# Experimental Investigation of Thermal Contact Conductance in a Bundle of Flat Steel Bars
## 2 Materials and Methods  
The starting point for the analysis is the measurement results of the effective thermal conductivity performed with the use of a guarded hot plate apparatus. This parameter is commonly used in the theory of porous [2; 23; 24] and nonhomogeneous [25; 26; 27] media. To perform the measurement of the effective thermal conductivity a guarded hot plate apparatus in a one side mode was used [28; 29]. In case of consolidated media the tested samples has a form of flat plates, whereas when the tested medium is porous, which happens in case of bundles of bars, the samples are flat beds with a certain degree of packing. The measurement principle involves forcing of unidimensional, steady heat flux \(q\) in the direction perpendicular to the main (bottom and top) surfaces of the sample. After the steady state was achieved, the temperatures on these surfaces--the bottom surface \(t_{bo}\) and the top surface \(t_{to}\)--were measured. The effective thermal conductivity is defined in a similar way to the thermal conductivity of solid material \(k_{s}\)[30]:  
\[k_{ef}=\frac{q\cdot l_{sp}}{t_{bo}-t_{to}}=\frac{q\cdot l_{sp}}{\Delta t}, \tag{1}\]  
where: \(t_{bo}\)--temperature of the bottom surface, \(t_{to}\)--temperature of the top surface, \(l_{sp}\)--sample dimension in the direction of heat flow (this parameter is a total height of the sample and is a function of: bar size, number of layers in the sample and its arrangement). The values of \(l_{sp}\) parameter for all the investigated samples are summarized in Table 1.  
A custom experimental stand--a general view of which is shown in Figure 2a--was used for the measurement [13]. This stand consists of: a heating chamber, a temperature measurement system, a control system (consisting of the main heater and guarded heaters) and a cooling system. The main component of the stand is the heating chamber, the scheme of which is shown in Figure 2b. The investigated samples are put in the rectangular retort  
Figure 1: Bundles of flat steel bars: (**a**) a charge with an ordered arrangement; (**b**) a charge with a disordered arrangement. made from 4 mm boiler plate, with internal dimensions of the base of 400 \(\times\) 400 mm and a height of 200 mm. There is a main heater under the retort, with the same transverse dimensions of 400 \(\times\) 400 mm. All the heat generated in the main heater is directed towards the test sample. This condition is achieved by two guarded heaters (the side one and the bottom one). Power of the main heater is adjusted manually by means of an autotransformer. Due to this solution, it is possible to control the value of mean measurement temperature, whereas the power supply of guarded heaters is adjusted automatically by a special control system. To reduce the heat loss from the side surfaces of the heaters and the retort, the heating chamber was wrapped in a 100 mm layer of the ceramic fabric. From the top, the chamber is closed tightly with a steel cover in which a water cooler is installed. Thanks to this solution the cooler did not lower the sample temperature significantly, however, at the same time it forced a unidirectional heat flow. Temperatures on the bottom and top surfaces were measured in five opposite points by 0.5 mm K-type sheathed thermocouples TP-201 [31]. Temperature sensors were connected to the WRT-9 multichannel temperature logger [32]. Temperatures on the hot (lower) surface \(t_{b-i}\) and cold (top) surface \(t_{b-i}\) were measured in five opposite points. One point was located in the geometrical centre of the surface, whereas four other points were in the corners of the square with the side of 260 mm, and its centre overlapped with the sample centre. The tips of the thermocouples used for measurement of \(t_{b}\) temperature were fastened to the retort bottom that served as the hot plate, whereas the tips of the thermocouples used for measurement of \(t_{b}\) temperature were fastened to the 15 mm thick steel plate that covered the samples.