**RSICC CODE PACKAGE PSR-399**

**1. NAME AND TITLE**

ORMDIN: 2-D Nonlinear Inverse Heat Conduction Code.

**2. CONTRIBUTOR**

Oak Ridge Gaseous Diffusion Plant, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

Fortran IV; IBM3033 (P00399/I3033/00)

**4. NATURE OF PROBLEM SOLVED**

ORMDIN is a finite-element program developed for two-dimensional nonlinear inverse heat conduction analysis as part of the Oak Ridge National Laboratory Pressurized Water Reactor Blowdown Heat Transfer (BDHT) program. One of the primary objectives of the program was to determine the transient surface temperature and surface heat flux of fuel pin simulators from internal thermocouple signals obtained during a loss-of-coolant accident experiment in the Thermal-Hydraulic Test Facility (THTF). ORMDIN was designed primarily to perform a transient two-dimensional nonlinear inverse heat conduction analysis of the THTF bundle 3 heater rod; however, it can be applied to other cylindrical geometries for which the thermophysical properties are prescribed functions of temperature. The program assumes that discretized temperature histories are provided at three thermocouple locations in the interior of the cylinder. Concurrent with the two-dimensional analysis, ORMDIN also generates one-dimensional solutions for each of the three thermocouple radial planes.

**5. METHOD OF SOLUTION**

The inverse heat conduction problem is generally solved by determining the surface temperature and surface heat flux from the temperature history measured at a set of discrete points in the interior of the body. ORMDIN, in treating an electrically heated composite rod with two-phase flow boundary conditions, uses temperature transients recorded by thermocouple probes in the rod to investigate the time history of surface conditions. The solution technique, which is an extension of a previously developed one-dimensional formulation, utilizes a finite-element heat conduction model and a generalization of Beck's one-dimensional nonlinear estimation procedure. The technique assumes several thermocouple sensors judiciously positioned in the interior of the material body. The unknown surface heat flux is discretized on the boundary domain of the body using a prescribed set of nodal points and suitable interpolating functions. These nodal point values are determined in a given time step with a procedure that utilizes interior temperatures at future times. The discretized approximation of the surface heat flux provides a conventional boundary condition for the forward problem in the next time step. An important feature of the method is that small time steps are permitted while avoiding severe oscillations or numerical instabilities due to experimental errors in measured data.

**6. RESTRICTIONS OR LIMITATIONS**

Maxima of 25 points to input the temperature-specific heat function, 25 points to input the temperature-thermal conductivity function and 8 nodes to describe the two-dimensional elements.

**7. TYPICAL RUNNING TIME**

Not noted.

**8. COMPUTER HARDWARE REQUIREMENTS**

ORMDIM was developed on the IBM 3033 mainframe computer.

**9. COMPUTER SOFTWARE REQUIREMENTS**

ORMDIN requires a Fortran IV compiler.

**10. REFERENCE**

B.R. Bass, J.B. Drake, and L.J. Ott, "ORMDIN: A Finite Element Program for Two-Dimensional Nonlinear Inverse Heat Conduction Analysis," NUREG/CR-1709, ORNL/NUREG/CSD/TM-17 (December 1980).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document and the Fortran IV source on one DOS diskette.

**12. DATE OF ABSTRACT**

August 2001.

** KEYWORDS:** HEAT TRANSFER; LOCA