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Applications of thermoelectric modules on heat flow detection

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This paper presents quantitative analysis and practical scenarios of implementation of the thermoelectric module for heat flow detection. Mathematical models of the thermoelectric effects are derived to describe the heat flow from/to the detected media. It is observed that the amount of the heat flow through the thermoelectric module proportionally induces the conduction heat owing to the temperature difference between the hot side and the cold side of the thermoelectric module. In turn, the Seebeck effect takes place in the thermoelectric module where the temperature difference is converted to the electric voltage. Hence, the heat flow from/to the detected media can be observed from both the amount and the polarity of the voltage across the thermoelectric module. Two experiments are demonstrated for viability of the proposed technique by the measurements of the heat flux through the building wall and thermal radiation from the outdoor environment during daytime.

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Applications of thermoelectric modules on heat flow detection

2. 2. 346 T. Leephakpreeda / ISA Transactions 51 (2012) 345–350 Fig. 1. Experiment on heat flux through the building wall. Fig. 2. Experiment on thermal radiation within the outdoor environment. 3. Mathematical modeling of the thermoelectric module This section is to describe mathematical models for governing physical behaviors of a thermoelectric module so as to approach practical applications of thermoelectric modules on heat flow detection. For commercial products, the thermoelectric module is typically made of two ceramic plates of various sizes and shapes covering an array of (n − p) sequentially-paired semiconductors in between those as shown in Fig. 3. In general, the thermoelectric modules are widely used as heat pumps in electric cooling/heating when the DC current from a power source flows through the thermoelectric module, which subsequently causes heat transfer from one side (cold side) of the thermoelectric module to the other (hot side). In turn, cooling effects and heating effects are generated according to thermal demands at the cold side and at the hot side, respectively. In fact, the thermoelectric module can be considered a thermal–electrical circuit as depicted on the right side in Fig. 3, which is mathematically described by: v = β (Th − Tc ) + RI (1) where v is the voltage across the thermoelectric module, β is the Seebeck coefficient, Th is the temperature at the hot side, Tc is the temperature at the cold side, R is the resistance of the thermoelectric module, I is the electrical current flowing within the circuit. The amount of heat rejected by the thermoelectric module at the hot side can be determined by: QH = βITh + 1 2 I2 R − k (Th − Tc ) . (2) On the other hand, the amount of heat pumped by the thermoelec- tric module at the cold side can be determined by: QC = βITc − 1 2 I2 R − k (Th − Tc ) (3) where k is the thermal conductivity coefficient of the thermoelec- tric module. The first term on the right side of Eqs. (2)–(3) is the Seebeck heating/cooling effects. The second term characterizes the Joule heating effect associated with electrical power developed in the resistance. The third term represents the Fourier effect of heat conduction from the hot side to the cold side. From the principle of energy balance, the electrical power and the rate of heat pumped from the cold side as well as the rate of heat rejected to the hot side can be written as: QH = QC + IV. (4) It can be interpreted that the heat can be pumped from the cold side to the hot side by the electrical drive of the thermoelectric module. The parametric values of the material properties in the mathematical models can be determined experimentally with elaborated details in Section 4. In this work, the heat-flow detection is proposed by making use of the thermoelectric effects of the thermoelectric modules. As illustrated in Fig. 4, without supplying the electrical power, the circuit of the thermoelectric module is opened (I = 0) instead. While the amount of the heat, which is to be detected, transfers to the thermoelectric module instead, it is observed that the voltage measured across the thermoelectric module is proportionally varied according to the amount of heat transfered through the thermoelectric module. In this paper, it is called inflow heat detection, where the temperature of the detected media is higher than the thermoelectric module, whereas it is called outflow heat detection, where the temperature of the detected media is lower than the thermoelectric module. Without loss of generality, the inflow heat detection, for which the hot side is facing in this case, is considered in analytical study while the outflow heat detection, for which the cold side is facing, can be regarded as a similar process where the direction of the heat flow is opposite to the direction of the heat flow through the thermoelectric module in Fig. 4. Now, let us consider a schematic diagram of the inflow heat detection presented in Fig. 4. Since the thermal–electrical circuit is opened so as to obtain the corresponding condition on that there is no electrical current within the circuit, the heat rejected from the thermoelectric module and the heat pumped to the thermoelectric module in Eqs. (2)–(3) can be reduced to: QH = QC = −k (Th − Tc ) . (5) The negative sign indicates the direction of the heat flow, which is now opposite to the direction in the case that the power source is used to supply the electrical current to the thermoelectric module
3. 3. T. Leephakpreeda / ISA Transactions 51 (2012) 345–350 347 Fig. 3. Schematic diagram of the thermoelectric module and the thermal–electrical circuit. Fig. 4. Installation during inflow heat detection. in Fig. 3. To continue the analysis, let us consider the amount of the heat transfer through the thermoelectric module to be: Q o H = Q o C = k (Th − Tc ) . (6) By applying the principle of heat balance to the thermal system in Fig. 4, the dynamics of the temperatures of the hot side and the cold side as well as the heat sink can be governed by the following three equations. ρcV dTh dt = Q − Q o H (7) ρcV dTc dt = Q o C − Qs (8) ρscsVs dTs dt = Qs − Qa (9) where Q is the detected heat flow to the thermoelectric module, ρ is the density of the ceramic substrate, c is the specific heat of the ceramic substrate, V is the volume of the ceramic substrate, and the subscript s indicates those properties belonging to the heat sink. Eqs. (7)–(9) are applied in order to describe each lumped solid temperature considered in the heat flow direction from the detected media to the heat sink as shown in Fig. 4, since the heat transfer area of the thermoelectric module is noticeably larger than the perimeter area. Explicitly, Eq. (7) represents the rate of change in the internal energy stored within the hot-side control volume of the thermoelectric module due to the rates at which heat transfer enters and leaves the hot-side control volume. The same consideration is applied for the cold-side control volume and the heat sink, which are governed by Eqs. (8)–(9), respectively. However, there are temperature differences across the interfaces between the cold side of the thermoelectric module and the heat sink as well as the heat sink and the air. The temperature differences are attributed to the thermal contact resistance and the thermal resistance of the natural convection, as expressed in Eqs. (10)–(11), respectively. The heat conduction from the cold side of the thermoelectric module to the heat sink can be expressed as: Qs = Tc − Ts rs . (10) The heat convection from the heat sink to the air can be written as: Qa = Ts − Ta ra (11) where rs is the thermal contact resistance between the thermoelec- tric module and the heat sink, ra is the thermal resistance of the natural convection at the heat sink, Ts is the temperature of heat sink, and Ta is the temperature of air. It can be seen from Eqs. (7)–(11) that the temperatures of the hot side, the cold side, and the heat sink can be changed with respect to time according to the capability of heat capacity, heat conduction among the contact materials, and heat convection by cooling air. In fact, temperatures of the hot side, the cold side and the heat sink rise up until the heat transfer from the thermoelectric module to the air is the same as the amount of the heat flow from the detected media. Without loss of generality, an ideal case of perfect heat dissipation is considered in such a way that the heat sink can draw the temperature of the cold side and the temperature of the heat sink itself to the temperature of air. In other words, the thermal resistances in Eqs. (10)–(11) are assumed to be sufficiently small, where the heat sink is designed for efficient cooling. The temperature at the cold side is to be retained at a
4. 4. 348 T. Leephakpreeda / ISA Transactions 51 (2012) 345–350 Fig. 5. Response of temperature difference after contacting detected media. Table 1 Parameters of the thermoelectric module and the copper plate. Parameters Numerical values Seebeck coefficient β, (V/K) 0.0488 Thermal conductivity k, (W/K) 0.831 Size of alumina substrate V, (cm × cm × cm) 4 × 4 × 0.09 Specific heat of alumina c, (J/g K) 0.88 Density of alumina ρ, (g/cm3 ) 3.89 Heat capacitance of copper plate (J/K) 32.725 constant temperature until the steady state is reached. With the hypothesis (dTc /dt = 0), this yields mathematical manipulations of Eqs. (6)–(7) to be expressed as Eq. (12). ρcV d (Th − Tc ) dt = Q − k (Th − Tc ) . (12) Therefore, the analytical solution of Eq. (12) for a given amount of the heat flow can be obtained by: Th − Tc = Q k  1 − e −  k ρcV  t  . (13) It should be noted that obtaining the analytical solution is to give insight on how fast the response time of the theoretical case is to reach the steady-state conditions. In actual cases, the characteristics of dynamic responses may vary. From Eq. (13), once the heat flow is detected while the detected media is attached by the thermoelectric module, the magnitude of the temperature difference starts increasing with respect to time and then it reaches steady-state heat conduction with a magnitude of the ratio of the heat flow to the conductivity coefficient. The dynamic response time to the heat flow to reach the steady condition is dependent on the properties of the thermoelectric module, that is, the density, specific heat, volume of the ceramic plate and the conductivity coefficient. With property parameters in Table 1 of materials used in this study, Fig. 5 shows the dynamic response of the temperature difference of the thermoelectric module after contacting the detected media. The response time to reach the steady condition is estimated to be slightly less than 30 s. In fact, it is sufficiently fast to thermally detecting for general purpose. It should be noted that the actual response time deviates from these ideal results based on the dissipative efficiency of the heat sink as mentioned earlier. It can be noted that the more the amount of the heat flow, the larger the temperature difference it requires. Therefore, it is better to maintain the temperature of the heat sink to be as low as possible to cover the ranges of the amount of the heat flow to be detected. Under the opened thermal–electrical circuit (I = 0) at steady-state condition, the model of Eq. (13) at (t → ∞) can be substituted to Eq. (1) or the model of Eq. (6) can be substituted to Eq. (1) in order to yield the relations of the heat flow to the voltage measured across the thermoelectric module. Q = k β v. (14) It can be interpreted form Eq. (14) that the amount of heat that transfers to a given area of the thermoelectric module causes proportionally the voltage across the thermoelectric module. The thermal–electrical relation in Eq. (14) can be applied to determine the heat flow from the detected media to the thermoelectric module and vice versa. It should be noted that the inflow heat detection and the outflow heat detection can be indicated in the polarity of voltage measurement. 4. Results and discussion This section is to demonstrate examples of how the proposed technique of heat flow detection via a thermoelectric module is applied in practical uses. Initially, a thermoelectric module coupled with a heat sink, which is commonly available in product market, is experimentally tested in order to determine its properties for thermoelectric relation in Eq. (14), that is, the Seebeck coefficient and the thermal conductivity coefficient. In fact, the details of parametric determination can be found as follows. Fig. 6 shows the plots of the measured voltage against the temperature difference between the temperature at the hot side and the temperature at the cold side after the circuit of the thermoelectric module is cut off from the DC source (open circuit or I = 0). It is observed that the voltage decreases as the temperature difference reduces. From Eq. (1), the slope of the linear relation in Fig. 6 is quantified, by the best fitting method, to be the Seebeck coefficient of 0.0487 V/K, which is listed in Table 1. To determine the thermal conductivity coefficient, a hot copper plate with the same size of the thermoelectric module is well insulated at one side and another side is attached to the thermoelectric module so that all the internal energy of the copper plate is only transferred to the thermoelectric module. Therefore, the heat conduction through the thermoelectric module takes place due to the decrement of the internal energy within the hot copper plate as expressed in Eq. (6). Fig. 7 shows plots of the decreasing temperature of the copper plate against time, which can be used to determine the rate of change in the temperature of the copper plate. With the heat capacitance of the copper plate in Table 1, the heat rejected to the thermoelectric module can be determined and then it is plotted with respect to the corresponding temperature difference between the temperature at the hot side and the temperature at the cold side as illustrated in Fig. 8. The slope of the linear relation in Eq. (6) is quantified to be the thermal conductivity coefficient of 0.831 W/K, which is listed in Table 1. To verify the thermoelectric relation with those obtained parameters in Eq. (14), the plate-type heaters with different power capacities are prepared as known heat sources. Fig. 9 illustrates the comparisons of the results between the heat flow determined from Eq. (14) corresponding to measured voltages, illustrated in the solid line and the known heat flow from the plate-type heaters to the thermoelectric module as well as the known heat flow from the thermoelectric module to the cooled plates, depicted in dotted marks. It is found that results from the proposed model in Eq. (14) have good agreement on the actual heat inflow and the actual heat outflow of the thermoelectric module, where the average value of the absolute relative differences is 6.7% with a standard deviation of 2.7% in the testing experiments. Now, two practical scenarios are demonstrated as real appli- cations of the thermoelectric module on heat flow detection. The thermoelectric module is used to measure the heat flux (W/m2 ), which is determined from the heat flow through the thermoelec- tric module in Eq. (14) per the area of the thermoelectric module
5. 5. T. Leephakpreeda / ISA Transactions 51 (2012) 345–350 349 Table 2 Statistical summaries of absolute relative differences of experimental results and simulated results. Figure Minimum values (%) Maximum values (%) Average values (%) Standard deviations (%) Numbers of data 6 0.1 14.6 5.4 4.7 13 8 0.2 8.6 4.0 3.1 6 9 0.1 10.5 6.7 2.7 13 11 0.3 11.7 4.8 3.9 18 Fig. 6. Plots of voltage against temperature difference. Fig. 7. Temperature evolution of copper plate during decrease in internal energy. Fig. 8. Plots of the heat flow to the thermoelectric module against temperature difference. itself (4 cm×4 cm, listed in Table 1). Fig. 10 shows the implementa- tion of the proposed technique in determining the heat flux passing Fig. 9. Comparison of simulated results from the model in Eq. (14) with the actual heat flow. Fig. 10. Detected heat flux through the building wall during daytime. through a side of the building wall exposed to sunlight against the time. It is observed that the amount of heat flux through the wall increases and decreases corresponding to the time from sunrise to sunset. It is a fact that the thermoelectric module is used to mea- sure the amount of the heat transfer through the detected-media facing area, which is not identical to the amount of the heat transfer through the wall (without the thermoelectric module). However, those measurements can be used as proportional indicators of the heat flow in system design techniques. There are two main factors causing such differences: 1. changes in boundary conditions due to attaching the thermoelectric module to the wall and 2. contact- ing effect on thermal resistance between the detected media and the thermoelectric module. In turn, the relationship may change from one scenario to another. Fig. 11 shows variations of thermal radiation obtained from the thermoelectric module during day- time when the equipment is exposed to the outdoor atmosphere as mentioned in Section 2. Results from the proposed technique yield good agreement with the measured results from a pyranome- ter, where the average value of the absolute relative differences is 4.8% with a standard deviation of 3.9%. For Figs. 6, 8, 9 and 11, the statistical summaries of absolute relative differences between the experimental results and the simulated results such as min- imum value, maximum value, average value, standard deviation, and numbers of data are reported in Table 2.
6. 6. 350 T. Leephakpreeda / ISA Transactions 51 (2012) 345–350 Fig. 11. Detected heat flux within the outdoor environment during daytime. 5. Conclusion The proposed technique is analytically presented for viability of simple-to-use and effective application of the low-cost thermo- electric module on heat flow detection. To implement, the thermo- electric module is typically coupled with a heat sink and then it is well attached to the detected media. The heat flow from/to the de- tected media is observed from both the amount and the polarity of the voltage across the thermoelectric module. Two practical sce- narios in heat conduction through the building wall and thermal radiation within the outdoor environment are demonstrated as examples of hands-on implementations. Likewise, the identifica- tion on heat-flow thresholds can be applied to trigger appropriate action of real-time control. Acknowledgments The author sincerely thanks Tanawat Boonpanya for assistance in experiments. Also, the author appreciates the reviewers’ com- ments and suggestions for improvement. References [1] Riffat SB, Ma X. Thermoelectrics: a review of present and potential applications. Applied Thermal Engineering 2003;23(8):913–35. [2] Chein R, Huang G. Thermoelectric cooler application in electronic cooling. Applied Thermal Engineering 2004;24(14–15):2207–17. [3] Xu X, Dessel SV, Messac A. Study of the performance of thermoelectric modules for use in active building envelopes. Building and Environment 2007;42(3): 1489–502. [4] Rowe DM, Min G. Evaluation of thermoelectric modules for power generation. Journal of Power Sources 1998;73(2):193–8. [5] Hsiao YY, Chang WC, Chen SL. A mathematical model of thermoelectric module with application on waste heat recovery from automobile engine. Energy 2010; 35(3):1447–54. [6] Champier D, Bedecarrats JP, Rivaletto M, Strub F. Thermoelectric power generation from biomass cook stoves. Energy 2010;35(2):935–42. [7] Ploteau JP, Glouannec P, Noel H. Conception of thermoelectric flux meter for infrared radiation measurements in industrial furnaces. Applied Thermal Engineering 2007;27(2–3):674–81.