Measurement of the Convective Heat Transfer Coefficient and Temperature of Vehicle-Integrated Photovoltaic Modules

Abstract

To improve the thermal design of vehicle-integrated photovoltaic (VIPV) modules, this study clarifies the characteristics of the convective heat transfer coefficient h between the vehicle roof surface and the surrounding air with respect to vehicle speed. Experiments on two types of vehicles with different body shapes indicate that h is strongly affected by vehicle speed, and it is also affected by body shape depending on the position on the roof. Empirical equations for approximating h as a function of vehicle speed and position on the vehicle roof are derived from the experimental datasets, and the differences between the equations derived herein and traditional equations that have been used for the heat transfer analysis of conventional stationary photovoltaic (PV) modules are clarified. Furthermore, the temperature change characteristics of the VIPV module were measured experimentally, confirming that h is the dominant factor causing the high temperature change rate of the VIPV module under driving conditions. In sunny summer conditions, the measured temperature change rate reaches up to 16.5 °C/min, which is approximately 10 times greater than that in the standard temperature cycle test for conventional stationary PV modules.

1. Introduction

Vehicle-integrated photovoltaics (VIPVs) are an emerging technology implemented in the transportation sector to reduce carbon emissions [1,2]. It is estimated that a vehicle with a VIPV module with a rated power generation capacity of 1 kW can be driven for 30 km/day [3], which is effective in reducing CO₂ emissions [4] and the number of connections required to a charging station. However, from the perspective of reliable product design, the thermal design of the VIPV module becomes crucial compared to that of traditional ground-mounted stationary photovoltaic (PV) modules because convective heat transfer is expected to change drastically depending on vehicle speed.

The temperature of a PV module affects its power-generation performance and long-term reliability [5,6]. The conversion efficiency of a solar cell decreases with the increase in cell temperature [7,8], and the PV module undergoes a temperature cycle owing to changes in solar radiation, ambient temperature, and wind velocity. The difference in thermal expansion coefficients among the PV module components—that is, solar cells, busbars, ribbon electrodes, encapsulants, glasses, and backsheets—causes cyclic stress among the materials during the temperature cycle. This often leads to degradation of the materials and structures, resulting in functionality loss of the PV module [9,10]. Therefore, PV modules are usually tested for their robustness to temperature cycling in accordance with international standards [11,12]. However, the temperature conditions for such temperature cycling tests are intended for stationary PV modules and not for VIPV modules. The temperature change in the VIPV modules is expected to be strongly influenced by the airflow around the vehicle, especially when driving, as reported by recent simulation studies on trucks [13,14]. The airflow velocity around the vehicle while driving at a speed of 50 km/h may exceed 14 m/s, even on windless days, which is considerably higher than the typical airflow speed around stationary PV modules. Additionally, owing to the repetitive and frequent acceleration and deceleration of the vehicle, VIPV modules can be exposed to drastic temperature changes compared to stationary PV modules. Therefore, it is important to estimate the temperature characteristics of VIPV modules under given environmental conditions in the thermal design process to improve their conversion efficiency and reliability. To estimate the module temperature accurately, it is necessary to know the convective heat transfer coefficient around the VIPV module when the vehicle is being driven. However, to the best of our knowledge, experimental studies on the convective heat transfer coefficient of vehicle roof surfaces while the vehicle is being driven are limited in the literature. For conventional stationary PV modules and solar thermal collectors, empirical equations for the convective heat transfer coefficient as a function of wind speed have been traditionally used. For example, Polyvos compares six categories of several empirical equations for modeling heat loss due to convection, including Nusselt–Jürges and McAdams [15]. Armstrong et al. compared empirical equations from five indoor wind tunnel experiments (including McAdams) and three outdoor experiments to investigate the temperature response of PV modules [16]. Sharma et al. reported the results of a thermal design of a concentrated PV system using McAdams’ equation [17]. Lindholm et al. calculated the convective heat transfer with air for floating PV modules using Watmuff’s and McAdams’ equations [18]. Jurčević et al. compared experiments and computational simulation for convective heat transfer in a PV thermal collector using McAdams’ equation and others [19]. Khodadadi et al. used McAdams’ equation for a design of PV/thermal units involving phase change materials [20]. Kurz et al. evaluated temperature changes in PV roof tiles using empirical equations from outdoor experiments by Test et al. [21,22]. These empirical equations were derived for flat plates or rectangular objects in an air flow. However, the flow field around a three-dimensional curved vehicle body can differ from that around conventional flat-plate PV modules. The most frequently used equation is McAdams’ equation [15,23], which has also been used for the thermal model of the vehicle [24]. A few studies that focus on the thermal model of vehicle cabins have used different equations; however, the original research paper is written in Chinese and is currently unavailable [25,26,27]. Therefore, further clarification of the convective heat transfer coefficient on the vehicle roof is required.

Motivated by this fact, we experimentally clarified the convective heat transfer coefficient of a real vehicle roof and the temperature change characteristics of a VIPV module. First, the convective heat transfer coefficients were measured through nighttime driving experiments, and the accuracy of the measurement was improved by eliminating the effect of solar radiation fluctuation. Subsequently, empirical equations for calculating the convective heat transfer coefficient as a function of vehicle speed and position on the vehicle roof were presented, and deviations from the present equations to the traditional equations were elucidated. Finally, the temperature change rate of a real VIPV module attached to the vehicle roof was measured during daytime driving experiments, and the significant contribution of convective heat transfer to the module temperature change was verified quantitatively using the empirical equations obtained from the nighttime driving experiments.

2. Measurement of Convective Heat Transfer Coefficient

2.1. Experimental Setup

The convective heat transfer coefficient (h) between the vehicle roof surface and ambient air was measured using typical commercial vehicles. Figure 1 shows the dimensions and shapes of the experimental vehicles: a small van (Mazda Motor Corporation, AZ Wagon) and sedan (Toyota Motor Corporation, Prius). A small van is a small box-type car with a mostly flat roof, whereas a sedan is a middle-class car with a more rounded roof. Figure 2 shows photographs of the experimental setup for the vehicle roofs. Eight film heat flux sensors depicted as F1–F8, four pyranometers depicted as P1–P4, an anemometer, and an infrared (IR) radiometer were mounted on the roof to measure the net heat flux through the sensor plane, solar irradiance, airflow speed, and IR thermal radiation flux from the sky, respectively. The heat flux sensors and anemometers have built-in temperature sensors (K-type thermocouples) that measure the heat flux and air temperatures, respectively.

Table 1. Specifications of the sensors used.

Heat flux sensor (HIOKI, Z2012-01)	Thickness 0.25 [mm] Thermal resistance 1.3 × 10−3 [m2·K/W] Sensitivity 0.01 [mV/W·m−2] Responsivity 0.4 [s] Uncertainty 2%
Thermocouple (HIOKI, Z2012-01)	Type K (Class 2) Compensating cable KX (Class 2) Responsivity 0.3 [s] Uncertainty 2.5%
IR radiometer (Kipp & Zonen, CG3)	Spectral range 4.5–42 [μm] Sensitivity 0.01 [mV/W·m−2] Responsivity 8 [s] Uncertainty 5%
Anemometer (KANOMAX, 6542-21)	Wind speed range 0.01–30 [m/s] Responsivity 1 [s] Uncertainty 2%
Pyranometer (EIKO, ML-02)	Spectral range 0.4–1.1 [μm] Sensitivity 0.05 [mV/W·m−2] Responsivity 1 × 10−3 [s] Uncertainty 2%
Film heater (Heat lab, TP100-50-50SE)	Thickness 0.15 [mm] Size (heating area) 0.045 × 0.035 [m] Inter-terminal resistance 93.3 [Ω]

lists the specifications of the sensors including uncertainty values estimated from the catalogue accuracy values of each sensor and loggers according to the error propagation law. All the sensors were connected to a data acquisition instrument (HIOKI, LR8416) to monitor and record the sensor outputs during the experiment. The sampling interval was set to one second. The heat flux sensors F1, F3, F5, and F7 were installed along the centerline (symmetry line) of the roof, and the heat flux sensors F2, F4, F6, and F8 along the edge line of the roof. The heat flux sensors were placed at equal intervals (0.5 m) from the front to rear of the vehicle.

Table 2. Weather conditions during the nighttime experiments.

	Small Van	Sedan
Date and time	2 August 2021 22:00–23:30	4 October 2021 20:30–22:00
Average air temperature [°C] (Min.–Max.)	28.5 (28.1–28.7)	20.0 (19.5–20.8)
Average wind velocity [m/s]	1.12	1.50

summarizes the weather conditions used in the experiments. Calm days were chosen, and average wind speeds were low (1.12 and 1.5 m/s). The small van experiment was conducted in summer (2 August 2021), whereas that of the sedan was conducted in autumn (4 October 2021). The experiments were carried out at night to eliminate the effect of solar radiation because unsteady solar radiation complicates the calculation of h and can cause errors in the present measurement. Pyranometers were used to confirm the absence of solar radiation during the experiment. Transparent flexible film heaters were inserted between each heat flux sensor and roof surface via thin adhesive layers. These heaters were heated at a constant power (7 W) during the experiment to maintain the accuracy of the measurement by maintaining the heater temperature higher than the air temperature. Electrical power was supplied to the heater using a direct current (DC) power supply (Matsusada Precision, PK120-3.3). Similar methods using thin-film heating elements with low heat capacity have been studied [28,29]. These methods were employed to clarify the detailed spatial distribution of time-varying h in turbulent flows. Although the present study does not aim to clarify such a detailed spatial characteristic, but rather a coarse trend on the vehicle roof, the basis of the measurement methodology is the same. Similar methods using thin-film heat flux sensors have also been applied to measure the convective heat flux from parts of the human body [30,31,32]. It is noteworthy that this experiment was performed without the VIPV module to estimate h on the smooth surface of a real car because the actual VIPV module is generally integrated into the car roof without any roughness so that it does not create resistance to airflow. The driving route is illustrated in Figure 3. The vehicle speed was in the range of 20–60 km/h and was gradually increased as much as possible. The vehicle position was recorded using a global positioning system (GPS).

Figure 4 illustrates the measurement system at each heat flux sensor position. Considering the one-dimensional heat balance in the vertical direction to the roof surface and assuming a negligible heat capacitance of the heat flux sensor, the net heat flux q through the sensor can be expressed as

$$q=h\left(T_s-T_a\right)-\epsilon \sigma T_s^4+\epsilon R_{sky}.$$

(1)

From this equation, h is derived as

$$h=\frac{q-\epsilon \left(\sigma T_s^4-R_{sky}\right)}{T_s-T_a},$$

(2)

where R_sky is the downward IR thermal radiation from the sky measured by the IR radiometer, T_s is the temperature of the heat flux sensor, T_a is the air temperature, ε is the emissivity (absorptivity) of the heat flux sensor surface for IR thermal radiation (0.7), and σ is the Stefan–Boltzmann constant (5.67 × 10⁻⁸ W/m²⋅K⁴).

Figure 4. Measurement system at each heat flux sensor position. Heat flux sensor temperature T_s; net heat flux q; infrared (IR) thermal radiation flux from the sky R_sky; air temperature T_a.

Figure 4. Measurement system at each heat flux sensor position. Heat flux sensor temperature T_s; net heat flux q; infrared (IR) thermal radiation flux from the sky R_sky; air temperature T_a.

2.2. Experimental Results

Figure 5 shows the results of one experiment for the small van, specifically the time variation of vehicle speed and net heat flux measured at position F1 and the anemometer. An apparent correlation between vehicle speed and net heat flux was observed as well as one between vehicle speed and sensor temperature. In other words, net heat flux increased as vehicle speed increased, whereas the sensor temperature decreased. The sensor temperature was maintained higher than the air temperature by constant heating using a film heater. The average temperature difference was 13.0 K. A similar dataset was obtained for the sedan experiment.

Figure 6 shows the relationship between vehicle speed and wind speed for the small van and sedan. The vehicle speed was calculated from the GPS data, whereas the wind speed was measured using an anemometer attached at the front edge of the vehicle roof, as shown in Figure 2. Hence, wind speed represents the local airflow velocity near the vehicle roof surface. Each vehicle shows a similar trend, in which the wind speed increases nonlinearly as the vehicle speed increases. This indicates that the local airflow velocity near the roof surface at the front edge is larger than that outside the velocity boundary layer, owing to the slope of the roof. This phenomenon is similar to that occurring in the flow around the upper part of the airfoil. The local airflow velocity can vary depending on the roof position. Hereafter, the vehicle speed is used as a reference speed, that is, a representative wind speed, for the convective heat transfer coefficient.

Figure 7 shows the trend of h calculated from the measured dataset as a function of vehicle speed. Each graph corresponds to the positions F1–F8, as shown in Figure 2. For the small van, h at the frontmost positions F1 and F2 is clearly higher than at the positions behind it. For example, h at position F1 at 50 km/h was 2.2–2.5 times higher than that at positions F3, F5, and F7. There is no remarkable difference between the characteristics along the centerline of the roof (i.e., F1, F3, F5, and F7) and the edge line of the roof (i.e., F2, F4, F6, and F8). The higher h characteristic at the frontmost position could be attributed to the shape of the small van. The velocity boundary layer is expected to become thinner at the front of the roof, and the local airflow velocity can increase because the slope of the vehicle body rapidly changes from the front glass window to the flat roof, as shown in Figure 2. For the sedan, the trend along the centerline of the roof is similar to that of the small van, whereas the trend along the edge line of the roof is remarkably different. Position F2 in the edge line shows a lower h than position F1 in the center line, whereas position F8 in the edge line shows a significantly greater h than position F7 in the center line. This characteristic can be attributed to the rounded shape of the sedan. According to the literature on the aerodynamics of typical passenger vehicles [33,34,35], complicated turbulent flow structures occurring at the rear edge of the vehicle can contribute to convective heat transfer enhancement.

Figure 7 also shows h calculated from the McAdams equation [14,15,23], expressed as follows:

$$h=5.7+3.8w,$$

(3)

where w is the wind speed [m/s] and the velocity of the free stream around the surface is normally used. This equation has been employed in a wide range of applications, including PV modules and vehicles. Here, the vehicle speed is substituted for w. Therefore, the calculated h does not show a position dependency. As mentioned in the introduction, there are other empirical linear equations with different coefficients, but in this study the McAdams equation is selected as a representative equation for comparison since it is the most frequently used one. It is clarified that the McAdams equation shows smaller values than the present measurement at all positions and vehicle speeds and the largest differences at the front and rear positions. Figure 7 also shows the approximated curves and their equations, based on a second-degree polynomial function, as empirical equations.

Figure 8 shows the plots of the averaged empirical equations over the positions along the centerline of the roof (i.e., F1, F3, F5, and F7). A plot using the McAdams equation is also shown for comparison. The averaged empirical equations for both vehicles are close and are approximately two times larger than the McAdams equation on average. This discrepancy is attributed to smaller coefficients and the linearity of the McAdams equation.

3. Measurement of Temperature

3.1. Experimental Setup

Figure 9 shows photographs of the experimental setup on the vehicle roof for the temperature measurement of a real VIPV module. Driving experiments were conducted during the daytime when a greater temperature change rate is expected owing to the contribution of sunlight. To minimize the frequency of shadowing on the module surface by surrounding objects, the time of day with the highest solar altitude was selected. The same vehicles (small van and sedan) were used as in the nighttime experiments described in the previous section. A commercial flexible PV module (Dokio Solar, DFSP-100M, 1180 mm × 540 mm × thickness: 2 mm) consisting of monocrystalline Si solar cells was mounted on the roof. The perimeter of the module was fixed onto the roof surface using thin transparent adhesive tape (thickness: 0.04 mm). To avoid increasing resistance to airflow, the module was mounted using a thin adhesive tape to minimize roughness. We assumed that the resistance to air flow was negligible. The temperatures of the top and back surfaces of the module and bare roof surface were measured using K-type thermocouples at T1–T8. K-type thermocouples built in heat flux sensors were used for the module top surface and the bare roof surface. The open-circuit voltage V_oc of the VIPV module was also measured because it reflects the effect of temperature on the power generation performance of the PV module. A higher module temperature results in a lower V_oc, that is, a decrease in generated power [7,8]. The DC output of the module was connected to the input terminals of the data acquisition instrument. The other experimental setups were the same as those used in the nighttime experiments.

Table 3. Weather conditions during the daytime experiments.

	Small Van	Sedan
Date and time	5 August 2021 12:30–14:00	3 October 2021 13:30–15:00
Average air temperature [°C] (Min.–Max.)	34.5 (34.2–34.9)	26.9 (26.2–27.5)
Average wind speed [m/s]	2.97	1.65
Weather	Clear sky	Clear sky

lists the weather conditions during the daytime experiments. The dates of the daytime experiments were close to the dates of the nighttime experiments (i.e., in summer and autumn). The average air temperature in the small van experiment was 7.6 K higher than that in the sedan experiment. Both days were calm and sunny; however, the solar irradiation for the sedan was slightly lower than that for the small van because of the lower incident angle of direct solar radiation.

3.2. Experimental Results and Discussion

Figure 10 shows the time variations of vehicle speed, module temperatures at T1, bare roof surface temperature at T2, and solar irradiance at P1 for the small van and sedan. Notably, IR thermal radiation flux R_sky was nearly stable throughout the experiment. The experiments started after the vehicles were parked outdoors under sunshine for 3 h. Thus, the module temperature at the start (t = 0) was high and then dropped rapidly after the start of driving for both vehicles. This is due to the significant increase in convective heat transfer coefficient caused by the increase in wind speed, as clarified in the previous section. The module temperature fluctuated as vehicle speed changed. These facts indicate that forced convection by the wind while driving significantly contributed to the cooling of the VIPV module. One hour after the start of the driving experiment, the average module temperature at position T1 decreased by 37.1 K (small van in summer) and 33.3 K (sedan in autumn), and V_oc consequently increased by 2.4 and 1.9 V, respectively.

Figure 11 shows the relationship between the V_oc of the VIPV module and the average temperature of the module averaged over T1, T3, and T5. For reference, V_oc under the standard test conditions (STC, module temperature 25 °C, solar irradiance 1000 W/m², AM1.5 G) is also plotted in the figure. The linearly decreasing trend of V_oc with respect to average module temperature confirmed that the power generation performance of the VIPV module was primarily affected by forced convection. Regarding the small van experiment conducted in summer, the V_oc changed linearly in the range of 82% to 93% of the STC value over the course of 1.5 h due to the change in convective heat transfer. Furthermore, V_oc was affected not only by the module temperature but also by the fluctuation in solar irradiance, which was not caused by changes in weather conditions but by the shadows cast by building structures and trees on the vehicle roof. The scattered data below the linearly decreasing trend in Figure 11 can be attributed to the fluctuation in solar irradiance.

Figure 12 shows box plots of the absolute temperature change rate of the average temperature of the module |dT_ave/dt| at positions T1, T3, and T5 on the VIPV module. For the small van, the range and level of values were the largest at T1 and gradually decreased at T3 and T5. This trend is consistent with the position dependence of h described in the previous section. On the contrary, for the sedan, position T5 showed a similar temperature change rate to T1. This trend was not completely consistent with the position dependence of h, as described in the previous section. This is because the VIPV module in the sedan experiment is exposed to more frequent fluctuations in solar irradiance than in the small van experiment, which will be clarified in Figure 13. Additionally, the small van experiment showed a wider range and higher temperature change rate due to its higher ambient air temperature. As mentioned above, the small van experiment was conducted in hot summer, and the module was more heated during the parking period before the start of driving. Consequently, the temperature difference between the module and the air for the small van was approximately 20 K higher than that for the sedan. The |dT_ave/dt| observed in the experiments reached up to 16.5 °C/min, which is approximately 10 times greater than that regulated in the temperature cycling test (IEC61730-2) for reliability evaluation of the conventional stationary PV modules.

Figure 13 shows the heat budget of the VIPV module analyzed using the measured dataset averaged over T1, T3, and T5. The left graph shows the box plots of the incoming and outgoing heat fluxes. The incoming heat flux to the VIPV module is composed of solar irradiance and IR thermal radiation flux from the sky, whereas the outgoing heat flux from the VIPV module is composed of convective heat flux and radiative heat flux from the VIPV module. Here, the empirical equations obtained from the nighttime experiment were used to calculate the convective heat flux, and the measured module top temperature and emissivity were used to calculate the radiative heat flux from the VIPV module. The left graph clearly shows that the outgoing heat flux has a larger level and wider range than the incoming heat flux for both vehicles. The right graph shows the breakdown of the outgoing heat flux, that is, the convective and radiative heat fluxes from the VIPV module. Obviously, convective heat flux plays a dominant role in the heat budget of the VIPV module, that is, the module temperature, compared to radiative heat flux. Specifically, the range of fluctuation in the convective heat flux was 19–27 times wider than that in the radiative heat flux.

4. Conclusions

In this study, the convective heat transfer coefficient on the roof surface of a running vehicle was clarified through experiments with real vehicles. Based on analysis of the measured datasets, empirical equations for approximating the convective heat transfer coefficient were presented in comparison with the traditional equation. The heat transfer coefficient obtained from the present experiment is approximately twice that obtained by the frequently used McAdams equation. The obtained approximate equations will be applied to the thermal design of VIPV modules as well as the thermal design of the vehicle cabin environment in the future. The measurement results of the real VIPV module temperature quantitatively confirmed that the temperature change characteristics of the VIPV module during vehicle driving were primarily affected by convective heat transfer, and the temperature change rate of the VIPV module was approximately 10 times greater than that expected in conventional stationary PV modules. Furthermore, the effect of module temperature on the power generation performance of the VIPV module was quantitatively confirmed. In summer conditions, the VIPV module heated up to nearly 80°C during parking under sunshine and then rapidly cooled at −16.5 °C/min during driving. The module V_oc changes linearly in the range of 82% to 93% of the STC value over the course of 1.5 h due to the change in convective heat transfer. Cooling by heat convection contributes to power improvement; however, the temperature fluctuation due to vehicle speed changes results in a frequent temperature cycle with a high temperature change rate. These findings will be useful guides for future research and the development of VIPV modules.