3.1. Measurement Parameters
In this study, the operating parameters of the TEM heat pump, i.e., input current (
I), hot-side inlet fluid temperature (
Th,in), hot-side water flow rate (
), cold-side inlet fluid temperature (
Tc,in), cold-side water flow rate (
), and the heat exchange area (
Ahx), were selected. The heat exchange area is the surface area of channels inside the water block, as shown in
Figure 2. Each water block had a heat exchange area of 0.00455 m
2. In the experimental system, six TEMs were used, and water blocks were attached onto the cold and the hot sides of each TEM, as shown in
Figure 1. Therefore, the total heat exchange area at the cold or the hot sides of the TEM heat pump could be varied from 0.00455 m
2 to 0.02730 m
2 during the experiment, depending on the number of activated TEMs.
In order to design the series of experiments, the operating ranges (i.e., minimum and maximum values) of each parameter were determined. In the experimental TEM heat pump, the operable ranges of input current and water flow rate were 1 A to 4.2 A and 0.01 kg/s to 0.02 kg/s, respectively. The inlet water temperature range at the cooling and heating sides were 15 °C to 35 °C and 45 °C to 65 °C, respectively, which are the common inlet water temperature ranges in building mechanical system applications. The experimental cases could be designed by combining the minimum and maximum values of each operating parameter. However, in order to consider the impact of the non-linearity of each parameter on the heat exchange effectiveness, intermediate values within the predefined operating range of each parameter were also considered in the experiment design.
Table 2 shows the values of operating parameters that are considered in the series of experiments for obtaining data on the heat exchange effectiveness at both the cold and hot sides of the TEM heat pump.
As for the experiment design, we used a central composite design (CCD) approach with face centered method that is useful in response surface methodology (RSM) for developing a second order quadratic model that returns the heat exchange effectiveness. In CCD, the experimental cases were defined from three experiment design matrices: the 2
k factorial design matrix, the axial point matrix, and the center point matrix [
19]. The 2
k factorial design matrix is a combination of minimum and maximum values of each variable, where
k is the number of variables. The axial point matrix is composed of the minimum or maximum value of one variable, and the intermediate values of the remaining variables. Therefore, the number of experimental sets for the axial point matrix is 2
k. A center point matrix is composed of the intermediate values of all the variables. Consequently, a total of 77 experiment sets, i.e., 64 sets from the 2
k factorial design matrix, 12 sets from the axial point matrix, and one set from the center point matrix, were established.
In each experiment, the input current (I) was controlled by using SMPS, and water flow rates () were modulated by the direct current motor speed controller for the pumps. The inlet water temperatures (Tin) were adjusted by using electric water heaters. The heat exchange area (Ahx) was varied by changing the number of activated TEM units. Outlet fluid temperatures at the hot side (Th,out) and cold side (Tc,out) were measured in each experiment.
Temperature measurements were performed using a T-type thermocouple (Omega Engineering, Inc., Norwalk, CT, USA, Error rate ±0.5 °C) with MV1000 data logger applicable within the range of −200 to 400 °C with ±0.5 °C accuracy [
20]. Inlet and outlet fluid temperatures, and water block temperatures at the hot and cold sides of the TEM heat pump were measured at the total 16 measurement points (
Figure 1b). The data was logged for 10 min at one-second intervals in each measurement when the temperatures at all of the measurement points were sufficiently stable. The input current and water flow rates were consistently maintained at their set points in each experiment.
3.2. Operation Data
Among the 77 experiment sets, 57 sets of measurement data (
Data table in supplementary file) were used for developing the heat exchange effectiveness model of the TEM heat pump, while 20 sets of measurement data were excluded because the TEM heat pump did not produce meaningful water temperature variation between the inlet and outlet at both the hot side and cold side. The water temperature differences in the excluded data sets were smaller than the accuracy of the temperature sensor (i.e., ±0.5 °C).
Negligible water temperature differences between the inlet and outlet of the TEM heat pump were observed when the inlet water temperature difference between the hot and cold sides was too large, which showed that the Seebeck effect had overridden the Peltier effect. In the Seebeck effect, heat is transferred from the hot side to the cold side, and the TEM generates electricity. Conversely, in the Peltier effect, heat is transferred from the cold side to the hot side by supplying electric power from outside, and the TEM works as a heat pump. These two effects occur simultaneously; therefore, if one wants to use the TEM as a heat pump, then the Peltier effect should be more dominant than the Seebeck effect, which can only occur if the magnitude of input current that is supplied is enough to offset the Seebeck effect; otherwise, the TEM heat pump cannot produce a meaningful difference in the temperature of water at the inlets and outlets on both the hot and cold sides of the TEM.
Figure 3 shows the representative experiment data sets (i.e., Case 9 from
the table in supplementary file). One can see that, when the TEM heat pump was activated, the temperature difference between the cold and hot side water blocks increased rapidly, and the outlet water temperatures were close of those of the water blocks at both sides. Using Equations (1) and (2), the heat exchange effectiveness values were calculated, and average values of 0.828 and 0.809 were obtained for cooling and heating, respectively.
3.3. Uncertainty Analysis
The uncertainty analysis was performed to verify the experiments that were based on the ASHRAE guidelines [
21] and previous studies [
22,
23]. The overall uncertainty consists of propagation of error (
by) and random error (
py), as shown in Equation (3). The propagation error (
by) is the uncertainty propagated through a data reduction equation. In this study, heat exchange effectiveness is calculated using measured temperatures of the inlet, outlet, and surface. Therefore, the propagation error is calculated using Equation (4), based on the heat exchange effectiveness in Equations (1) and (2). The fixed error (
) is obtained by multiplying the sensor error in the technical specifications and the standard deviation of the measured parameter. The random error (
py) is derived using Equation (5) based on the standard deviation and mean value of the data. The overall uncertainty values are summarized in
Table 3. All of the temperatures values were lower than the value of the accuracy of the temperature sensor. Moreover, the overall uncertainty values of the heat exchange efficiencies for cooling and heating were below 0.03 (i.e., 3%).