The heated probe apparatus is a variation of the hot wire (line source) method used to measure the conductivity
of relatively low conductivity materials. The experimental configuration consists of a resistance wire separated
some distance from and parallel to a temperature sensor. The sample material is placed around the wire-sensor
assembly so that they are located in the central region and are completely surrounded by the sample material.
The method is a transient one. The resistance wire is Joulean heated and the resulting temperature rise of the
sensor is measured. Temperature rises are kept small, so the technique approximates an isothermal case. The
heated probe method differs from the hot wire method in that the heater and temperature sensor are located adjacent
(or are combined) to one another and are enclosed in a thin hypodermic needle. This method is ideally suited for
non-rigid materials which can be readily penetrated by the needle. The governing equation can be written as:
where λ is thermal conductivity, Q is the rate of heat input per unit length, T2 and T1
are temperatures of the sensor at times t2 and t1. This equation can be written as:
where S is the slope of the linear portion of the temperature-ln time curve. This is the basic equation of the
standard test. When the temperature is plotted against ln time, the resultant curve will be curved upward at the
beginning of the experiment and (usually) curved downward near the end of the experiment, with a linear portion in
between. The equations are only valid for the linear portion of the curve. The lower portion of the curve is
controlled by the heating of the probe itself and the heat transfer between the probe and the sample and the upper
portion of the heating curve is affected by heat reaching the sample outer walls - or in the case of fluids- by
initiation of convection. Thus only the linear portion of the curve is a function of the sample's conductivity.
It is imperative that a significant linear region be obtained experimentally.