International Journal of Thermophysics

, Volume 35, Issue 6–7, pp 1156–1168 | Cite as

Numerical Modeling of Thermal Effects in Fixed-Point Cells

  • V. Batagelj
  • J. Bojkovski
  • V. Žužek
  • J. Drnovšek


In recent years, numerical modeling of heat transfer in fixed-point cells has become a useful tool for the investigation of various thermal effects, leading to optimized measurement setups and procedures, as well as more realistic uncertainty estimations. Although numerical modeling of heat transfer is commonly used in many scientific and industrial projects, its application in primary thermometry presents several challenges. Besides the required high accuracy, the major challenge is the correct implementation of radiative heat transfer, which must take into account effects such as reflection, refraction, scattering, emission, absorption, etc. Correct modeling of thermal radiation is especially important for temperatures above \(400\,^{\circ }\hbox {C}\), where thermal radiation becomes the dominant mode of heat transfer. In this paper, the results of modeling with a custom-made numerical model are presented. The model is based on the finite difference method and calculates the steady-state solution in 2D cylindrical coordinates with axial symmetry. Radiation is modeled using the discrete ordinates method, which calculates the radiation intensity in every point in a specified number of fixed directions. Computation of the radiation intensity is extremely computationally demanding, but it provides a way of accurately handling all radiation-related thermal effects. The input data for the model geometrical properties are provided in a form of a bitmap image, which enables simple adjustment for different model configurations. Special emphasis is given to accurate modeling of total internal reflection in a glass assembly, which results in a light-piping effect. Reduction of this effect by sandblasting of glass surfaces is investigated.


Fixed-point cell Light piping Numerical modeling   Radiative heat transfer Sandblasting 



This work was partially supported by the Ministry of Economic Development and Technology, Metrology Institute of the Republic of Slovenia in scope of Contract 6401- 18/2008/70 for national standard laboratory for the field of thermodynamic temperature and humidity and EMRP project NOTED (Novel Techniques for Traceable Temperature Dissemination JRP NUMBER: SIB10).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • V. Batagelj
    • 1
  • J. Bojkovski
    • 1
  • V. Žužek
    • 1
  • J. Drnovšek
    • 1
  1. 1.Metrology Institute of the Republic of Slovenia/University of Ljubljana-Faculty of Electrical Engineering/Laboratory of Metrology and Quality (MIRS/UL-FE/LMK)LjubljanaSlovenia

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