For: Tech Traders
By: H. F. Poppendiek
April 2004

GEOSCIENCE LTD
6260 Marindustry Drive
San Diego, California 92121

1. Introduction
2. Mathematical Thermal Wall or Roof Model
3. Building Envelope Energy Savings and Add-On Mass Insulation Calculations
4. Calculation Results
5. Concluding Comments

Introduction

Geoscience was requested by Mr. David Page to 1) prepare a thermal model that can be used to determine the energy savings that result when painting the exterior surfaces of a building envelope with a solar reflective paint such as Insuladd, 2) perform such energy savings calculations for building envelopes having insulation R values ranging from R3 to R30 and 3) determine how much more mass insulation would have to be added to the building envelope to achieve the reduced heat flow into the building envelope when using the Insuladd paint.

The following sections of this report describe the modeling work, as well as the building envelope energy savings and add-on mass insulation calculations.

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Mathematical Thermal Wall or Roof Model

An elementary model is presented which gives the steady state wall or roof irradiated surface temperature and the required room cooling heat flux to maintain a given room temperature when the outside weather conditions are known (see Figure 1 A and 1B). Specifically, the solar heat flux absorbed at the outer building envelope is partially conducted through the insulation into the room and partially lost from the outer building envelope to the outside air and surroundings by convection and infrared radiation. The heat transfer balance for this system is,

It is noted that solar radiation information can be obtained from ASHRAE Fundamentals; this parameter is a function of time of the year, time of the day and the latitude. The convective conductance is a function of free convection and forced convection; ASHRAE can be consulted for more details. The radiation conductance is primarily controlled by the infrared emissivity of the outer building envelope surface.

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Building Envelope Energy Savings and Add-On Mass Insulation Calculations

Six different building envelope systems were analyzed for energy savings and mass insulation add-on using the thermal model Equations 1 and 2. Specifically, three different insulation resistances (R2, R10, and R30) were considered. Two different exterior paints were also included; one paint was the Insuladd type, having a solar reflectivity of 0.81 and an infrared emissivity of 0.75; a second paint was an ordinary type having a solar reflectivity of 0.75 and an infrared emissivity of 0.85. In addition, the sum Rwb + Ri = 0.63 + 0.68 = 1.3 hr ft2 °F/Btu. The outside surface heat transfer conductances for a 3 mph wind are hc + hr = 2 + 0.75 = 2.75 Btu/hr ft2 °F for an Insuladd paint surface and hc + hr = 2 + 0.85 = 2.85 Btu/hr ft2 for an ordinary paint surface. In addition, a mean solar irradiation of G = 200 Btu/hr ft2 was specified, as were t0 = 90 °F and ti = 75 °F.

The above set of representative data was used to calculate the temperature and heat flux values appearing in Equations (1) and (2) for the six different building envelope systems. The calculations for the additional mass insulations that would be required in the system having ordinary paint on the exterior surface of the building envelope (to obtain the reduced cooling heat fluxes) are a trial and error type. Table I shows the calculation results.

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Table I Calculation Results

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Concluding Comments

The representative calculations illustrate the advantages resulting from using Insuladd solar reflective paint on the outside of building envelopes. Specifically, the energy savings are significant.

It is also pointed out that the energy savings are controlled by a number of system parameters that appear in the model equations. When the magnitudes of these parameters change, the temperatures and heat flux values change.

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