Glazing Conduction Calculation

Window Conduction Gain, Glazing Conduction, EnergyPlus, Heat Balance Method Written by Patrick Pease
Updated over a week ago

There are many methods to calculate the heat gains from a glazing element. Typically the heat gains are divided into two components, the Conduction related to the U-value and the Radiation related to the SHGC. Dividing the heat gains in this fashion is helpful because it allows key characteristics of the glazing, U-value and SHGC, to be considered in regard to their impact on cooling loads.

# Focusing on Conduction

Conduction gain or loss can be calculated in various methods with different degrees of detail. The simplest calculation method is to consider the u-value, area, indoor, and outdoor temperature as described by Equation 14, ASHRAE Handbook Fundamentals Chapter 18.

Q = U * A * (Tout - Tin)

This method accounts for the thermal transmittance of the element and the respective temperatures and is very helpful for hand calculations.

EnergyPlus uses the Heat Balance method for calculations, which covers four specific heat transfer processes in a building:

1. Outdoor face heat balance

2. Wall conduction process

3. Indoor face heat balance

4. Air heat balance

The Heat Balance method is defined in ASHRAE Handbook Fundamentals Chapter 18 and is a well established and widely used method for cooling load calculations. In EnergyPlus, the Heat Balance methodology is applied to windows or glazing elements. Currently windows in the calculation default to a single layer which represents the performance values. A brief summary of the input variables and equations is included at the end of this article. In addition, here are links to the full documentation of the Windows Module and Window Heat Balance Calculation.

The Heat Balance method is used to calculate all peak, and coincident loads for zones, air systems, and the building. This method results in a single combined design load for each zone. To help understand the breakdown at peak times EnergyPlus utilizes a secondary method to estimate these values.

# Glazing Result Variables

EnergyPlus produces several output variables for every element of the model. This allows for powerful study of heat, energy, and radiation transfers throughout the building. Full documentation of the window outputs from EnergyPlus can be found here. For a window without interior shading the total heat flow is equal to:

• Surface Window Transmitted Solar Radiation Rate

• Convective heat flow to the zone from the zone side of the glazing

• Net IR heat flow to the zone from zone side of the glazing

• Short-wave radiation from zone transmitted back out the window

• Convection to zone from window frame and divider, if present

A good way to think about this is the sum of the solar and conductive gain to the zone from the window.

Glazing conduction results are reported for Rooms, Zones, and Air Systems on the platform. Checkout more about the load modeling results here.

In order to report a breakdown of heating and cooling load components the sensible and delayed loads a version of the Radiant Time Series method is performed for each zone. At time of peak, each surface of a zone contributes a convective heat loss or heat gain determined by the surface temperature.

For glazing the radiant gains from internals sources and solar are subtracted from the total convective gain on each surface. In this way glazing load is reported as conduction which is an instant gain and radiation which is a delayed gain. The image below shows reported variables by EnergyPlus and if the portion which is instantaneous and delayed. Note that Glazing is referred as Fenestration in this table.

Full description of EnergyPlus method to calculation the component load breakdowns is found in the Engineering Reference. The Estimated Component reports can be accessed for all simulations in the `eplustbl.htm` found in the Building Analysis Model export.

# Differences in calculations

When comparing the results of the simplified hand calculation to the detailed, physics based calculations used by EnergyPlus these will not match exactly. Why they are different and what this means for HVAC system designs that are based on these loads is important. Here are some key points:

• The glazing conduction reported by EnergyPlus includes the inward flow of heat from the internal and external surface temperatures.

• This include the heat flux from through the glass material and any gaps present in the assembly

• The calculation of U-value is determined at each time step as it is dependent on the temperatures

• Unlike the simplified method the EnergyPlus method includes impact of the solar radiation absorbed by the glass itself, this increases the heat transfer

But the simplified Q = U * A * (Tout - Tin) method of determining the glazing conduction gain has not caused a problem for the many years it has been in use, why the change?

• This is a fair question with millions of projects successfully delivered without problems. The goal of the EnergyPlus engine is to deliver more than just peak load sizing, such as the surfaces temperatures, energy consumed, and other performance values at each time step. These items require the more detail calculation to ensure accuracy for these complex calculations, hence the more advanced method is used.

• The more advanced calculations are including more details into the reported peaks for heating and cooling loads. The additional detail, while not required for many design tasks, can help with more complex designs and therefore are helpful to include.

## Glazing Heat Balance Equations

Summary of variables, equations, and diagram explaining location of the variables. Full description of the method can be found here.

 Mathematical variable Description Units N Number of glass layers - α Stefan-Boltzmann constant εi Emissivity of face i - ki Conductance of glass layer i W/m2-K ho, hi Outside, inside air film convective conductance W/m2-K hi Conductance of gap j W/m2-K To, Ti Outdoor and indoor air temperatures K Eo, Ei Exterior, interior long-wave radiation incident on window W/m2 θi Temperature of face i K Si Radiation (short-wave, and long-wave from zone internal sources) absorbed by face i W/m2 Iextbm Exterior beam normal solar irradiance W/m2 Iextdif Exterior diffuse solar irradiance on glazing W/m2 Iintsw Interior short-wave radiation (from lights and from reflected diffuse solar) incident on glazing from inside W/m2 Iintlw Long-wave radiation from lights and equipment incident on glazing from inside W/m2 φ Angle of incidence radians Afj Front beam solar absorptance of glass layer j - Af,diffj, Ab,diffj Front and back diffuse solar absorptance of glass layer j - A, B Matrices used to solve glazing heat balance equations W/m2, W/m2-K hr,i Radiative conductance for face i W/m2-K Δθi Difference in temperature of face i between successive iterations K

Glazing system with two glass layers showing variables used in heat balance equations. Source: EnergyPlus 22.2 Engineering Reference manual

The four equation used in the heat balance calculation are: