} \). Filtration upgrades this by capturing particulates: MERV ratings quantify fractional efficiency versus particle size.
Chapter 5: Putting It Together — Design Workflow
A complete design begins with the programmatic requirements: occupancy, ventilation, acoustic, and humidity targets. The envelope is specified and the block load is computed for the design day, using the radiant time series or a whole-building simulation. Zone loads drive primary and secondary airflow. Supply temperature and zone airflow are linked through
\[ \dot{Q}_{zone,s} = \dot{m}_a c_p (T_{zone} - T_{supply}). \]Ducts are sized; the fan is selected against the resulting system curve. The cooling coil is sized to the peak coincident sensible and latent load, with bypass factor chosen to hit the required apparatus dew point. Finally, heating equipment is sized to the 99 percent design day with no solar and typically no internal gains. Energy performance is verified against baseline by hourly simulation, and control sequences for outdoor-air economizers, demand-controlled ventilation, and reset schedules are specified.
The designer’s judgement lies in reconciling these numbers with realities: oversized equipment short-cycles and dehumidifies poorly; undersized equipment fails at peak; diverse zones require either simultaneous heating and cooling or careful grouping; and every pressure drop added in pursuit of filtration or acoustics is paid for daily in fan energy.
