Problem Description:

This problem was taken from Thermal Radiation Heat Transfer, by Robert Siegel and John R. Howell. 

Figure 3. Problem # 2 from R. Siegel and J.R. Howell, Thermal Radiation Heat Transfer (Hemisphere Publishing Corporation, New York, 1981) pp726-727.

This problem is similar to the previous validation, except there is one plate of glass above another surface with a given absorptivity. This second surface will be called the collector. The goal of this problem is to determine the fraction of energy absorbed by the collector.

Geometry Description:

The geometry for this validation consists of two elements 1.0m x 1.0m, separated by a 1.0mm air gap. The first element is the piece of glass and the second is the collector. The 1.0mm separation is to reduce the end effects due to solar radiation. The following diagram shows the glass plate and collector. It also shows how the energy reflected from the collector is reflected again off the glass and absorbed by the collector. 

Model Conditions:

The first element is Conventional Automotive Glass and the second element has an assigned surface condition. The back of the collector is insulated. The surface properties are listed in the table below:

Table 4:  Surface Properties for Problem #2

The collector will only absorb some energy and will reflect the rest. The amount reflected will be absorbed by the glass, transmitted through the glass, and reflected back to the collector. The problem is to test the accuracy of the fraction absorbed by the collector. 

Because the fraction of energy absorbed, transmitted, and reflected by the plates will not change over time, the time in which results are taken is irrelevant.  The numbers used here were taken at July 19, 1984 at 12:00. 

Environment:

The environment has a solar absorptivity equal to 1.0. This will eliminate any reflections from the background.  

Simplifying Assumptions:

There were no simplifying assumptions used in creating the RadTherm model. In order to calculate the fraction of energy absorbed by the collector, Equation 19-13 in Figure 3, only the transmittance, reflectance of the glass and the absorptivity of the collector are needed. Within RadTherm the amount of solar energy absorbed is readily available.  

Objective:

To produce the same results using an analytical solution and using the numerical solution within RadTherm.

TAI Results:

In order to get the energy fraction absorbed by the collector, you must first know the total solar energy. Total solar energy is available in the Post Processor – Environment Tab. This is the total solar energy in the entire environment at that time step.

The net solar energy (Q Solar) absorbed by the collector is available in the Post Processor – Results Tab. Once you have the net solar absorbed, divide this by the total solar to get the absorbed fraction.

Table 5: Results for Problem #2

Again the relative error between RadTherm and the analytical solution is insignificant.

Download this validation model.