Study Notes on Heat Conduction through Building Opaque Sections

HEAT CONDUCTION THROUGH BUILDING OPAQUE SECTIONS

Introduction

• Lecture Reference: Textbook - "Heating, Ventilating, and Air Conditioning Analysis and Design, Sixth Edition" by Faye C. McQuiston and Jerald D. Parker.
• Instructor: Dr. Rani Taher, Associate Professor of Mechanical Engineering.
• Contact Information: rani.taher@aum.edu.kw.

Learning Objectives

Upon completing the study of this chapter, students should be able to:

• Understand steady-state heat conduction through building opaque sections.
• Comprehend the concept of thermal resistance and its limitations; develop thermal resistance networks for practical heat conduction problems.
• Predict steady-state heat flow and temperature gradients in single and multi-layered walls.
• Analyze parallel heat flows in real multilayer wall assemblies with thermal bridges.
• Understand heat conduction through below-grade and on-grade walls.
• Analyze transient heat conduction through walls.

Fundamentals of Heat Transfer in Buildings

• Definition of Heat Transfer: It is the transfer of thermal energy between objects at different temperatures.
• Importance:
  • Allows for the selection and sizing of HVAC equipment to maintain comfort.
  • Facilitates predictions of annual building energy consumption and costs.
  • Aids in understanding design trade-offs in energy-efficient buildings.

Energy Use Data Presentation

• Energy consumption chart for building cooling and heating.
  • Total cooling energy from January to December.
  • Heating energy in Btu during the same timeframe.

Building Science and Heat Transfer

• Basis of Heat Transfer in Buildings:
  • Arises from temperature differences between the interior and exterior.
  • The building envelope separates indoor and outdoor environments (walls, roofs, floors, windows, doors).
• Key Factors:
  • Internal heat gains that influence heating and cooling loads.
  • Understanding heat transfer principles is vital for HVAC and piping system design.

Modes of Heat Transfer

1. Conduction: Heat transfer through solids or stationary fluids.
2. Convection: Heat transfer from a surface to a moving fluid.
3. Radiation: Heat exchange between surfaces at different temperatures via electromagnetic waves.

Conduction

• Definition: Heat transfer resulting from molecular-level kinetic energy transfer in solids, liquids, and gases.
• Direction: Heat flows from areas of higher temperature to lower temperature (Example: heat loss through walls).
• Example Scenario:
  • External temperature: -10°C
  • Internal temperature of the wall surface: +18°C to +20°C.

Convection

• Definition: Involves larger-scale fluid motion (liquid or gas).
• Important Factors:
  • Velocity of fluid increases the rate of heat transfer.
  • Greater temperature differences enhance heat flow.
• Usage Example: Cold wind removing heat from a person's skin.

Radiation

• Definition: Energy transport by electromagnetic waves.
• Involves absorption by matter for energy conversion to internal energy.
• Examples:
  • Solar energy reaching the Earth (shortwave radiation).
  • Longwave radiation emitted by the Earth into the atmosphere.

Primary Modes of Heat Transfer in Buildings

• Conduction: Through opaque materials of the building.
• Convection: Includes infiltration/exfiltration processes.
• Radiation: Conduction and internal sources contributing to thermal performance.

Building Materials and Heat Transfer

• Common Construction Materials:
  • Wood, bricks, concrete, gypsum board, insulation materials (e.g., fiberglass, expanded polystyrene).
• Example Materials:
  • Thermal Conductivity Values:
  • Metallic alloys: 8-70 Btu/(h·ft·°F)
  • Pure metals: 30-240 Btu/(h·ft·°F)
  • Insulating materials: 0.02-0.12 Btu/(h·ft·°F).

Conduction Equation

• Fourier's Law for Heat Conduction:
  • $q = -k <br />\nabla T$
  • Where:
    • $q$ = heat flux per unit area [W/m²]
    • $k$ = thermal conductivity [W/(m·K)]
    • $<br />\nabla T$ = temperature gradient.

Simplified Conduction for One-Dimensional Flow

• $q = -k \frac{(T<em>1 - T</em>2)}{L}$
  • Where
  • $L$ = thickness of the material.

Heat Flow vs. Heat Flux

• Heat Transfer Calculation: For total heat $Q$:
  • $Q = qA$
  • Converts heat flux [W/m²] to total heat flow considering area A [m²].

Thermal Conductance and Resistance

• Definitions:
  • Conductance, $U$, is the rate of heat transfer through a structure.
  • Resistance, $R$, is the ability to resist heat flow.
• Formulas:
  • $R = \frac{L}{k}$
  • Inverse relation: $(U = rac{1}{R})$.

Units of R-values and U-values

• R-values used for insulating materials, while U-values are for conductive materials like windows.
• Conversion Factor:
  • $R<em>{ ext{IP}} = R</em>{ ext{SI}} imes 5.678$.

Thermal Conductivity of Materials (Typical)

• Key Examples Provided: Thermal conductivities for various materials, calculated across different conditions.
  • Examples include wood, concrete, and insulating materials such as glass fiber and expanded polystyrene.

Thermal Resistance in Series and Parallel

• Calculation of Overall Resistance: Total resistance is the sum for series resistors (i.e., construction layers).
• Formula for Series:
  • $R<em>{total} = R</em>1 + R<em>2 + R</em>3 + …$
• Parallel Resistance: Resistance models for structural elements like studs within insulating layers.

Example Calculation for a Wall with Insulation

• Composition: 10 cm of brick, 15 cm of fiberglass insulation, and 1 cm of gypsum board.
• Definitions: Given $k$ values for all materials, calculate overall R-value, $q$ through the layers, and interface temperatures.

Impact of Structural Elements on Thermal Resistance

• Thermal Bridges: The presence of structural elements like steel studs, leading to increased heat loss.
• This concept is crucial in calculating accurate thermal resistance and flow within buildings.

Insulation Placement in Buildings

• Common Locations: Roofs, exterior walls, foundation walls, and ductwork.
• Importance of following building codes and standards (e.g., ASHRAE, state regulations).

Combined Thermal Transmittance Calculation

• Formula:
  • $U = \frac{(U<em>{wall} A</em>{wall} + U<em>{window} A</em>{window} + U<em>{door} A</em>{door})}{A_{total}}$
• Practical example given involving walls, doors, and windows for overall thermal performance assessment.

Conclusion

• Understanding heat conduction through building materials and assemblies is crucial for energy-efficient design, ensuring comfort while being mindful of heat losses across various building elements.