Question

Why are the windows considered in three regions when analyzing heat transfer through them? Name those regions, and explain how the overall \(U\)-value of the window is determined when the heat transfer coefficients for all three regions are known.

Short answer

Answer: Windows are divided into three regions - the glazing system, edges of the glazing system, and the frame - due to the different heat transfer mechanisms and properties in each region, making it necessary for accurate evaluation of heat transfer. To determine the overall U-value, we need the heat transfer coefficients (U-values) for each region and their respective areas, then apply the formula: Overall U-value = Σ(U_i × A_i) / Σ(A_i). The overall U-value represents the average heat transfer rate through the entire window per unit area, with lower values indicating better insulation properties.

Step-by-step solution

Introduction to Heat Transfer through Windows

Windows play a vital role in maintaining the energy balance and comfort level inside a building. Heat transfer through windows occurs via three mechanisms: conduction, convection, and radiation. To accurately analyze the heat transfer, windows are divided into three regions.

Naming the Three Regions

The three regions of a window are: 1. The glazing system (glass or other transparent materials) 2. The edges of the glazing system 3. The frame (surrounding the glazing system)

Importance of the Three Regions

Each of the three regions exhibits different heat transfer mechanisms and properties, so they must be considered individually to establish an accurate overall heat transfer model for the entire window. For example, the glazing system's heat transfer may be dominated by radiation, while the frame and edge regions may be affected more by conduction and convection.

Determining the Overall \(U\)-value

The \(U\)-value, also known as the thermal transmittance, is a measure of how effective a building material is as an insulator. To determine the overall \(U\)-value of the window, we need the heat transfer coefficients (U-values) for all three regions and their respective areas. The formula is: Overall \(U\)-value = \(\frac{\sum{U_i \cdot A_i}}{\sum{A_i}}\) Where \(U_i\) is the \(U\)-value for each region (glazing, edge, and frame) and \(A_i\) is the area of each region. The overall \(U\)-value represents the average heat transfer rate through the entire window per unit area. The lower the \(U\)-value, the better the insulation properties of the window.