Determination of Thermal Conductivity

Responsible:

Bodo Erdmann, Jens Lang, Rainer Roitzsch

Cooperation:

M.J. Lourenco, S.C.S. Rosa, C.A. Nieto de Castro, C. Albuquerque
University of Lisbon, Portugal

Literature:

M.J. Lourenco, S.C.S. Rosa, C.A. Nieto de Castro, C. Albuquerque, B. Erdmann, J. Lang, R. Roitzsch, Simulation of the Transient Heating in an Unsymmetrical Coated Hot-Strip Sensor with a Self-Adaptive Finite-Element Method, Int. J. Thermophysics, Vol. 21, No.2 (2000) , 377-384.

Measurement of the thermal conductivity of molten materials is very difficult, mainly because the mathematical modelling of heat transfer processes at high temperatures, with several different media involved, is far from being solved. However, the scatter of the experimental data presented by different authors using several methods is so large that any scientific or technological application is strongly limited without serious approximations.
The development of new instruments for the measurement of the thermal conductivity of molten salts, metals, and semiconductors implies the design of a specific sensor for the measurement of temperature profiles in the melt, apart from the necessary electronic equipment for the data acquisition and processing, furnaces, and gas/vacuum manifolds.
In our application, we consider a planar, electrically conducting (metallic) element mounted within an insulating substratum. This equipment is surrounded by a material whose thermal properties have to be determined, see Figure 1. From an initial state of equilibrium, Ohmic dissipation within the metallic strip results in a temperature rise on the strip, and a conductive thermal wave spreads out from it through the substratum into the surrounding material. The temperature history of the metallic strip, as indicated by its change of electrical resistance, is determined partly by the thermal conductivity and the diffusivity of this material.

Figure 1: Scheme of the hot-strip sensor
In order to identify the thermal conductivity of the material from available measurements, a heat transfer equation in two space dimensions has to be solved several times. Due to strongly localised source terms and different properties of the involved materials, we observe at the beginning steep gradients of the temperature profiles that decrease in time. In such a situation, a method with automatic control of spatial and temporal discretization is an appropriate tool, see Figure 2.

Figure 2: Adaptive grid and isotherms of the corresponding solution at time t = 1.0.
Figure 3 shows the result obtained for a specially designed sensor. The agreement is quite satisfactory, and it results in a water thermal conductivity of 0.606 Wm^-1K^-1 at 25^oC, a value within 0.1 % of the recommended one.
Preliminary numerical calculations with mercury, NaCl aqueous solutions, and toluene showed the same trend.

Figure 3: Simulation for water at 25^oC