Assessing the RELAPS-3D Heat Conduction Enclosure Model Page: 3 of 12
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2008 RELAP5 International Users Seminar B-T-3741
Idaho Falls, ID
November 18-20, 2008
(2) The heat conduction enclosure model heat flux is advanced in time explicitly. For radial conduction
enclosure connections, calculational stability can be affected by the choice of conductance. If there is
real thermal resistance modeled, such as a gap, then that should be used and should result in stable
calculations. However, problems can arise if the two conductors are in physical contact and a very
large conductance is appropriate.
(3) The conductance is time-invariant. Therefore any thermal conductivity used in calculating the
conductance should represent an average value over the transient.
Although the axial limitation and the time-invariant conductance are unavoidable, there is a rule of thumb that
can be applied to help choose a conductance value for conductors in contact that gives stable calculations. That rule
of thumb is Equation (1).
Conductance < (0.5(Ax)2/(aAt) - 1)(k/Ax) (1)
Equation (1) was derived from guidance on computational stability in explicit numerical integration of the heat
conduction equation (Incropera, 1985).
RELAP5-3D COMPARED TO CONDUCTION MODEL SOLUTIONS
In the following sections three conduction problems which are exact solutions to the heat conduction equation
will be discussed. Each problem will be described, the equation for its exact solution presented, the RELAP5-3D
model will be summarized and the calculational results compared in the following sections. The stability check for
each problem will also be discussed.
In order to derive exact solutions to the heat conduction equation, simplifying assumptions are usually required.
Some of those assumptions tend to be consistent with the limitations in the RELAP5-3D heat conduction enclosure
model. For example, in the three exact solutions analyzed in this paper, all assume time invariant conductance. In
addition, the long thin rod assumes constant temperature over the cross section, which is consistent with the
limitation in the heat conduction enclosure model that connections can only be made at the radial faces. Thus, real
problems may not be predicted as accurately as those analyzed in this paper.
Problem 1: Steady-State Temperature in a Rectangle
The steady-state temperature distribution in a rectangle (no temperature dependence on the 3rd dimension) using
Cartesian coordinates with three sides held at temperature T and the fourth side at To is described by Equation (2)
(Carslaw, 1959).
4(T-T00) . (2n+1),n. (b-y)(2n+1)z (2n+1)b
T(x,y) -T = sin sinh csch (2)
n=0(2n+1) a a a
The rectangle goes from 0 to a in the x dimension and 0 to b in the y dimension. In this example, the
value for a is 0.92 and the b value is 1.0.
In the RELAP5-3D model, 25 heat structures were developed with 25 axial and 1 radial conductors in each. The
heat conduction enclosure model was used to connect the heat structures to one another both radially and axially.
The radial conductance used was chosen to be large to reflect excellent contact between the two conductor surfaces.
The conductance value used was chosen to maintain temperatures in radial mesh points in contact within 1 K of each
other. The conductance axially is the metal thermal conductivity divided by the distance between heat conductor
centers.
A RELAP5-3D model without the axial heat conduction provided by the heat conduction enclosure model
calculates linear temperature variation in the y-coordinate between the temperature at 0 and the temperature at 1.0.
The heat conduction enclosure model is needed to connect the axial conductors to the lower temperatures at the ends
of the x-coordinates of the rectangle. That heat transfer causes the non-linear temperature response.
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McCann, Larry D. Assessing the RELAPS-3D Heat Conduction Enclosure Model, report, September 30, 2008; West Mifflin, Pennsylvania. (https://digital.library.unt.edu/ark:/67531/metadc895755/m1/3/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.