*2.3. Data Reduction and Measurement Uncertainty*

The calculation of relevant heat transfer parameters is based on measured temperatures. The parameters which are most relevant in boiling heat transfer systems are heat transfer coefficient, heat flux, and superheat of the surface. The methodology used for the calculation of the spatial temperature gradient between the highest positioned and the lowest positioned thermocouple in the sample utilizing the following linear interpolation (1) is suggested in [54]:

$$\frac{\Delta T}{\Delta x} = \frac{T\_{\rm TC3} - T\_{\rm TC1}}{2\Delta x\_1} \tag{1}$$

Heat losses during the experiments are neglected because of favorable insulative properties achieved using a very low thermal conductivity material (PEEK). Consequently, a simplified case of 1D conduction through the sample towards the boiling surface is considered. The heat flux is calculated using Fourier's law of conduction:

.

$$
\dot{q} = -k \frac{\Delta T}{\Delta \mathbf{x}} \tag{2}
$$

To accurately calculate the heat flux, thermal conductivity needs to be precisely evaluated. This is achieved by using a temperature-dependent value of thermal conductivity. Based on the average of all three temperatures measured within the sample, the thermal conductivity is calculated at the mean temperature (*T*) of all three temperatures in the sample according to the following equation:

$$k(T) = 0.000283T^2 - 0.1646T + 378.07\,\text{J}\tag{3}$$

The laser-flash measurement method of thermal diffusivity at various temperatures, and the determination of thermal conductivity based on temperature-dependent density and specific heat capacity are used to determine the latter expression. All temperature values are expressed in ◦C, and the thermal conductivity, as the result value, is returned in W m−<sup>1</sup> K−<sup>1</sup> . The temperature of the boiling surface is calculated by linear extrapolation using the previously determined heat flux and the temperature measured with the highest positioned thermocouple in the sample. The thermal conductivity is first determined at the highest positioned thermocouple in the sample, *T*TC1, utilizing Equation (3) to obtain an estimate of surface temperature. The mean temperature of the top part of the sample is determined as the arithmetic average value between the estimated surface temperature and the temperature of the highest positioned thermocouple. The mean temperature of the top part of the sample is used to determine the average thermal conductivity, which is then used to evaluate the surface temperature with increased accuracy. The saturation temperature of the working fluid is calculated as the arithmetic average value of the temperatures measured with two immersed thermocouples. The difference between the saturation temperature of the working fluid and surface temperature is the surface superheat (*T*<sup>w</sup> − *Tsat*). Dividing the heat flux by the corresponding surface superheat is used to determine the heat transfer coefficient: .

$$h = \frac{\dot{q}}{T\_w - T\_{\text{sat}}},\tag{4}$$
