# Front-surface cooling of infrared thermophotovoltaic cells

Haolin Wang, Makoto Shimizu, Rodolphe Vaillon, Daniel Chemisana Villegas,

Oriol Teixido, Hiroo Yugami

► To cite this version:

Haolin Wang, Makoto Shimizu, Rodolphe Vaillon, Daniel Chemisana Villegas, Oriol Teixido, et al. Front-surface cooling of infrared thermophotovoltaic cells. Solar Energy Materials and Solar Cells, 2026, 295, pp.113940. 10.1016/j.solmat.2025.113940. hal-05246028

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# Front-surface cooling of infrared thermophotovoltaic cells

Haolin Wang<sup>a, ID</sup>, Makoto Shimizu<sup>a, * ID</sup>, Rodolphe Vaillon<sup>b, D</sup>, Daniel Chemisana Villegas<sup>c</sup>, Oriol Teixido<sup>c, D</sup>, Hiroo Yugami<sup>a</sup>

## ARTICLE INFO

### Keywords:

Thermophotovoltaic

PV cell cooling

Front-surface cooling

Thermal management

## ABSTRACT

This paper proposes a front-surface cooling method for thermophotovoltaic (TPV) cells utilizing microfluidic channels for efficient heat dissipation. Unlike conventional back-surface cooling, front-surface cooling minimizes thermal resistance by directly cooling the top surface of the cell. The microfluidic channel layer also functions as an antireflection layer through the gradual change in the refractive index. The proposed cooling method was evaluated using a thermo-fluid analysis, considering factors such as the emitter temperature, cell reflectance, thermal resistance, and fluid optical properties. We examined liquids with ideal absorption characteristics and actual liquids whose absorption coefficients were measured. The results showed that front-surface cooling significantly outperformed back-surface cooling in terms of the net power density. This method is particularly advantageous for high emitter temperatures or in cases where the thermal resistance between the cell and back-surface liquid is high. Moreover, this study highlights the potential application of the cooling method in bifacial TPV cells, which can generate electricity from thermal radiation incident on both sides. Bifacial cells offer higher power generation per unit area but face cooling challenges. The proposed cooling technique addresses these challenges, paving the way for innovative TPV system configurations and improved performance.

## 1. Introduction

Thermophotovoltaic (TPV) systems, which typically comprise a primary energy source, an emitter, and TPV cells, utilize the photovoltaic effect to convert thermal energy into electricity. The TPV technology has emerged as a promising alternative to conventional heat engines [1], owing to its ability to operate with a variety of energy sources, potential for high conversion efficiencies, and scalability. Energy sources can be fuels, nuclear energy, solar and other renewable energy sources, or waste heat. By tailoring the radiation spectrum using spectral emitters [2,3], filters [4], or back reflectors [5-7], TPV systems can achieve conversion efficiencies exceeding the Shockley-Queisser limit [8], which represents the theoretical maximum efficiency for conventional solar photovoltaic cells. Moreover, with the rapid advancements in ultra-high-temperature thermal energy storage, the TPV technology provides an efficient way to convert stored thermal energy into electricity, offering a high-energy-density and low-cost solution for large-scale electricity storage [9,10]. Further, compared with electrochemical batteries, TPV systems represent a promising approach for

mitigating the mismatch between electricity generation and demand arising from the intermittency of renewable energy sources such as solar and wind. Although the current conversion efficiency of TPV systems is lower than that of many electrochemical batteries, ongoing advancements suggest significant potential for improvement in the future.

Recent advancements have significantly improved the pairwise conversion efficiency, bringing it closer to theoretical limits. However, there is considerable scope for further improvement [11]. Narayan et al. [12] reported a TPV device achieving a pairwise efficiency of approximately 30 % using GaAs and In<sub>0.53</sub>Ga<sub>0.14</sub>As cells at emitter temperatures of 2330 and 1300 °C, respectively, with corresponding electrical output power densities of 2.45 and 0.658 W/cm<sup>2</sup>. Tervo et al. [13] reported a 0.75 eV GaInAs cell reaching a pairwise efficiency of approximately 39 % and a power density of 3.78 W/cm<sup>2</sup> at an emitter temperature of 1850 °C. LaPotin et al. [7] demonstrated a 1.4/1.2 eV TPV cell achieving a pairwise efficiency of over 40 % and a power density of 2.39 W/cm<sup>2</sup> at an emitter temperature of 2400 °C. Roy-Layinde et al. [14] achieved a pairwise efficiency of up to 44 % using InGaAs(P) air-bridge TPV cells under blackbody emission (1435 °C).

<footnote><sup>a</sup> Department of Mechanical Systems Engineering, Graduate School of Engineering, Tohoku University, Aoba 6-6-01 Aramaki, Aoba-ku, Sendai, 980-8579, Japan</footnote>

<footnote><sup>b</sup> LAAS-CNRS, Université de Toulouse, CNRS, Toulouse, France</footnote>

<footnote><sup>c</sup> Department of Chemistry, Physics, and Environmental Science, University of Lleida, 25001, Lleida, Spain</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: wang.haolin.p2@dc.tohoku.ac.jp (H. Wang), makoto.shimizu.a3@tohoku.ac.jp (M. Shimizu).</footnote>
Although the TPV technology is a promising high-efficiency approach for thermal-to-electrical energy conversion, significant advancements are required for practical applications, particularly in terms of thermal management of TPV cells [15,16]. Because only a portion of the incident radiation is converted into electricity, the remaining energy—resulting from the thermalization of in-band photons (the energy of which is higher than the bandgap), absorption of out-of-band photons (lower-energy photons that cannot be converted by the cell), non-radiative recombination, and Joule heating—becomes thermal loss. A failure to efficiently dissipate the generated heat can lead to an increase in cell temperature. The TPV cell performance deteriorates with increasing temperature, and excessive heating not only reduces efficiency but also causes operational failure or permanent damage [17–19]. The power density of the radiation from the emitter in a TPV system, particularly with a high view factor between the emitter and cell, is significantly greater than that in the case of conventional solar cells, even at relatively low emitter temperatures. Effective cell cooling remains a critical challenge for achieving high efficiency and output power density. Although research on TPV cell cooling is limited [19,20], various cooling strategies for PV cells and solar TPV systems under high solar concentrations have been extensively studied, including conventional rear-surface heat exchangers using forced water flow [21,22], radiative cooling [23,24], jet impingement cooling [25,26], and microchannel cooling [27,28]. Among these methods, coolant is generally separated from the cell back surface by intermediate layers, except in Ref. [21], where it contacts the PV panel (though a substrate remains beneath the cell) directly.

Despite significant developments in these techniques, most existing methods rely on back-surface cooling, which introduces a greater thermal resistance between the p-n junction and the cooling liquid, as the p-n junction is closer to the front surface. For example, in typical GaSb TPV cells, the p-n junction is located within <1 µm of the front surface [29,30], while the total cell thickness is up to 100 µm [31] and can be as large as ~650 µm for commercial cells [32]. Back-surface cooling requires heat to conduct through this entire thickness and across additional interfaces, such as the cell-substrate boundary and any attached heat sinks, further increasing thermal resistance. Hence, this paper proposes a front-surface liquid-cooling method for infrared TPV cells. Compared with conventional back-surface cooling, this approach significantly reduces thermal resistance, leading to a lower p-n junction temperature and improved cell performance. In addition, it minimizes the temperature gradient across the cell thickness, which may help reduce thermal stress and potential damage to the cell. Several immersion-cooling techniques have been proposed for solar PV systems [33,34]. However, it remains challenging to apply the same methods to TPV cells, such as gallium antimonide (GaSb) cells with a bandgap of approximately 0.7 eV. These cells primarily convert near-infrared light, which has a high absorption coefficient in many fluids, making the direct implementation of conventional immersion-cooling methods impractical.

The objective of this study is to achieve higher output power density and efficiency using this novel front-surface cooling approach. Numerical simulations were conducted to compare front- and back-surface cooling methods under various conditions. First, we analyzed front-surface cooling with ideal liquids, considering factors such as the fluid inlet velocity, temperature coefficient, emitter temperature, thermal resistance in back-surface cooling, and cell out-of-band reflectance. Subsequently, we evaluated the performance of front-surface cooling using real liquids to determine its potential advantages. Although real liquids may provide limited benefits due to their higher absorption, they could still be advantageous in bifacial TPV configurations [35,36], which offer significantly higher power densities. Although this study focused on GaSb cells, the proposed cooling method can be applied to other TPV cells with modifications based on the spectral properties of the chosen liquid.

## 2. Methods

This section outlines the modeling approach and experimental procedures used to evaluate the thermal and electrical performance of the TPV system. A numerical model was developed to simulate heat transfer, fluid flow, and radiation processes in the TPV converter, followed by experimental measurements of the optical properties of cooling liquids. The methodology is divided into model development, simulation setup, and material characterization.

### 2.1. Model description

#### 2.1.1. Geometric model

A front-surface liquid-based cooling approach was developed for TPV cells to enhance the conversion performance. The front-surface cooling method was compared with the conventional back-surface cooling approach to evaluate its potential advantages. Fig. 1 shows the TPV converter under consideration.

In the converter, a blackbody emitter was positioned directly above a GaSb TPV cell. A commercially available GaSb cell (JX Crystals) was selected as the reference cell in the model to evaluate the converter performance. Both the components had the same dimensions (16.5 mm × 12 mm). In the front-surface cooling configuration, a liquid layer and a calcium fluoride (CaF₂) window (2 mm thick) were placed above the TPV cell, as CaF₂ offers high transparency from the visible to the near-infrared range, ensuring efficient light transmission. Additionally, the liquid layer serves not only as a cooling medium but also as an optical layer that reduces reflection losses at the cell surface. This occurs because its refractive index lies between that of the CaF₂ window (or vacuum) and the GaSb cell, creating a gradual refractive index transition that suppresses Fresnel reflections and enhances light coupling into the cell. In the back-surface cooling configuration, the liquid layer was situated behind the cell and separated by a thermal-resistance layer. This layer simulates the combined thermal resistance of the cell itself, the substrate used for mounting and connecting the cell, and the contact thermal resistance between the cell and substrate. The thickness of the thermal resistance layer was set to 1 mm, and its thermal conductivity was adjusted to control the total thermal resistance. In both the configurations, the TPV cells had a thickness of 0.01 mm. For the front-surface cooling configuration, no explicit thermal resistance layer was included because the thermal resistance between the p-n junction and the cooling liquid is negligible. For the GaSb cell, the p-n junction lies <1 µm from the front surface, and the front metal grid (silver with a 25 % shading ratio, and assumed to be 10 µm thickness) together contribute a total thermal resistance of approximately $3 \times 10^{-8} \text{ m}^2 \text{ K/W}$. Even under an extreme scenario with a 2000 K blackbody emitter and assuming the entire heat flux passes through the cell, this results in a temperature difference of less than 0.03 K between the junction and front surface, which is insignificant relative to the overall system thermal behavior. At this scale, its intrinsic thermal resistance is negligible and has virtually no effect on the results; it simply defines the heat-sink region where thermal energy is removed to generate electricity. To minimize the impact of view-factor losses, the distance between the emitter and window (for front-surface cooling) or the TPV cell (for back-surface cooling) was set to zero in the model. Initial simulations with an extremely thin vacuum layer ($10^{-5} \text{ m}$) showed negligible differences in the results. Therefore, a zero-distance assumption was used for simplicity in the numerical simulations. This setup minimizes thermal radiation leakage and approximates a view factor of one. The liquid cooling layer was modeled with a uniform thickness of 100 µm unless specified otherwise (see Section 3.2).

#### 2.1.2. Simulation assumptions and governing equations

A finite-volume model was developed in ANSYS Fluent 2023R2 to simulate coupled heat transfer, fluid flow, and radiation transfer processes. The detailed governing equations, boundary conditions, and
<figure><img src="image_3.png" /><figcaption>Fig. 1. (a) Schematic of a front-surface cooling TPV system; (b) Side view schematic of the energy flow in the calculation model.</figcaption></figure>

numerical methods are provided in Section 1 in the Supplementary material.

Two ideal cooling liquids, referred to as Liquid 1 and Liquid 2, were considered to investigate the influence of optical properties. Both liquids were assigned the same thermophysical properties as water (e.g., density, viscosity, and thermal conductivity) to isolate the effects of radiation absorption. Liquid 1 was transparent across the entire spectrum ($\alpha_{\lambda} = 0$), while Liquid 2 was transparent in the in-band spectrum region ($\alpha_{\text{in}} = 0$) and opaque in the out-of-band spectrum region ($\alpha_{\text{out}}$ was varied with the liquid layer thickness to obtain an absorptance of 99.9 %). The refractive indices of both the liquids matched that of the CaF$_2$ window, thus minimizing the impact of refractive index variations and simplifying the problem.

The absorption coefficients of CaF$_2$ are 0.002/0.05 m$^{-1}$ for the in-band/out-of-band regions, respectively [37], and the calculated average refractive indices are 1.43/1.41. Table 1 presents the thermophysical properties of the candidate liquids [38–44], along with the calculated average refractive indices $\bar{n}$, absorption coefficients $\bar{\alpha}$, and reflectance $\bar{R}$ at the surface between the liquid and the GaSb [45,46] cell for both in-band and out-of-band radiations (for a 1500 K blackbody emitter and a liquid thickness of 100 µm). The reflectance at the surface between the vacuum and the GaSb cell, which is applicable for back-surface cooling, was 0.37/0.34.

<table><caption>Table 1
Thermophysical and optical properties of candidate liquids.</caption><thead><tr><th></th><th>Water</th><th>Acetone</th><th>Ethyl acetate</th><th>Liquid paraffin</th><th>Silicone oil</th></tr></thead><tbody><tr><td>Density (kg/m<sup>3</sup>)</td><td>998</td><td>785</td><td>901</td><td>819</td><td>913</td></tr><tr><td>Specific heat (J/ kg·K)</td><td>4182</td><td>2140</td><td>1925</td><td>2222</td><td>1550</td></tr><tr><td>Thermal conductivity (W/m·K)</td><td>0.6</td><td>0.18</td><td>0.14</td><td>0.14</td><td>0.12</td></tr><tr><td>Viscosity (kg/ m·s)</td><td>0.001</td><td>0.00031</td><td>0.00044</td><td>0.004</td><td>0.0046</td></tr><tr><td>n̄ (in-/out-of- band)</td><td>1.32/ 1.33</td><td>1.35/ 1.35</td><td>1.36/ 1.36</td><td>1.42/ 1.40</td><td>1.39/ 1.38</td></tr><tr><td>ᾱ (m<sup>-1</sup>) (in-/out- of-band)</td><td>1187/ 14,730</td><td>193.2/ 5084</td><td>95.81/ 3644</td><td>171.8/ 2698</td><td>75.58/ 2363</td></tr><tr><td>R̄ (in-band/out- of-band)</td><td>0.27/ 0.25</td><td>0.26/ 0.24</td><td>0.26/ 0.24</td><td>0.24/ 0.21</td><td>0.25/ 0.23</td></tr></tbody></table>

### 2.1.3. Parameter definitions and calculations

The pumping power for flowing liquids is given by:

$$P_{\text{pump}} = A_{\text{cross}} \cdot (P_{\text{in}} - P_{\text{out}}) \cdot V_{\text{in}} \quad (1)$$

where $A_{\text{cross}}$ is the cross-sectional area of the flow passage, $P_{\text{in}}$ and $P_{\text{out}}$
are the inlet and outlet liquid pressures, respectively, and $V_{in}$ is the liquid inlet velocity.

The net output power density is defined as:

absorption coefficient $\alpha_{\lambda}$ of the liquid can then be calculated using the following equation [33]:

$$ \alpha_{\lambda} = - \ln(\tau_{\lambda1} / \tau_{\lambda2}) / (d_1 - d_2) \quad (5) $$

$$ p_{\text{net}} = p_{\text{out}} - P_{\text{pump}} / A_{\text{cell}} = p_{\text{ref}} (Q_{\text{abs,cell}} / Q_{\text{in}}) \cdot (1 - TC \cdot (T_{\text{cell}} - 300)) - P_{\text{pump}} / A_{\text{cell}} \quad (2) $$

where $p_{\text{ref}}(Q_{\text{abs, cell}}/Q_{\text{in}})$ is the ideal power output density of the cell with a view factor of $Q_{\text{abs, cell}}/Q_{\text{in}}$; $T_{\text{cell}}$ is the average cell temperature; $TC$ is the temperature coefficient; $Q_{\text{abs, cell}}$ is the net radiation power absorbed by the cell; $Q_{\text{in}}$ is the total radiation power emitted by the emitter; $A_{\text{cell}}$ is the cell area, which equals the emitter area.

The sub-system efficiency is calculated as:

$$ E = p_{\text{net}} \cdot A_{\text{cell}} / (Q_{\text{in}} - Q_{\text{reflection}}) \quad (3) $$

where $Q_{\text{reflection}}$ is the radiation power reflected back to the emitter.

The thermal resistance between the TPV cell and the cooling liquid in the back-surface configuration is expressed as

$$ TR = w_{\text{tr}} / k_{\text{tr}} \quad (4) $$

where $w_{\text{tr}}$ is the thickness of the thermal resistance layer, and $k_{\text{tr}}$ is the thermal conductivity.

### 2.1.4. Verification and validation

A mesh-independent study was conducted to ensure the accuracy, reliability, and repeatability of the simulation results. The calculation domain was discretized into cubic meshes. Fig. 2(a) illustrates the influence of the mesh resolution on the average cell temperature and fluid pressure drop (defined as the difference between the average fluid inlet and outlet pressures) for a 1500 K blackbody emitter and front surface cooling using Liquid 1 (see Section 3.1). Based on the results, a grid with 262,500 meshes was chosen for subsequent simulations in this study because further refinement yielded negligible variations in the computed values. The discretization error was estimated using the grid convergence index (GCI) method [47], with the numerical uncertainties in the average cell temperature and fluid pressure drop calculated to be 0.07 % and 0.2 %, respectively.

To validate the simulation models and methods, numerical simulations were performed and compared with reference experimental data [48] on immersion cooling for solar cells. The validation case was conducted under conditions of incident radiation at 9.1 suns (DNI = 920 W/m²), with silicon solar cells operating at an efficiency of 12.76 % and a cooling liquid (silicone oil) exhibiting a Reynolds number (Re) range of 2700–13,600. As shown in Fig. 2(b), the simulated average cell array temperature ($t_{\text{avg}}$) and heat transfer temperature difference ($\Delta t$) closely match the experimental measurements reported in Ref. [48], with discrepancies generally within 2 °C.

### 2.2. Measurements of absorption coefficients

The absorption coefficients of candidate liquids were measured using two spectrometers: a UV/VIS/NIR spectrometer (Lambda 950, PerkinElmer) for the spectral interval of 0.3–2.2 µm with a resolution of 0.002 µm, and the FT-IR spectrometer (FI/IR-6100, JASCO) for the spectral interval of 1.28–20 µm with a resolution of 4 cm⁻¹. The measurement procedure followed a method similar to that described in Ref. [33], in which the liquids were sandwiched between two CaF₂ windows, allowing control over the liquid thickness. The transmittance of the entire window–liquid–window structure was obtained. The transmittances at two different liquid thicknesses, $d_1$ and $d_2$, were measured as $\tau_1$ and $\tau_2$, respectively. The wavelength-dependent

This method eliminates the influence of reflectance on the outer surface of the window and the interface between the window and the liquid, as well as the absorption in the window itself. Although this

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2. (a) Effects of mesh resolution on the average cell surface temperature, fluid outlet temperature, and fluid pressure drop between the inlet and outlet. (b) Comparison of the simulation results with experimental data from the reference.</figcaption></figure>
approach provides reliable transmittance measurements for a specific liquid thickness, it may not be sufficiently accurate if absorption coefficients are required to calculate the transmittance at different liquid thicknesses over a broader range. Specifically, if the liquid has low absorption (high transmittance) at a given wavelength and liquid thickness, the difference between $τ₁$ and $τ₂$ will be low when $d₁$ and $d₂$ are close, resulting in a greater measurement error. Conversely, if the liquid has a high absorption (low transmittance) at a given wavelength, increasing $d₁$ and $d₂$ leads to lower transmittance values, further increasing the measurement error. To mitigate these issues, we modified the measurement approach using two different sets of thicknesses: 25/50 µm and 10/20 mm for high- and for low-absorption-coefficients measurements, respectively. By combining the results from both the sets, we ensured that the measured absorption coefficients can be used for accurate transmittance calculations across the liquid thickness range

of 10–1000 µm in our calculation model (for details, see Section 2 in the Supplementary material).

### 3. Results and discussion

#### 3.1. Liquids with ideal absorption properties

Initially, front-surface cooling was compared with back-surface cooling under specific settings: an emitter temperature of 1500 K, a temperature coefficient of –0.5 % (comparable to previously measured values for GaSb cells [16]); for details on the influence of the temperature coefficient, see Section 3 in the Supplementary material), no anti-reflection coating in the in-band spectral region, and no backside reflector. Under these conditions, the reflectance of both the in-band and out-of-band radiations depended solely on the refractive index

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** (a) Spectral transmittance of the 2 dummy liquids. Effects of fluid inlet velocity on (b) cell temperature, (c) pumping power and net output power density, and (d) sub-system efficiency. The emitter temperature is 1500 K, the temperature coefficient is –0.5 %, and there is no anti-reflection coating in the in-band spectral region, and no backside reflector which means a relatively low out-of-band reflectance.</figcaption></figure>
difference between the cell and the material on top, that is, the ideal liquid for front-surface cooling and vacuum for back-surface cooling. Consequently, the reflectance values for front- and back-surface cooling were 0.24 (in-band)/0.22 (out-of-band) and 0.37 (in-band)/0.34 (out-of-band), respectively. The refractive-index transition between the liquid and TPV cells helps mitigate reflection losses, offering a secondary advantage. In contrast, the high refractive-index mismatch between the cell and vacuum leads to significant Fresnel reflection, causing an in-band radiation loss of over 30 % and severely limiting the output power density. A common solution is the application of antireflective coatings [49]; however, these require precisely designed multilayer structures, increasing the fabrication complexity and cost [50]. At longer wavelengths, achieving an optimal antireflective performance requires thicker coatings, which further complicates fabrication and increases light scattering and absorption [51]. In comparison, the front surface layer provides a simpler and lower-cost method for mitigating reflection losses. Thermal resistance is a key drawback of back-surface cooling, arising from various sources such as the cell material, contact resistance, and the recently popular air-bridge back-reflector (typically between $10^{-4}$ and $10^{-5}$ m² K/W [6,14]). Three thermal resistance values were considered for back-surface cooling: $10^{-5}$ m² K/W for low thermal resistance; $10^{-4}$ m² K/W for medium thermal resistance, which was close to our experimentally measured value [16]; and $10^{-3}$ m² K/W for high thermal resistance, representing an inefficient heat transfer case, such as the contact resistance of an air gap with a thickness of 26 µm.

Fig. 3 illustrates the effects of the fluid inlet velocity on the cell temperature, pumping power, and net output power density. These results were obtained under the condition of no backside reflector, which resulted in relatively low out-of-band reflectance, as described in the preceding paragraph. Liquid 2 achieved the lowest cell temperature due to its ability to directly absorb out-of-band radiation and dissipate heat through the liquid, followed by Liquid 1 with front-surface cooling. Back-surface cooling yielded the highest cell temperature owing to its greater thermal resistance. When the thermal resistance was low, the cell temperature was very close to that of front-surface cooling with Liquid 1. This slight difference is attributed to the marginally lower reflectance at the cell surface in the front-surface cooling, which causes a small increase in absorbed radiation and thermal load. As the thermal resistance increased, the temperature rise became more pronounced. High thermal resistance led to excessively high cell temperatures, making operation infeasible. This underscores the critical need for efficient thermal conduction in the back-surface cooling, even at an emitter temperature of 1500 K. In addition, the temperature difference between the front and back surfaces of the cell was also calculated: below 0.1 K for front-surface cooling, compared to 1.7, 17, and 187 K for back-surface cooling with low, medium, and high thermal resistances, respectively, confirming its effectiveness in reducing temperature gradients.

As shown in Fig. 3(c), pumping power increased with fluid inlet velocity because of the fixed viscosity, while higher velocities also lowered cell temperature and improved electrical power generation. Thus, an optimal fluid inlet velocity emerged as a trade-off between the cell temperature and pumping power. Regarding the net output power, front-surface cooling with both ideal liquids outperformed back-surface cooling, due to lower in-band reflectance and reduced cell temperature. Between the two ideal liquids, Liquid 2 led to a better net output power owing to its lower cell temperature.

However, as shown in Fig. 3(d), in terms of the sub-system efficiency, Liquid 1 was superior because its transparency in the out-of-band spectral region allowed radiation reflected at the liquid-cell interface (due to the refractive index mismatch) to return to the emitter for photon recycling, a process in which out-of-band radiation is reflected back to the emitter and reused, thereby reducing the net radiation power exchanged. In contrast, Liquid 2 absorbed all the out-of-band radiation, which was then carried away as heat. Back-surface cooling with a low thermal resistance exhibited a slightly higher efficiency than front-

<figure><img src="image_7.png" /><figcaption>Fig. 4. Influence of the emitter temperature on (a) net output power density and (b) sub-system efficiency. The temperature coefficient is –0.5 %, with no anti-reflection coating in the in-band spectral region and no reflector at the backside.</figcaption></figure>

surface cooling with Liquid 2 owing to out-of-band photon recycling, despite a marginally higher in-band reflectance. For back-surface cooling with a medium thermal resistance, the advantage of front-surface cooling with both ideal liquids was apparent, even in terms of the sub-system efficiency. These advantages were observed partly because there was no backside reflector, which resulted in relatively low out-of-band reflectance, so the out-of-band absorptance of Liquid 2 had limited influence on photon recycling. In TPV systems with high out-of-band reflectance, the effect of front-surface cooling liquids on sub-system efficiency can be more significant, as discussed later.

An increase in emitter temperature raises the thermal load in the cell due to higher thermalization losses and out-of-band absorption. As shown in Fig. 4 (a), the net output power density generally increased with emitter temperature, except for back-surface cooling with high
thermal resistance, where adequate cooling was only achieved up to 1200 K. Front-surface cooling consistently yielded higher net output power density. For Liquid 2, the net output power density was the highest among all configurations, and this advantage became more pronounced at higher emitter temperatures, owing to its superior cooling performance under severe thermal loads.

As shown in Fig. 4(b), the sub-system efficiency trends differed from those observed in net output power. For this case without a back reflector, resulting in relatively low out-of-band reflectance, front-surface cooling led to higher sub-system efficiency except in the case of the lowest thermal resistance. For back-surface cooling with a medium thermal resistance, the efficiency began to decline above 1800 K because the cooling became inadequate, and more of the increased

incident power was lost as heat rather than converted to electricity. Front-surface cooling with Liquid 1 achieved higher efficiency due to lower in-band reflectance and better cooling. With Liquid 2, front-surface cooling surpassed the others at higher temperatures (>1800 K) due to the lowest cell temperatures.

Finally, the front-surface cooling approach was analyzed in conjunction with photon recycling by introducing a backside reflector. Increasing the out-of-band reflectance enhanced photon recycling, improving sub-system efficiency and reducing the thermal load, assuming that out-of-band absorption by the cell was negligible. As shown in Fig. 5 (a), higher reflectance increased the net output power density for all configurations, except for front-surface cooling with Liquid 2, where out-of-band absorption prevented this benefit. As the reflectance approached 1, the power density for Liquid 1 converged with that of Liquid 2 because the thermal load on the cell became identical. Similarly, back-surface cooling with low and medium thermal resistances performed almost indistinguishable, as the low thermal load from perfect photon recycling resulted in minimal cell temperature differences for a 1500 K blackbody emitter. However, for back-surface cooling with a high thermal resistance, the net output power remained noticeably lower than that for the other configurations, underscoring the detrimental effect of poor thermal conduction.

Regarding the sub-system efficiency in Fig. 5 (b), for out-of-band reflectance above 0.6, back-surface cooling with low and medium thermal resistance achieved the highest efficiencies (15–50 %). Front-surface cooling with Liquid 1 performed comparably (15–45 %), since this ideal liquid was defined to have zero out-of-band absorptance. The slightly lower efficiency for Liquid 1 at high reflectance was partly due to increased multiple reflections between the cell surface and the liquid–window and vacuum–window interfaces. These reflections caused more radiation to escape through the flow inlet and outlet, resulting in greater radiation losses. For Liquid 2, which fully absorbed out-of-band radiation, the efficiency remained constant (~11 %) across all reflectance values. For reflectance below 0.6, all configurations showed lower and more comparable efficiencies, as the ability to recycle out-of-band radiation was inherently limited.

<figure><img src="image_8.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(b)</figcaption></figure>

**Fig. 5.** Influence of the cell out-of-band reflectance ($R_{out-of-band}$) on (a) net output power density and (b) sub-system efficiency. The emitter temperature is 1500 K, and the temperature coefficient is –0.5 %.

## 3.2. Real liquids

Real liquids were used in the calculations to evaluate whether front-surface cooling with a non-ideal optical performance can still have advantages over back-surface cooling. This analysis also helped compare the performance of real liquids with those of ideal liquids, highlighting the potential improvements achievable through liquid selection.

Five candidate liquids were selected: water, acetone, ethyl acetate, liquid paraffin, and silicone oil. Using the measured absorption coefficients, we calculated the average transmittances in the in-band and out-of-band spectral regions based on the emitter temperature and liquid thickness, as shown in Fig. 6. Water exhibits characteristics similar to those of Liquid 2, with a high in-band transmittance and low out-of-band transmittance. In contrast, the other liquids resembled Liquid 1, with high transmittance (higher than that of water) in the in-band region and relatively high transmittance in the out-of-band region. The total transmittance increased with the emitter temperature, as the majority of the incident radiation shifted toward shorter wavelengths relative to the bandgap of the GaSb cell, where these liquids were more transparent. The total transmittance increased with decreasing liquid thickness. For liquids resembling Liquid 1, thinner layers are generally more favorable from an optical perspective. In contrast, for water, which behaves similarly to Liquid 2, achieving a high in-band transmittance and low out-of-band transmittance requires careful optimization of the liquid thickness to balance these competing effects. This allows the liquid to act as an optical filter for cells designed with a low out-of-band reflectance, blocking out-of-band radiation to reduce the thermal load on the cell while enabling recovery of the absorbed heat as thermal energy.
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Wavelength-weighted average transmittance of five candidate liquids—water, acetone, ethyl acetate, liquid paraffin, and silicone oil—depending on the emitter temperature for a liquid thickness of 100 µm for the (a) in-band and (b) out-of-band spectral regions; and liquid thickness for a 1500 K blackbody emitter temperature for the (c) in-band and (d) out-of-band spectral regions.</figcaption></figure>

To understand the influence of the liquid thickness on the TPV cell performance, its effect on the net output power density and sub-system efficiency was analyzed for a 1500 K blackbody emitter and a temperature coefficient of -0.5 %. Two cases were considered: a low-reflectance cell (Fresnel reflectance) and a high-reflectance cell ($R_{\text{out-of-band}}$ = 0.95), as shown in Fig. 7(a)–(d). For simplicity, we present only the calculation results for three typical liquids—water, liquid paraffin, and acetone—along with back-surface cooling with medium thermal resistance. Acetone and liquid paraffin are both representatives of the liquid 1 type; however, they differ in key physical properties: acetone offers a slightly higher thermal conductivity and significantly lower viscosity, whereas liquid paraffin features a significantly lower out-of-band absorption coefficient. For complete results, including additional liquids and back-surface cooling with low thermal resistance, see Figs. S7 and S8 in the Supplementary material. In all the back-surface

cooling configurations, water was used as the cooling liquid. All the liquids exhibited an initial increase in both the output power density and sub-system efficiency as the liquid thickness decreased, reaching a maximum at an optimal point, and then declined for extremely thin layers. This trend is primarily driven by the cooling performance. As the liquid thickness decreases, the velocity and temperature gradients within the boundary layer increase, enhancing heat transfer due to higher Nusselt numbers and reduced hydraulic diameters. However, for extremely thin layers, the cooling improvement slowed as the Nusselt number approached a constant value. In addition, thinner liquid channels reduce the total flow rate and heat capacity, leading to higher average flow temperatures and diminished cooling effectiveness. The combination of these effects resulted in an optimal thickness (~100 µm, varying by cases) where the cooling performance was maximized, with a rapid improvement in the net output power density before this point and
<figure><img src="image_11.png" /><figcaption>**Fig. 7.** Effects of liquid thickness on (a) net output power density and (b) sub-system efficiency for low-reflectance TPV cells, and (c) net output power density and (d) sub-system efficiency for high-reflectance TPV cells ($R_{out-of-band}$ = 0.95), with a 1500 K blackbody emitter and a temperature coefficient of –0.5 %. In all back-surface cooling configurations, water is used as the cooling liquid.</figcaption></figure>

a gradual decline thereafter, as shown in Fig. 7(a) and (c). For back-surface cooling, the output power density and sub-system efficiency increased sharply before reaching the optimal thickness and then decreased slightly with minimal change beyond this point. This is because of the combined effect of varying the cooling performance and decreasing the pumping power, both of which were negligible at larger thicknesses. In contrast, for front-surface cooling, the performance declined more rapidly beyond the optimal thickness. This was attributed to the increased radiation leakage at the liquid inlet and outlet. In addition, real liquids absorb more radiation than ideal liquids with increasing liquid thickness.

In the low-reflectance case of the cell, front-surface cooling configurations with acetone and liquid paraffin achieved a maximum net output power density of approximately 2.2 W/cm², which was 20 %

higher than that achieved by back-surface cooling with a medium thermal resistance. Front-surface cooling with water achieved a net output power density of approximately 2 W/cm², representing an 8 % improvement over the medium thermal resistance case. Acetone exhibited the highest output power owing to its low viscosity and relatively high thermal conductivity. Despite its lower in-band reflectance (owing to a higher refractive index), liquid paraffin exhibited a lower output power owing to its significantly higher viscosity. As for water, for liquid thicknesses below 20 µm, it performed similarly to Liquid 2, though slightly worse due to its lower refractive index. However, for thicknesses above 20 µm, its net output power declined sharply due to the increased in-band absorption by the liquid. For small thicknesses, where the liquid remained optically transparent, however, the cooling was insufficient, and the net output power was primarily determined by
the thermal conductivity and viscosity of the liquid. For larger thicknesses, the cooling performance improved (for real liquids, with increasing thickness, more radiation was absorbed by the liquid, thereby decreasing the cell temperature), and the in-band absorption coefficient became more important. A similar trend was observed in the sub-system efficiency, although front-surface cooling resulted in lower values due to the additional out-of-band radiation absorption by the liquid. Only acetone achieved maximum conversion efficiencies comparable to those of back-surface cooling with a medium thermal resistance, whereas the other liquids performed significantly worse.

In the high-reflectance cell, the net output power density was slightly higher owing to the lower thermal load on the cell. In the front-surface cooling configurations, liquid paraffin achieved the highest maximum net output power density (~2.4 W/cm²), while acetone showed slightly lower values, and water remained the least effective. This ranking differed from the low-reflectance case; this is because with a high out-of-band reflectance at an emitter temperature of 1500 K, the total thermal load is minimal. Because the cooling performance was sufficient for all these liquids, the optical properties, particularly the absorption coefficient and refractive index, became the dominant factors favoring liquid paraffin owing to its low in-band absorption and high refractive index. Back-surface cooling with medium thermal resistance achieved a net output power density of ~2.1 W/cm², which was approximately 10% lower than that of front-surface cooling with top-performing liquids. In terms of the sub-system efficiency, front-surface cooling performed significantly worse than back-surface cooling, with a maximum efficiency of ~15% at a very low liquid thickness, whereas back-surface cooling exceeded an efficiency of 40%. Despite Liquid 1 bringing about an efficiency of over 35%, the much lower efficiency of the real liquids highlights the large gap between the real and ideal absorption coefficients, which is a major limitation of front-surface cooling.

To further illustrate these losses, Fig. 8 presents a Sankey diagram of the energy flow in the front-surface cooling case with water and liquid paraffin, and back-surface cooling with medium thermal resistance, at a thickness of 100 µm and $R_{\text{out-of-band}} = 0.95$ for a 1500 K emitter. For front-surface cooling, most of the energy losses stem from liquid absorption, with water absorbing more than 70% of the total input power owing to its high absorption coefficient, particularly in the out-of-band range. Even for liquid paraffin, more than half of the incident power is absorbed, which explains its significantly lower efficiency. In contrast, back-surface cooling avoids optical losses, with most out-of-band radiation reflected back to the emitter, resulting in much higher efficiency, though lower in-band absorption reduces the generated power compared with front-surface cooling using liquid paraffin. Further improvements for front-surface cooling in the sub-system efficiency require the discovery of liquids with very low absorption coefficients. Moreover, the radiation leakage from the inlet and outlet was slightly higher for liquid paraffin than for water because more transparent liquids allow radiation to pass through. However, these losses were minimal. The power returned to the emitter also varied. For water, it mainly occurred at the window interface due to refractive-index mismatches, whereas for liquid paraffin, photon recycling from the out-of-band reflectance of the cell increased the power returned to the emitter. Moreover, liquid paraffin achieved a slightly higher fraction of the input energy converted to electricity than water because of its lower in-band absorption coefficient and higher refractive index.

By leveraging the superior cooling performance and net output power density of front-surface cooling, its application in bifacial TPV devices can further enhance the power output while providing better thermal management than edge-cooled bifacial TPV cells [35]. In a bifacial TPV device, front-surface cooling is applied to both the surfaces of the cell (as shown in Fig. 9(a)); however, it is still referred to as front-surface cooling, with “front” indicating the surface facing the emitter. Owing to the symmetry of the system, the same calculation model was used as before, with the bottom surface set as a symmetric boundary and the out-of-band reflectance of the cell set to 1 to simulate

<figure><img src="image_12.png" /><figcaption>(a) Water</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>(b) Liquid paraffin</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>(c) Back-surface cooling with medium thermal resistance</figcaption></figure>

**Fig. 8.** Sankey diagrams illustrating power losses and energy transfer for front-surface cooling with (a) water, (b) liquid paraffin, and (c) back-surface cooling with medium thermal resistance. All cases assume a liquid thickness of 100 µm, $R_{\text{out-of-band}} = 0.95$ and a 1500 K blackbody emitter.
<figure><img src="image_15.png" /><figcaption>**Fig. 9.** (a) Side-view schematic of the front-surface cooling in a bifacial TPV device. (b) Net output power density as a function of the liquid thickness for different cooling configurations: front-surface cooling in a bifacial TPV device and back-surface cooling in a mono-facial TPV device, using a high-reflectance cell ($R_{\text{out-of-band}}$ = 0.95) and a 1500 K blackbody emitter.</figcaption></figure>

the radiation passing through the cell. For comparison, an edge-cooled bifacial TPV device was modeled with a 200 µm-thick TPV cell, where its edges were maintained at 300 K (assuming that the edge-cooling pipe keeps them at a constant temperature, similar to Ref. [35]) but with a 1.2 mm-wide GaSb cell. At a blackbody emitter temperature of 1500 K, side-surface cooling proved ineffective; the average temperature of the cell reached 539 K, preventing any power generation. Fig. 9(b) shows a comparison of front-surface cooling in a bifacial TPV device with back-surface cooling in a mono-facial TPV device using a

high-reflectance cell ($R_{\text{out-of-band}}$ = 0.95). Similar to the previous high-reflectance case, front-surface cooling with liquid paraffin achieved the highest maximum net output power density (~5.1 W/cm²), which was 2.4 times higher than that of the mono-facial TPV device with back-surface cooling and medium thermal resistance. The optimal liquid thickness was also lower (~50 µm) due to the reduced thermal load. Other liquids showed a similar trend, with maximum net output power densities 2.3 times higher than those of the mono-facial TPV device with back-surface cooling—except for water, which still produced a net output power twice that of the latter. A similar trend was observed for the sub-system efficiency as a function of liquid thickness compared to the high-reflectance TPV case (Fig. 7(d)), as shown in the Supplementary material Fig. S8 (b). In this case, out-of-band absorption can be reduced, which leads to an increase in the sub-system efficiency.

These results highlight the significant benefits of front-surface cooling in bifacial TPV systems, even when real liquids are used, because the net output power density can be more than doubled. However, a key challenge is the high current density in bifacial TPV devices, which leads to increased Ohmic losses. This issue can be mitigated by adopting vertical cell designs [36], which help reduce the current density and associated losses.

## 4. Conclusions

A novel front-surface cooling method for TPV cells was designed to enhance the cell performance through improved thermal management. By directly cooling the front surface, this approach reduces the thermal resistance and achieves lower cell temperatures. In addition, the use of single flow passage microchannels minimizes in-band liquid absorption while enhancing heat dissipation. The liquid layer also functions as an antireflection coating through the gradual change in the refractive index, which can be further optimized by modifying the refractive index of the liquid, for example, by adding nanoparticles to enhance the antireflection effect.

The performance of front-surface cooling was systematically compared with that of the conventional back-surface cooling approach using numerical simulations that coupled fluid dynamics, heat transfer, and radiation effects. The results showed that front-surface cooling consistently achieved higher net output power densities than back-surface cooling, with the advantages being more pronounced at high thermal resistances and thermal inputs. For cells with low out-of-band reflectance (no back reflector), at emitter temperatures above 1800 K, front-surface cooling achieved a higher sub-system efficiency than back-surface cooling with a low thermal resistance owing to its superior cooling performance. Although back-surface cooling may offer efficiency advantages at high cell reflectance values, front-surface cooling remains superior in terms of the power output, owing to its lower in-band reflectance and better thermal management.

In terms of its effectiveness, front-surface cooling using real liquids is highly sensitive to the channel thickness and optical properties of the liquids, with an optimal liquid channel thickness required to balance the thermal and optical factors. Despite the suboptimal properties of real liquids compared with ideal ones, front-surface cooling, particularly with acetone for low-reflectance cells and liquid paraffin for high-reflectance cells, can still achieve a net output power density up to 10 % higher than that of back-surface cooling at a low thermal resistance with a 1500 K blackbody emitter. However, the sub-system efficiency of front-surface cooling was significantly lower than that of back-surface cooling when the out-of-band reflectance was sufficiently high. Therefore, from a thermal-to-electrical energy conversion perspective, it is necessary to find a liquid that has high transmittance even at out-of-band wavelengths. Alternatively, the overall energy utilization efficiency can be increased if the heat absorbed by the liquid can be utilized. Furthermore, its incorporation into bifacial TPV devices can help enhance the overall power density. Even when using real liquids, such as liquid paraffin, the maximum net output power density can be up to 2.4
times higher than that of back-surface cooling in mono-facial cells with a low thermal resistance.

In summary, the front-surface cooling method offers significant advantages over conventional back-surface cooling, particularly in terms of output power density and thermal management. Although cell cooling has not been a major concern in laboratory-scale TPV systems, practical applications require a higher input power, making efficient TPV cell cooling essential for maintaining a high performance. In this context, the proposed front-surface cooling method can be useful for the development of high-performance TPV systems.

### CRediT authorship contribution statement

**Haolin Wang:** Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Makoto Shimizu:** Writing – review & editing, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Rodolphe Vaillon:** Writing – review & editing, Supervision, Project administration, Methodology, Formal analysis, Conceptualization. **Daniel Chemisana Villegas:** Writing – review & editing, Supervision, Project administration, Methodology, Formal analysis, Conceptualization. **Oriol Teixido:** Methodology, Formal analysis. **Hiroo Yugami:** Supervision, Funding acquisition, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

This work was supported by JST SPRING, Grant Number JPMJSP2114; and JSPS KAKENHI, Grant Number JP24K00814. We would like to thank Editage (www editage.jp) for English language editing.

### Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.solmat.2025.113940.

### Data availability

The data that support the findings of this study are available from the corresponding author, H. Wang or M. Shimizu, upon reasonable request.

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