Notes on 3.1–3.21: The Physics of Heat Flow for Heating and Cooling Buildings

3.1 INTRODUCTION

• Context: Climate change relevance to heating, cooling, and lighting in buildings; need for solar design and policy action.
• Key quotes referenced: Sir Norman Foster on survival; J. Bronowski on informed public action (1973).
• Objective of chapter: Provide a review of well-known concepts and introduce less familiar ideas important for building energy behavior.
  • Concepts to cover: mean radiant temperature, time lag, insulating effect of mass, embodied energy.
• Scope: Foundations for energy principles; later chapters cover lighting systems separately.

3.2 HEAT

• Energy exists in many forms; focus here is energy in the form of heat.
• Heat forms relevant to buildings:
  1) Sensible heat: measurable with a thermometer.
  2) Latent heat: associated with phase changes (melting/boiling).
  3) Radiant heat: form of electromagnetic radiation.

3.3 SENSIBLE HEAT

• Sensible heat is the random motion of molecules.
• Temperature reflects the intensity of molecular motion; hotter objects have more intense motion and contain more heat (Fig. 3.1a).
• When two objects at different temperatures come into contact, heat flows by conduction from the hotter to the cooler object; air is a poor conductor due to larger molecular spacing; vacuum provides no conduction.
• Temperature alone does not determine heat content; mass matters. Example: two blocks at the same temperature can have different heat contents if their masses differ (Fig. 3.1b).
• Heat content depends on: mass, temperature, and heat capacity.
• In US customary units: temperature in °F; heat in Btu; In SI: temperature in °C (or K); heat in J or cal; Common prefixes: mega, giga, tera for energy/power scales.
• Table references:
  • Table 3.1A: Units of heat and temperature (Btu, Btu/h, °F; J or cal, W or J/s, °C or K).
  • Note: 0 K = -273.15 °C; °C and K scales are interchangeable apart from zero reference.
  • Table 3.1B: Energy prefixes: Mega (10^6), Giga (10^9), Tera (10^12) with examples (e.g., Megawatts, Terawatts).

3.4 LATENT HEAT

• Phase changes involve large energy but little to no temperature change (latent heat).
• For water: changes as examples:
  • Melting: 1 lb of ice to 1 lb water requires about 144 Btu.
  • Vaporization: 1 lb water to 1 lb steam requires about 1000 Btu.
• Heat of fusion: energy required to melt a solid; heat of vaporization: energy to convert a liquid to gas.
• Critical points: during phase changes, the material’s temperature remains near the phase-change temperature while substantial energy is absorbed or released.
• Important takeaway: latent heat is a compact way to store/transfer energy; not measurable by thermometer.

3.5 EVAPORATIVE COOLING

• Evaporation requires large heat of vaporization; cooling occurs as sweat absorbs heat to become vapor.
• Heat drawn from skin cools body; latent heat transfer accompanies sensible heat change.
• Applications to buildings: evaporative cooling can cool air or surfaces; effectiveness depends on humidity and air movement (Fig. 3.3).
• Practical notes:
  • Evaporation is rapid with low humidity and/or high air movement.
  • High humidity or still air slows evaporative cooling.
• Applications: roof spraying in dry climates; air cooling of entering air with water sprays (to be described in Chapter 9, Passive Cooling).

3.6 CONVECTION

• Convection occurs when a gas or liquid gains heat by conduction, expands, and becomes less dense, causing it to rise (natural convection, Fig. 3.4a).
• Gravity drives natural convection; in air, heat generally rises; important for indoor comfort.
• Natural convection in rooms creates vertical stratification: warm air near ceiling, cold air near floor (Fig. 3.4b).
  • Stratification can help in summer (cooling) or hinder in winter (heat distribution).
• Forced convection: when air or water is moved by a pump/fan/wind (Fig. 3.4c); improves heat transfer by increasing fluid movement.

3.7 TRANSPORT

• Historical note: warming pans (≈12 inches/30 cm diameter, ≈4 inches/10 cm deep) used to preheat beds with hot embers; long wooden handle (Fig. 3.5).
• Early 20th century: warming methods evolved to using energy-transfer fluids (air or water) for space heating and cooling.
• Key idea: today, buildings are heated/cooled via an energy-transfer fluid (air or water).
• Practical comparison: air vs. water as heat-transfer media depends on their heat capacities and densities (3.9 discussion).
• Relative heat capacities:
  • Air has much lower density and much less specific heat than water; storing/transferring equal amounts of heat requires ~3000 times the volume of air compared to water (Fig. 3.6).

3.9 RADIATION

• Radiant heat is energy transfer via electromagnetic waves; all bodies emit and absorb radiant energy continuously.
• Net radiative heat loss occurs from hotter to cooler bodies; hotter objects emit more energy.
• Emission depends on temperature and surface properties; radiation can occur through vacuum or air.
• Surface interactions (Fig. 3.9b):
  • Transmittance: radiation passes through a material (transparent/ translucent).
  • Absorptance: radiation is absorbed and heats the material.
  • Reflectance: radiation is reflected off the surface.
  • Emittance: surface emits radiation, reducing the surface’s sensible heat content.
• For opaque materials: absorptance + reflectance = 1 (the remaining portion is emitted or absorbed depending on properties).
• Shortwave vs longwave interactions:
  • Glass interacts differently with solar shortwave radiation vs thermal longwave infrared radiation.
  • Glass is mostly transparent to shortwave solar radiation; opaque to longwave infrared radiation, absorbing and re-emitting some energy.
• Radiant barriers: polished metals (e.g., aluminum foil) can reflect and emit poorly, reducing radiant heat transfer; used as radiant barriers in buildings.
• Radiation description by wavelength/frequency: often described by wavelength; important to distinguish solar shortwave radiation from longwave infrared emitted by objects at room temperature.

3.10 GREENHOUSE EFFECT

• Core idea: glazing transmits shortwave solar radiation but blocks longwave infrared radiation, trapping heat (heat trap).
• Mechanism (Fig. 3.8a): solar radiation passes through glass, is absorbed by indoor objects, which then re-emit in the longwave infrared; glass is opaque to much of this radiation, trapping heat indoors.
• Glass transmission windows (Fig. 3.8b): glass transmits about 90% of visible and short-wave IR, but blocks most long-wave IR; UV is largely transmitted (0–80% depending on wavelength) but UV contributes to fading and solar effects; UV exposure is more damaging at shorter wavelengths.
• Conceptual takeaway: greenhouse effect explains how building interiors warm when exposed to sun through glazing; important for design decisions about glazing, shading, and ventilation.

3.11 EQUILIBRIUM TEMPERATURE OF A SURFACE

• Equilibrium temperature depends on absorptance (how much solar energy is absorbed) and emittance (how much longwave energy is emitted).
• Colors and finishes influence equilibrium temperature:
  • White paint is a poor absorber and a good emitter, leading to a low equilibrium temperature and less heat gain.
  • White metal/radiant barriers have high reflectance/low emittance, reducing heat absorption and heat storage.
  • A selective black surface (high absorptance for solar radiation but high emittance) can heat more than ordinary black due to greater emission of stored heat.
• Practical implication: white surfaces minimize heat gain in summer; polished metals (radiant barriers) reduce heat flow by limiting both absorption and emission; reflective strategies depend on both absorptance and emittance.
• Terminology: high emittance surfaces emit heat readily; low emittance surfaces retain heat; selective coatings balance absorption and emission for desired temperatures.

3.12 MEAN RADIANT TEMPERATURE (MRT)

• MRT explains radiant thermal environment for a point in space.
• Definition: MRT is the weighted average radiant temperature of all surfaces in view, taking into account exposure angles.
• Conceptual formula (simplified two-dimensional version, Sidebox 3.1):
  • ext{MRT} = rac{igl( extstylerac{T1}{ heta1} + rac{T2}{ heta2} + rac{T3}{ heta3} +
    dotsigr)}{360^ ext{o}}
  • A more precise form uses solid angles: ext{MRT} = rac{rac{T1}{ heta} + rac{T2}{ heta} + rac{T_3}{ heta} +
    dots}{360^ ext{o}}
• Practical interpretation: MRT reflects radiant exposure from all surfaces; warmer exposure angles or higher surface temperatures increase MRT and radiant heating; cooler windows can reduce MRT.
• Example: radiant heat from a fireplace (high temperature, small exposure angle) can yield a high MRT; radiant ceiling (lower temperature but large exposure area) can yield comparable radiant effect.
• MRT and thermal comfort are connected; MRT effects are discussed further in the next chapter.

3.13 HEAT FLOW

• Fundamental principle: heat flows naturally from higher to lower temperature; does not flow between bodies at the same temperature.
• Water analogy: heat flow depends on temperature difference (potential) rather than total heat content; equal reservoirs with different levels have flow from high to low; adding a pump can raise heat to a higher temperature (Fig. 3.11).
• Heat pumps (e.g., refrigerators) move heat from lower to higher temperature; refrigeration and air-conditioning systems operate on this principle (to be elaborated in Chapter 18).
• Units of heat flow:
  • In I-P (inch-pound) system: heat flow is measured in Btu/h; heat-delivery equipment rated in Btu/h.
  • In SI: heat flow is measured in watts (W) = J/s.
• Relationship between heat flow and temperature difference is governed by thermal resistance and conductance; leads to definitions of R-values and U-factors (see 3.16–3.17).

3.14 HEAT SINK

• Concept: a heat sink absorbs heat; the term “coolth” is discouraged; heat sink describes cooling via heat absorption.
• In a room cooled by chilled water, the water acts as a heat sink and warms up as it absorbs heat from the room (Fig. 3.12, top).
• The mass of a building can act as a heat sink: during the night, stored heat is released to the cool night air, recharging the building’s heat-sink capacity for the next day (Fig. 3.12, bottom).
• Limitation: in very humid climates, nighttime temperatures may not drop enough to recharge the heat sink effectively; massive buildings are not as effective heat sinks in such climates.
• Practical takeaway: mass and water temperature strategies work with proper climatic context.

3.15 HEAT CAPACITY

• Definition: the amount of heat required to raise the temperature of a material by 1 unit (°F or °C).
• Characteristics:
  • Heavy materials generally have higher heat capacity, but water is an exception with the highest heat capacity per mass.
  • In architecture, heat capacity per volume (volumetric heat capacity) is often more relevant than per mass (Fig. 3.13).
• Comparison (illustrated): water vs concrete; for equal temperatures, water stores more heat per volume than concrete; hence water is widely used for heat storage and transfer (Fig. 3.6).
• Related concept: specific heat (per unit mass) vs volumetric heat capacity (per unit volume).

3.16 THERMAL RESISTANCE

• Thermal resistance measures opposition to heat flow via conduction, convection, and radiation.
• Material resistance depends heavily on air spaces within materials (cellular structure reduces conduction/convection).
• Example: 1 inch (or 1 cm) of wood can have similar resistance to 12 inches (12 cm) of concrete due to air pockets in wood (Fig. 3.14); this equivalence holds under steady-state conditions.
• Dynamic conditions require the concept of time lag (3.18) to explain apparent differences in effective resistance.
• Radiant barriers (e.g., aluminum film) provide resistance to radiant heat transfer; they reflect radiation and have high reflectance and low emittance.

3.17 HEAT-FLOW COEFFICIENT (U-COEFFICIENT)

• In many technical texts, thermal characteristics are described as U-values (heat-flow coefficient) rather than pure R-values.
• Key relationships:
  • Thermal resistance: $R<em>{ ext{total}} = ext{sum of all resistances} = R</em>1 + R<em>2 + R</em>3 + \ldots$
  • U-coefficient: $U = \frac{1}{R_{ ext{total}}}$
• Interpretation: smaller U-coefficients indicate better insulation (lower heat flow); larger R-values indicate better insulation. In practice, higher R is desirable and lower U is desirable.
• Additional descriptors: some sources provide conductivity (k) and conductance (c) for specific materials:
  • Conductivity: $k$ = heat flow rate through a material per unit thickness for a given temperature difference (e.g., W/(m·K)).
  • Conductance: $c$ = heat flow rate through a material per unit area for a given thickness (e.g., W/(m^2·K)).

3.18 TIME LAG

• Time lag: delay in heat flow through a wall due to thermal mass and storage capacity.
• Example (Figure 3.14): two walls with equal steady-state heat flow in a constant difference; however, in dynamic conditions (diurnal outdoor temperature swings), heat penetrates the wall at different rates due to storage in mass.
• Key idea: heavy walls with high heat capacity warm slowly in the day and release stored heat at night, delaying indoor heat gain; lightweight walls heat up faster.
• Water analogy for time lag: pipe friction = thermal resistance; storage tank = thermal capacity; larger storage leads to greater time lag (Fig. 3.15).
• Practical implication: time lag can reduce peak cooling/heating loads in summer, depending on climate and mass; the effect is climate-dependent.

3.19 INSULATING EFFECT OF MASS

• In hot, dry climates with large daily temperature swings, mass can act as an insulator by delaying heat flow and reducing peak interior temperatures (the insulating effect of mass).
• Visualization: Gothic cathedrals and earth-sheltered buildings benefit from mass for cooling; the mass stores heat during the day and releases it at night.
• Limitations:
  • Benefits require significant diurnal temperature swings; in climates with small swings or very humid conditions, mass may not provide benefits and can be counterproductive.
  • The insulating effect of mass does not replace conventional insulation; mass works best in conjunction with proper insulation.

3.20 ENERGY CONVERSION

• First law of thermodynamics: energy cannot be created or destroyed; it can only change form.
• Second law: energy quality or ability to do work can degrade; not all energy can be converted to useful work at the same efficiency.
• Example: high-temperature steam can drive a turbine to generate electricity; warm water cannot provide the same work as steam.
• Concept: electricity is a high-grade energy; using it to provide heating is less efficient than using heat directly (thermal energy) where possible.

3.21 COMBINED HEAT AND POWER (CHP)

• CHP (cogeneration): on-site generation of electricity and useful heat from the same energy source (e.g., natural gas).
• Benefits: reduces energy losses associated with electricity transmission; captures heat that would otherwise be wasted at a central power plant.
• Efficiency: on-site CHP can yield up to about 80% useful energy, compared to about 30% usable energy from centralized gas-powered electricity (Fig. 3.18a).
• Economic and environmental implications: reducing transmission losses and improving overall energy efficiency; aligns with goals of minimizing fossil energy waste when using fossil fuels.

Sidebox 3.1 Mean Radiant Temperature (MRT)

• MRT is the weighted average radiant temperature at a point, considering exposure angles of all surfaces in view.
• Practical two-dimensional version (plan/section):
  • $ext{MRT} = \frac{ ext{sum of }T<em>i imes ext{exposure angle } heta</em>i}{360^ ext{o}}$
• Example interpretation: a large, cooler surface with a high exposure angle (e.g., radiant ceiling) can contribute significantly to MRT even if its temperature is lower than a fire, due to the larger exposure area.
• Importance: MRT is one of four factors determining thermal comfort; central to evaluating radiant heat gains and comfort in spaces.

Sidebox 3.2 RSI (R-value) and Sidebox 3.3 U-coefficient

• RSI (Metric): RSI value = $R$-value in metric units; used to express thermal resistance per area.
• R-value (I-P units) and RSI conversion: $R$-value = sum of thermal resistances; larger R means greater resistance to heat flow.
• U-coefficient (heat-flow coefficient) = reciprocal of total thermal resistance: $U = \frac{1}{R_{ ext{total}}}$
• Conductivity (k) and conductance (c) definitions, to be used with material properties for design calculations.

Summary of key relationships and concepts

• Sensible heat: $Q = m c \, \Delta T$
• Latent heat: $Q = m L<em>f \quad\text{(fusion)}$; $Q = m L</em>v \quad\text{(vaporization)}$
• Heat flow through a layer: $\dot{Q} = \frac{\Delta T}{R<em>{ ext{total}}} = U A \Delta T</em>{ ext{lm}}\text{ (for problems using R or U)}$
• Thermal resistance: $R<em>{\text{total}} = \sum</em>i R<em>i$; U-value = $U = \frac{1}{R</em>{\text{total}}}$
• Equilibrium temperature depends on absorptance and emittance; color/finish affects both.
• Greenhouse effect: glazing transmits shortwave solar radiation but blocks longwave infrared; glass properties define heat gain.
• Mean Radiant Temperature (MRT): radiant environment effect from all visible surfaces; calculated with exposure angles and surface temperatures.
• Time lag: storage capacity delays heat flow; mass can provide a thermal buffer in appropriate climates.
• CHP: on-site generation improves overall energy use by reclaiming heat; high overall efficiencies possible.

Practical and real-world implications

• Surface color and finish selection dramatically influence cooling loads; white or low-emittance surfaces reduce heat gains.
• Radiant barriers and reflective strategies can materially reduce cooling loads, especially in hot climates.
• Community and policy relevance: energy efficiency measures, building codes, and material choices impact embodied energy and climate goals.
• Climate considerations: insulating mass helps in hot-dry climates with large day-night temperature swings, but may be detrimental in humid climates with small swings.
• Modern design should balance insulation (R-values), radiant control (emittance/reflectance), and sensible heat management (mean radiant temperature) for comfort and efficiency.

Formulas and units (quick reference)

• Sensible heat: $Q = m c \Delta T$
• Latent heat of fusion: $Q = m L_f$
• Latent heat of vaporization: $Q = m L_v$
• Radiant temperature balance (MRT): $\text{MRT} = \frac{\sum<em>i T</em>i \Theta_i}{360^\circ}$
• Thermal resistance: $R<em>{\text{total}} = \sum</em>i R_i$
• Heat flow (coefficient): $U = \frac{1}{R_{\text{total}}}$
• Energy conversion and CHP considerations: efficiency gains when using CHP vs centralized generation; on-site efficiencies can reach ~80% vs ~30% for centralized plants when considering useful energy delivered (illustrative).

Notes on units and prefixes

• Heat and temperature units:
  • I-P: Btu, Btu/h; °F.
  • SI: J, cal; W, J/s; °C or K; 0 K = -273.15°C.
• Prefixes: Mega (10^6), Giga (10^9), Tera (10^12) with examples such as MW, GW, TW scales.

End of notes on 3.1–3.21 (and related sideboxes)

• Core themes: energy forms (sensible, latent, radiant), heat transfer mechanisms (conduction, convection, radiation), the role of materials and surface properties, the importance of temperature differences and mass, and the practical implications for building design and operation (insulation, mass, moisture, glazing, and energy systems like CHP).