## 2 Thermal Conductivity Methods
### Transient Hot-Wire
In practice, the use of the THW technique introduces a set of departures from the ideal model, presented in equation, and the ideal temperature rise can be written as [20]:  
\[\Delta T_{\text{id}}(r_{0},t)=\Delta T_{\text{exp}}(t)+\sum\limits_{i}\delta T _{\text{i}}(t) \tag{7}\]  
where \(\Delta T_{\text{id}}(r_{0},t)\), \(\Delta T_{\text{exp}}(t)\) and \(\delta T_{\text{i}}(t)\) stand for the ideal temperature rise obtained from Equation (6), the experimentally measured temperature rise, and the \(i\)-th temperature correction, respectively. [PERSON] et al. [24] obtained the analytical expressions for all these corrections, which approach the experimental temperature rise. Some recommendations concerning the use of each \(\delta T_{\text{i}}\) have been proposed by [PERSON] and [PERSON] [3]. These effects should be minimized to obtain reliable thermal conductivity data. Standard instruments based on the THW method have been manufactured over the years. Generally speaking, these instruments consist of a metallic wire, used as line heat source as well as temperature sensor, which is soaked within the testing fluid. Temperatures of the wire as well as the fluid are increased by a constant heat flux supplied by the wire itself. The temperature rise depends on the thermal conductivity of the fluid in which the hot-wire is submerged. The higher the thermal conductivity, the lower the temperature rise, due to increased thermal dissipation from the wire to the surrounding fluid [5; 25]. Most of the conventional THW instruments use platinum wires as probes due to the linear relationship between the electrical resistance and the temperature. [PERSON] et al. [26] investigated the effect of fluid radiation on the measurements of the thermal conductivity of propane and designed a transient hot-wire cell for measurements of both thermal conductivity and thermal diffusivity. The cell used two platinum wires of 12.7 um in diameter, each of different length. [PERSON] et al. [27] presented the design, fabrication, and characterization of a transient hot-wire device for measuring the thermal conductivity of non-conductive fluids. The probe used was a 20 um-diameter platinum hot-wire. [PERSON] et al. [28] used a THW apparatus to carry out thermal conductivity measurements of pure argon, methane, propane, and a methane:propane binary mixture along several isotherms at pressures up to 33 MPa. The device presented two wires made of platinum with diameters approximately 10 um. [PERSON] et al. [29] investigated the wire-length dependence of transient hot-wire tests. Thermal conductivities of water Ih-ice, and \(n\)-eicosane, were measured by an apparatus based on the transient hot-wire method. The core of this device was composed by three platinum wires of different lengths with a diameter of 50 um. Likewise, wires made of different materials were also studied. [PERSON] [30] developed an apparatus for the measurement of the thermal conductivity of samples of non-metallic materials whose thermal conductivity is quite low, between 0.2 and 4 W m\({}^{-1}\) K\({}^{-1}\). Thermal conductivity was measured by tracking the thermal pulse propagation induced in the sample by a heating source consisting of a nickel alloy wire. [PERSON] et al. [13] constructed and evaluated a low-cost transient hot-wire device for the measurement of thermal conductivity of fluids with the same accuracy of the conventional methods. In this case, a copper micro-wire of 80 \(\upmu\)m diameter was chosen in contrast to conventional transient hot-wire devices, which use platinum wire, as mentioned above. [PERSON] et al. [31] developed an apparatus for the measurement of the thermal conductivity of geothermal grouting materials. This device was constructed using a wire made of nichrome (nickel and chromium alloy) with a diameter of 0.2 mm. [PERSON] et al.