Module 4: Heat Load Calculations - Heat Transfer in Buildings

Fundamental Modes of Heat Transfer in Buildings

Heat transfer in buildings occurs through molecular motion or radiative transport and is governed by three fundamental modes: conduction, convection, and radiation. Heat naturally flows from a warmer space to a cooler space whenever a temperature difference exists. In the building envelope, heat moves via all three modes, though the primary mechanisms for solid, opaque building elements are conduction and radiation. Advanced building science utilizes thermal insulation to reduce this heat transfer through the envelope, which serves to decrease energy consumption, increase occupant comfort, and save money for the building owner.

Definitions and Mechanisms of Heat Transfer

Conduction is defined as the movement of heat through a substance or between two substances that are in physical contact with each other. In this mode, heat energy moves from one molecule to another molecule in direct contact with it. Convection heat transfer occurs through the motion of a heated or cooled mass, specifically between a surface and a moving fluid such as a gas or liquid. It also refers to the movement of molecules from one region in a fluid to another due to the motion of the heated fluid itself. Convection inherently involves conduction because heat is transferred by the contact of molecules during movement. However, because it involves the natural or forced movement of a fluid, convection is generally considered less efficient than conduction heat transfer.

Radiation heat transfer involves the movement of energy by electromagnetic waves. All substances that exist above absolute zero temperature can emit radiant energy. When unimpeded, radiative energy travels in a straight-line path at approximately the speed of light, which is recorded as $186\,000\text{ miles per second}$ or $300,000,000\,m/s$, unless it is influenced by gravitational, magnetic, or other forces. When two surfaces of different temperatures are within view of each other, an exchange of radiative energy occurs from the hot body to the cold body.

Building Materials Heat Transfer Properties and Energy Balance

The heat transfer properties of building materials dictate the behavior of the heat transfer rate. A high resistance to heat transfer results in a more insulated conditioned space, which saves energy during both heating and cooling processes. The basic energy balance in a building for determining the cooling or heating load is represented by the equation: $H_{\text{produced}} + H_{\text{transmitted}} + H_{\text{infiltration}} + H_{\text{ventilation}} = H_{\text{rejected}}$. This equation illustrates that the heat load to be rejected or added to the building envelope must be handled by the air conditioning system. Therefore, the capacity of the cooling or heating equipment is equal to $H_{\text{rejected}}$. To predict this capacity, it is essential to consider the hottest and coldest months of the year.

Analysis of Transmission Heat Loads

Transmission heat loads result from heat passing through materials in the building envelope, such as glass, or through assemblies like walls, ceilings, and floors. While heat transfer can be calculated for each material and mode separately, it is common practice to combine the three modes into a single heat transfer coefficient denoted as $U$. For an external wall, which is defined as any wall facing direct rays of sunlight, the thermal heat load in Watts, $H$, is calculated as $H = U_w A \text{CLTD}_{\text{adj}}$. In this formula, $U_w$ is the heat transfer coefficient ($1/R$) in $W/m^2\text{-}K$, $A$ is the wall area in $m^2$, and $\text{CLTD}_{\text{adj}}$ is the adjusted value of the cooling load temperature difference.

The adjusted CLTD is determined by the formula $\text{CLTD}_{\text{adj}} = (\text{CLTD}_{\text{sel}} + LM)K + (25 - t_i) + (t_{\text{avg}} - 29)$, where $\text{CLTD}_{\text{sel}}$ is the selected value from specific tables. In scenarios where the material thickness $t$ and temperature difference $\Delta T$ are given, the heat transfer rate is $H = K t \Delta T$, where $K$ is conductivity in $W/m\text{-}k$. For a series of composite materials, the equivalent conductivity is calculated as $K_T = \frac{1}{(\frac{1}{K_1}) + (\frac{1}{K_2}) + \dots + (\frac{1}{K_n})}$. If the area and temperature difference are provided, the rate is $H = (1/R) A \Delta T$. For composite materials in series, the total heat transfer coefficient is $U_T = \frac{1}{R_1 + R_2 + \dots + R_n}$.

Glass and Partition Heat Loads

The heat load for glass, including window glass and skylights, is the sum of the solar heat gain and the thermal heat gain: $H = H_{\text{SG}} + H_{\text{TH}}$. Solar heat gain, which occurs if the glass or roof is exposed to direct sunlight, is calculated as $H_{\text{SG}} = (\text{SHGF})(\text{SC})(A)(\text{CLF})$. Here, $\text{SHGF}$ is the maximum solar heat gain factor, $\text{SC}$ is the shading coefficient, and $\text{CLF}$ is the cooling load factor for a selected solar time. Thermal heat gain, caused by simple temperature differences, is calculated as $H_{\text{TH}} = U A \Delta T$. Partition loads are created by any partitions not directly hit by sunlight where a temperature difference exists between internal and external spaces. These partitions can be walls, glass, floors, or ceilings. The partition heat load is calculated as $H_p = U A \Delta T$, where $A$ is the area of the medium and $\Delta T$ is the temperature difference between the sides of the partition.

Infiltration and Ventilation Heat Loads

Infiltration heat losses correspond to air leakage through the building envelope and the energy needed to treat this unconditioned air. This leakage occurs around doors and windows regardless of construction quality. Infiltration involves both sensible and latent heat loads. Sensible heat load is given by $H_S = 1.23 Q (t_o - t_i)$, and latent heat load is given by $H_L = 3000 Q (w_o - w_i)$, where $Q$ is the volume of air in $Li/s$, $t$ is temperature in $\text{Celsius}$, and $w$ is the humidity ratio. The airflow $Q$ is calculated by multiplying the number of air changes per hour by the room volume. The number of air changes per hour is determined by $a + bV + c(t_o - t_i)$, where $V$ is the wind velocity (average in the Philippines is $6.5-7\,m/s$). The constants $a$, $b$, and $c$ depend on construction quality: for tight construction they are $0.150$, $0.010$, and $0.007$; for average construction they are $0.200$, $0.015$, and $0.014$; and for loose construction they are $0.250$, $0.020$, and $0.022$. Ventilation heat loads use the same $H_S$ and $H_L$ formulas, but $Q$ is defined as the minimum outdoor air requirement of the conditioned space.

Internal Heat Generating Loads

Internal heat loads include heat released by occupants, lighting, and equipment. Occupant load consists of sensible heat, $H_S = (\text{Heat Gain/person})(\%SHG)(\text{No. of occupant})(\text{CLF})$, and latent heat, $H_L = (\text{Heat Gain/person})(\%LHG)(\text{No. of occupant})(\text{CLF})$. Here, $\text{Heat Gain/person}$ and the percentages of sensible ($SHG$) and latent ($LHG$) heat are found in reference tables. Lighting load affects the cooling load based on wattage and is calculated as $H_S = (\text{Lamp Rating in watts})(F_u)(F_b)(\text{CLF})$, where $F_u$ is the utilization factor and $F_b$ is the ballast factor (noted as $1.2$ for fluorescent lights). Miscellaneous equipment heat load is calculated as $H_S = (\text{Equipment Rating in watts})(F_u)(\text{CLF})$. All these internal loads must be accurately accounted for and rejected from the air to maintain thermal comfort inside the conditioned space.