Hot Wire Method

Hot Wire Methods for the Thermal Conductivity Measurement

1. Description of the method

The hot wire method is a standard transient dynamic technique based on the measurement of the temperature rise in a defined distance from a linear heat source (hot wire) embedded in the test material. If the heat source is assumed to have a constant and uniform output along the length of test sample, the thermal conductivity can be derived directly from the resulting change in the temperature over a known time interval [1]. The hot wire probe method utilizes the principle of the transient hot wire method. Here the heating wire as well as the temperature sensor (thermocouple) is encapsulated in a probe that electrically insulates the hot wire and the temperature sensor from the test material [2].

The ideal mathematical model of the method is based on the assumption that the hot wire is an ideal, infinite thin and long line heat source, which is in an infinite surrounding from homogeneous and isotropic material with constant initial temperature. If q is the constant quantity of heat production per unit time and per unit length of the heating wire (W.m^-1), initiated at the time t=0, the radial heat flow around the wire occurs. Then the temperature rise DT(r,t) at radial position r (see Fig. 1) from the heat source conforms to the simplified formula

(1)

where k is the thermal conductivity (W.m^-1.K^-1), a thermal diffusivity (m².s^-1) (a=k/rc_p, with r is the density (kg.m^-3) and c_p the heat capacity (J.kg^-1.K^-1) of the test material and C=exp(g), g=0,5772157 is the Euler’s constant.

Fig. 1 Schematic view of the sample

The equation (1) is valid only when r²/4at<<1 is fulfilled, i.e. for a sufficiently long time t larger than certain minimum time t_min and for a small distance r. Thus the measurement of temperature rise DT(r,t) as a function of time is be employed to determine of the thermal conductivity k, calculating of the slope K of the linear portion of temperature rise DT(r,t) vs. natural logarithm of the time (lnt) evolution from

(2)

The hot wire temperature rise reaches usually up to 10ºC and its time evolution has typically the form as shown in the Fig. 2.

Fig. 2 Typical temperature rise curve (a - ideal, b – non-ideal case)

The hot wire method can be applied in several experimental modifications. In the standard cross technique the wire cross is embedded in ground grooves between two equally sized specimens. The cross consists of a heating wire and the legs of a thermocouple, which acts as the temperature sensor. The hot spot of the thermocouple is in direct contact with the heating wire. In the resistance technique the heating wire acts also as the temperature sensor. Here the temperature is measured by the change in resistance caused by the heating-up of the hot wire. In the measurement of electrically conducting materials the heating wire and thermocouple wires, or potential leads, are insulated from the sample. This is done either by making of a non-conducting coating on the wires, or to enclose the heater and temperature sensor in a thin sheath or needle probe, which is inserted into the test material, respectively. The second approach is called as the hot-wire-probe method.

2. Experimental apparatus

The home-made computer controlled hot wire apparatus allows the determination of thermal conductivity of solids, powders, sands and granular materials.. Three measuring techniques are there available: standard cross wire technique, resistance - potential lead method, that is based on the four point principle and the probe modification of the hot wire method. In the cross wire technique the platinum (Heraeus) or kanthal (Bulten Kanthal AB) wires, with various diameter (0,1 – 0,4 mm), depending on the measured material and the measurement temperature act as the linear heat source. The temperature rise vs. time evolution is measured by the spot welded K type thermocouple, made from Ni-NiCr wires (Heraeus), or S type – Pt/PtRh 90/10% (Heraeus). The hot spot of the thermocouple is in direct contact with the heating wire and is placed in the center of sample. The reference junction is immersed in the Dewar cup at 0°C. In the resistance technique the platinum wire acts as the heating wire as well as the temperature sensor. Potential leads consist of thin platinum wires, fixed to the heating wire at about 1,5 cm from the end of the sample. The probe method uses home-made cylindrical probe original construction, consisting of the heating wire and the temperature sensor, both placed in the ceramic microcapilar (Degussa).

The apparatus currently allows performing in-situ measurements of solid materials in the temperature range 20 – 1200 ºC. Details concerning the apparatus can be find in [3]

Fig. 3 Typical experimental temperature rise vs. time evolution.

3. Sample sizes

The solid samples consist either of two cuboids, or of two cylinder halves, respectively. They dimensions are up to 100x100x50 mm or the cylinder should be up to 10 mm in diameter with length 100 mm, all depending on the thermal diffusivity of the measured material.

The sand, powder and granular materials are usually put into cube container of 100x100x100 mm.

4. References

[1]	Davis W R, Hot-Wire Method for the Measurement of the Thermal Conductivity of Refractory Materials, in Maglić K D, Cezairliyan A, Peletsky V E, (Eds.) Compendium of Thermophysical Property Measurement Methods, Vol. 1 Survey of Measurement Techniques, 1984, New York, London, Plenum Press, p. 161
[2]	Wechsler A E, The Probe Method for Measurement of Thermal Conductivity in Maglić K D, Cezairliyan A, Peletsky V E, (Eds.) Compendium of Thermophysical Property Measurement Methods, Vol. 2 Recommended Measurement Techniques and Practices, 1992, New York, London, Plenum Press, p. 281
[3]	Vozár L, A Computer-Controlled Apparatus for Thermal Conductivity Measurement by the Transient Hot Wire Method, 1996, Journal of Thermal Analysis, 46, 495-505