Energy performance and heat transfer characteristics of photovoltaic double skin facades (PV-DSFs): a review

Abstract

Building-integrated photovoltaics (BIPV) have become a promising technology due to the urgent demand for sustainable energy supplies. Effective thermal regulation of BIPV is of great importance because the undesirable heat produced by photovoltaic (PV) modules will not only decrease the energy conversion efficiency, but also increase the building cooling load. The photovoltaic double skin façade (PV-DSF), regarded as one of the most feasible approaches to mitigate these problems, has been widely adopted and constructed globally. This paper presents a comprehensive literature review on PV-DSFs in terms of both energy performance and heat transfer characteristics. The energy performance of PV-DSFs involves a combination of energy supply from PV systems and energy demand for indoor heating, cooling and lighting. Investigations on the air flow and heat transfer characteristics in PV-DSFs are essential for understanding the heat transfer mechanisms and optimizing the system configurations. Based on the literature review, an outlook for future research is provided. This review article is expected to serve as a useful reference for future research and development of the PV-DSF technology.

---

Weilong Zhang

Weilong Zhang is a PhD candidate in the Department of Building Services Engineering at the Hong Kong Polytechnic University (PolyU). He received his Bachelor's and Master's degrees from the Harbin Institute of Technology (HIT). He was a visiting graduate student at the University of California, San Diego (UCSD). His research interests include HVAC systems, building energy efficiency and solar power systems.

Lin Lu

Dr Lin Lu joined the Hong Kong Polytechnic University in 2006. She has successfully secured over 26 research grants as PI, and has authored/co-authored three handbook chapters, two books and over 120 SCI journal papers (h-index of 24). Recently, she received the Global Innovation Awards in 2017 (TechConnect 2017), Gold Medal from 44th International Exhibition of Inventions of Geneva 2016, Faculty Dean's Award for Outstanding Achievement in Research Funding in 2010 and 2014, and HKIE Innovation Award 2013. Her current research includes renewable energy applications, green building nanomaterial development, and fluid mechanics and heat/mass transfer related to building studies.

---

1. Introduction

The potential threat of global climate change and the rapidly growing demand for energy have made it necessary to implement sustainable energy technologies. Energy efficiency and renewable energy are two major commitments required for sustainable energy development.¹ Energy efficiency is crucial to energy demand reduction, while utilizing renewable energy can reduce the reliance on fossil fuels. The buildings sector is the largest energy consuming sector in the world, and accounts for more than one-third of the total final energy consumption, and is an equal source of carbon dioxide (CO₂) emissions;² therefore, promoting sustainable energy supplies in buildings has become more and more pressing.

Building envelopes, which separate the interior conditioned space from the exterior unconditioned environment, are the key determinants of building energy efficiency and indoor thermal comfort.³ Heating, ventilation and air conditioning (HVAC) and lighting are two major energy consumers in buildings, accounting for 35% and 11% of total building energy consumption, respectively.⁴ As a principal component of building envelopes, building facades play an important role in the energy performance of buildings, especially when glazed facades are extensively used in modern architectures to enhance building aesthetics and maximize daylight quality.⁵ Therefore, developments and improvements in building facades have great potential to accelerate building energy efficiency. One of the most promising façade design concepts in recent years is the double skin façade (DSF), which is made up of two parallel façade layers and a ventilated air cavity in between.⁶ The ventilated air cavity can reduce the heat gain during the cooling season and the heat loss during the heating season, while mitigating the thermal discomfort caused by asymmetric thermal radiation.⁷

On the other hand, the growing awareness of energy and environmental challenges has encouraged the development of renewable energy technologies such as the solar photovoltaics (PV). PV modules, made up of multiple solar cells connected in series or in parallel, are electrical devices that convert the energy of light directly into electricity via the photovoltaic effect.⁸ Integrating PV modules into conventional building envelopes, such as roofs and facades, to form the building-integrated photovoltaics (BIPV) system is considered one of the most effective ways to promote renewable energy technologies.⁹ The development of semi-transparent solar cells enables the incorporation of PV modules into windows and glazed facades.¹⁰ A well-designed BIPV system can not only generate electricity in situ, but also contribute to the building comfort by providing weather protection, thermal insulation, noise protection and daylight modulation.¹¹

At present, however, only a small fraction of the solar energy incident on a PV module can be converted into electricity, with most of the absorbed solar energy transformed into heat.¹² This heat can increase the operating temperature and thereby decrease the energy conversion efficiency of the PV module.¹³ With every Kelvin increase in the cell temperature, the PV power output drops by approximately 0.4% for a crystalline silicon (c-Si) PV module and 0.1% for an amorphous silicon (a-Si) PV module.¹⁴ In addition, the excess heat may be transferred through the building envelope and increase the building cooling load;¹³ many researchers are therefore seeking solutions to mitigate these problems. During the last few years, the photovoltaic double skin facade (PV-DSF) has gained more and more attention among scholars. The external skin of the DSF is extremely suitable for the PV integration because the ventilated air cavity can not only lower the PV module temperature, but also improve the thermal performance of the building facade.¹⁵

Current research on PV-DSF systems mainly focuses on two aspects: one is the energy performance of PV-DSFs, including both the energy supply from PV systems and the energy demand for HVAC and lighting; the other is the air flow and heat transfer characteristics in PV-DSFs, which are essential for understanding the heat transfer mechanisms and optimizing the system configurations. Despite the fact that considerable research has been devoted to PV-DSF systems, little attention has been paid to analysing and summarising previous studies. This review article aims to enable better understanding of the PV-DSF technology, and indicate the opportunities for future research.

2. Classification of PV-DSFs

PV-DSFs can be classified in different ways. In this article, the classification schemes of PV-DSFs are based on transparency and driving force for airflow.

Commercial PV modules are either opaque or semi-transparent, so PV-DSFs can be classified into opaque PV-DSFs and semi-transparent PV-DSFs according to the transparency. Opaque PV modules, made of monocrystalline silicon (mc-Si) or polycrystalline silicon (pc-Si) solar cells, can be integrated into roofs and walls. With the development of semi-transparent PV technologies, PV glazings are widely used as windows and glazed facades, owing to their energy saving potentials.^16–30 The transparency of semi-transparent PV modules is normally achieved by two approaches. Firstly, semi-transparent c-Si solar cells can be achieved by laser cutting, mechanical grinding and dicing procedures.³¹ As a second approach, thin-film solar cells with a certain degree of visible light transmittance, such as a-Si, cadmium telluride (CdTe), copper indium gallium selenide (CIGS) and dye-sensitized solar cells, are applicable for PV glazings.³²Fig. 1 shows the structure of an opaque PV-DSF, consisting of an opaque PV module as the external skin, a conventional wall as the internal skin, and a ventilated air cavity in between. Opaque PV-DSFs can be used for both new buildings and the renovation of older buildings with poorly performing walls. In contrast, a semi-transparent PV-DSF is generally made up of an outside layer of semi-transparent PV modules, an inside layer of windows or glazed facades, and a ventilated air cavity, as shown in Fig. 2. Semi-transparent PV-DSFs can be adopted as windows and glazed facades.

Fig. 1 The structure of an opaque PV-DSF.³³ Reproduced with permission. Copyright 2013, Elsevier.

Fig. 2 The structure of a semi-transparent PV-DSF.³⁴ Reproduced with permission. Copyright 2015, Elsevier.

According to the driving force for airflow, PV-DSFs are classified into naturally ventilated PV-DSFs and mechanically-ventilated PV-DSFs. The driving force for airflow in naturally ventilated PV-DSFs can be buoyancy, caused by the heat transferred from the rear of the PV module to the air in the cavity, and/or a pressure difference between the inlet and outlet of the cavity, caused by wind effects.³⁵ In contrast, the driving force for airflow in mechanically ventilated PV-DSFs is supplied by mechanical devices like fans. Compared to mechanically ventilated PV-DSFs, naturally ventilated PV-DSFs do not need extra mechanical devices, which may produce noise and raise the installation and maintenance costs. However, the mechanically ventilated PV-DSF can operate at a certain air flow rate, regardless of the varying ambient temperature and the varying wind speed.³⁶

3. Energy performance of PV-DSFs

A PV-DSF is a multifunctional building envelope that provides both shelter and power. The energy performance, including thermal, daylighting and power performance, is one of the most important considerations in the design and evaluation of PV-DSFs. Both experimental and numerical studies have been conducted to evaluate the energy performance of PV-DSFs. Some building simulation software, such as ESP-r, TRNSYS and EnergyPlus, can be used to predict the energy performance of the PV-DSF systems. The major findings of research on the energy performance of PV-DSFs are summarized in Table 1.

Table 1 Major findings of research on the energy performance of PV-DSFs

Reference	Transparency (cell type)	Region (climate)	Study	Findings
37	Opaque (c-Si)	Hong Kong, Shanghai and Beijing	Determining the cooling load component through PV walls using a simplified method	The PV integration on a massive wall could lead to a reduction of the corresponding cooling load component by 32.5% in Hong Kong, 41.1% in Shanghai and 50.1% in Beijing. Generally, the higher the local solar intensity, the higher the cooling load component reduction ratio.
38	Opaque (c-Si)	Tianjin	Assessment of the impact of BIPV on building heating and cooling loads based on the one-dimensional transient model	The optimum method for BIPV application in summer was the PV with the ventilated air gap because of the high PV conversion efficiency and the low building cooling load; whereas, the PV with the non-ventilated air gap was appropriate in winter, due to the combination of the low building heating load and the high PV power output.
33	Opaque (c-Si)	Hong Kong (subtropical)	Investigation on the annual thermal performance of a PV wall based on numerical heat transfer models	In summer, the total heat gain of the south-facing PV wall was less than 50% of that of the corresponding normal wall. In winter, 69% of the heat gain during daytime and 32% of the heat loss during nighttime were reduced by mounting PV modules on the south-facing normal wall. The optimal thickness for the air gap of the south-facing PV wall could be 0.06 m
39	Semi-transparent (a-Si)	Hong Kong (subtropical)	Evaluation of the overall energy performance of a ventilated PV window using an energy model	The power output from the ventilated PV window decreased linearly with the solar cell transmittance. The surface convective and radiative heat transfer through the ventilated PV window was dominated by the inner glazing property, while the overall heat transfer was affected by both outer and inner glazing properties. The optimal solar cell transmittance for the best integrated electricity saving in air-conditioning and lighting was around 0.45–0.55
40	Semi-transparent (a-Si)	Hong Kong (subtropical)	Experimental evaluation of the energy performance of four configurations of PV glazing systems on a typical summer day	PV glazing could effectively reduce the direct solar transmission and enhance the thermal comfort. The energy saving potentials of PV glazing systems were generally better in air-conditioning power consumption, but much inferior in lighting power consumption compared to the absorptive glazing
41	Semi-transparent (a-Si)	Hong Kong (subtropical)	Investigation of the annual energy performance of ventilated PV glazing in office environment	The single PV glazing and naturally ventilated double PV glazing were able to save 23% and 28% of the annual space cooling electricity consumption, respectively, compared with the commonly used single absorptive glazing. However, the space heating demand was increased by 9.6% for single PV glazing and 0.92% for natural-ventilated double PV glazing
42	Semi-transparent (a-Si)	Hefei	Experimental and numerical investigation on the thermal and power performance of PV single-glazed window and ventilated PV double-glazed window	The average second heat gain (convective and infrared radiation heat transfer) and the total heat gain of the ventilated PV double-glazed window were 45.8% and 53.5% of those of the PV single-glazed window. The ventilated PV double-glazed window improved the thermal comfort of the indoor occupants, due to its lower inner glazing surface temperature
43	Semi-transparent (a-Si)	Hong Kong (subtropical)	Experimental and numerical evaluation of the thermal and power performance of a ventilated PV-DSF, compared with a conventional clear glazed facade	The internal air temperature for the PV-DSF was much lower and less affected by the outdoor environment than that for the conventional clear glazed facade. The PV-DSF could not only generate electricity, but also reduce the building cooling load and provide indoor visual comfort
34 and 44	Semi-transparent (a-Si)	Hong Kong (subtropical)	Experimental study on the thermal and power performance of a semi-transparent PV-DSF under ventilated, buoyancy-induced ventilated and non-ventilated conditions	The ventilated PV-DSF has the lowest average solar heat gain coefficient (SHGC), while the non-ventilated PV-DSF has the lowest U-value. The dynamic power output of the ventilated, buoyancy-induced ventilated and non-ventilated PV-DSFs decreased in sequence. The optimum operation strategy for the PV-DSF under different weather conditions was proposed to maximize its overall energy efficiency
45	Semi-transparent (a-Si)	Hong Kong (subtropical)	Developing a method for evaluating the overall energy performance of a ventilated semi-transparent PV-DSF	A comprehensive simulation model based on the EnergyPlus was developed for simulating the overall energy performance of a ventilated PV-DSF, taking thermal, daylighting and dynamic power output performances into account. This model was validated by the experimental data and could be used for sensitivity analysis and design optimization for PV-DSFs in various climate zones
46	Semi-transparent (a-Si)	Berkeley (cool-summer Mediterranean climate)	Numerical investigation on the energy saving potential of a semi-transparent PV-DSF	The optimal air gap depth for a PV-DSF ranged from 400 mm to 600 mm, taking into account energy use, cost, facade cleaning and maintenance, and the optimal ventilation mode was natural ventilation in terms of energy saving. The PV-DSF was able to reduce incoming solar radiation, but provide considerable interior daylight as well. Around 50% of the net electricity consumption could be reduced by PV-DSFs, compared with other commonly used glazing systems
47	Semi-transparent (a-Si)	Harbin, Beijing, Changsha, Kunming and Hong Kong	Comparative study of energy performance between PV-DSFs and PV insulating glass units (PV-IGUs)	The PV-DSF was better than the PV-IGU in reducing solar heat gain, while the PV-IGU was more exceptional than the PV-DSF in thermal insulation performance. On average, the PV-DSF and PV-IGU were able to save 28.4% and 30% of energy, respectively, compared to the conventional insulating glass windows in the five regions. The PV-DSF outperformed the PV-IGU if the louvers were closed in the heating season
48	Semi-transparent (c-Si)	Toulouse	Experimental evaluation of a full-scale prototype naturally-ventilated PV-DSF operating under real conditions	A full-scale prototype naturally-ventilated PV-DSF operating under real conditions was carried out. The energy performance of a simplified double-skin component could be extended to real complex systems with regard to geometry and environment
49	Semi-transparent (c-Si)	Nice, Paris and Lyon	Numerical study of a semi-transparent naturally-ventilated PV-DSF using the zonal approach	The cooling needs increased with the increase of the degree of transparency of PV-DSF. The heating load could be lowered by adopting PV modules with a higher degree of transparency and lower air change rate
50	Semi-transparent (c-Si)	Berkshire and Izmir	Assessment of the energy performance of a ventilated PV facade system based on a rigorous combined experimental and numerical approach	The effectiveness of ventilation was significant on the energy performance of a ventilated PV facade system. A long-term high resolution measurement of a typical ventilated PV facade system was carried out to assess the energy performance of the system in real outdoor conditions, and to provide a reliable database to verify a numerical model
51	Semi-transparent (c-Si)	Barcelona, Stuttgart and Loughborough	Investigation of the thermal performance of a ventilated PV facade with additional solar air collectors using a thermal building model	The cooling load of the building with the ventilated PV facade was marginally higher than that with the conventional structure in the three locations. 12% of heating load could be served by the ventilation heat gain in Barcelona, but only 2% in Stuttgart and Loughborough
52 and 53	Semi-transparent (c-Si)	Mataró, Barcelona and Stuttgart	Exploring a particular methodology to estimate the thermal performance of ventilated PV facades	A simplified approach based on an extension of U-value and g-value was developed to estimate the thermal performance of semi-transparent ventilated PV facades
54	Semi-transparent (c-Si)	Stockholm, London and Madrid	Evaluation of the overall energy performance of a ventilated PV facade using a new index	A new index, effectiveness of a PV facade (PVEF), was developed to evaluate the overall energy performance of a PV facade. The effects of changes in climate, building, facade and PV system elements on the overall energy performance were investigated. The air gap behind the PV modules was indispensable to prevent overheating in summer and the ventilation performance could be improved by locating the air outlet in a region of wind-induced negative pressure
55	Opaque (c-Si)	Volos	Assessment of the annual energy performance of an improved concept of PV-DSFs	Both the electricity and the heat generated by the PV modules were exploited to increase the building energy efficiency. The performance of the PV-DSF was determined by air flow rates and duct dimensions. Only an energy efficient building could benefit from such PV-DSF concept

---

The energy performances of opaque and semi-transparent PV-DSFs are different due to their module compositions. Commercial opaque PV modules are usually made of c-Si solar cells, while semi-transparent PV modules are made of see-through c-Si or thin-film solar cells; therefore, the overall energy conversion efficiency of the opaque PV-DSF is better than the semi-transparent PV-DSF. On the other hand, opaque PV-DSFs are generally incorporated into buildings by replacing external wall cladding materials, while semi-transparent PV-DSFs are employed as windows and glazed facades. Both generate electricity by absorbing the incoming solar radiation, but semi-transparent PV-DSFs also transmit solar radiation, bringing both daylight and solar heat gain into the buildings. As a consequence, different research methods are used for evaluating the energy performances of opaque and semi-transparent PV-DSFs.

3.1 Energy performance of opaque PV-DSFs

Compared to the normal wall, the PV-DSF can generate electricity as well as effectively reduce the building cooling load. In general, the higher the local solar energy density, the higher the cooling load reduction ratio.³⁷ Compared with the PV-DSF without ventilation, the ventilation in the PV-DSF cavity can reduce the PV module temperature and improve the PV conversion efficiency. The power generation performance of the ventilated PV-DSF is better than that of the non-ventilated PV-DSF, but the non-ventilated PV-DSF is better than the ventilated PV-DSF in reducing the heat loss in cold winters.³⁸ Under most circumstances, the excess heat removed by the air in the PV-DSF cavity is dissipated to the exterior environment. However, if this heat is exploited for heating purposes, such as space heating, the PV-DSF becomes a building-integrated photovoltaics/thermal (PV/T) system.^51–56

3.2 Energy performance of semi-transparent PV-DSFs

The energy performance of the semi-transparent PV-DSF is more complex than that of the opaque PV-DSF. The semi-transparent PV-DSF admits daylight into the building, resulting in more solar heat gain while providing daylight utilization to reduce lighting energy use. Fig. 3 illustrates the effects of semi-transparent PV-DSFs on building energy performance.

Fig. 3 Effects of semi-transparent PV-DSFs on building energy performance.

The overall heat transmission through a semi-transparent PV-DSF includes both the direct solar transmission and the inner surface convective and radiative heat transfer.³⁹ The energy performance characteristics for windows, such as solar heat gain coefficient (SHGC), U-value and g-value, were adopted in several studies to evaluate the thermal performance of semi-transparent PV-DSFs.^{34,44,47,52,53} Compared to the non-ventilated semi-transparent PV-DSF or the PV insulating glass units (PV-IGU), the ventilated semi-transparent PV-DSF have a lower SHGC, but a higher U-value.⁴⁷ The ventilation modes affect both the thermal and power performance of PV-DSFs and hence, the optimum operation strategies for semi-transparent PV-DSFs should be carefully assessed under different weather conditions.^34,44

The utilization of daylight can significantly affect the building energy performance. As in semi-transparent PV windows, the daylighting performance of a semi-transparent PV-DSF is mainly determined by its overall visible transparency. Increasing the overall visible transparency of the semi-transparent PV-DSF can improve the indoor daylight availability and thus reduce the lighting energy use. However, higher visible transparency also results in more solar heat gain and less power output.⁴⁹ Therefore, there is a complex interrelationship among the thermal, daylighting and power performance of a semi-transparent PV-DSF.

4. Air flow and heat transfer characteristics in PV-DSFs

It has been identified that the thermal behaviour dominates the energy performance of the PV-DSF. Understanding the air flow and heat transfer characteristics in PV-DSFs is of great importance to evaluate the thermal behaviour of PV-DSFs. However, the air flow and heat transfer in PV-DSFs involve complex phenomena, starting from the amount of solar radiation on the facade, the variation of the ambient temperature and the wind speed. This section will review some of the most important studies in this area.

4.1 Overview of the heat transfer process in PV-DSFs

A large number of studies were carried out on the air flow and heat transfer in opaque PV-DSFs. In an opaque PV-DSF, most of the incident solar radiation absorbed by the PV module is converted into heat. This heat is then transferred to the air in the cavity by convection and radiation. Radiative heat transfer carries energy across the air cavity. The net radiation, absorbed by the internal wall, is in turn transferred to the air in the cavity by convection. Therefore, the radiative heat transfer activates the convective heat transfer on the internal wall.⁵⁷ The internal wall is usually assumed to be adiabatic due to its thickness.

The energy flow in a semi-transparent PV-DSF is more complicated than that in an opaque PV-DSF. Fig. 4 presents the heat transfer process in a semi-transparent PV-DSF. The incident solar radiation is partly reflected and partly absorbed by the PV module, while the remainder passes through the PV module. The solar energy absorbed by the PV module is partly converted into electricity and the remainder appears as heat. The transmitted solar radiation is partly absorbed by the inner glass in the form of heat, and the remainder enters the room providing solar heat gain. The air in the cavity exchanges heat with the PV module and the inner glass by convection. The PV module and the inner glass also exchange heat by radiation.

Fig. 4 Heat transfer process in the semi-transparent PV-DSF.⁴⁴ Reproduced with permission. Copyright 2013, Elsevier.

Previous research on the air flow and heat transfer characteristics in PV-DSFs can be divided into analytical, numerical and experimental studies.

4.2 Analytical studies

Analytical studies can generally provide useful information for the preliminary prediction design of PV-DSFs without recourse to a complicated and time-consuming computation. However, a testable hypothesis must be made in an analytical study.

Brinkworth et al. have done a lot of analytical studies on the flow and heat transfer in PV cooling ducts. They presented a simplified method suitable for general use, based on single loop analysis in which the buoyancy force developed due to a change in temperature was balanced by the pressure drop due to friction.⁵⁸ The hypothesis was that the friction factors and internal heat gain coefficients for buoyancy-induced flows behaved the same as those for forced convection flows. This hypothesis was then validated against experiments for the case of developing laminar flow without any wind effects using a PV cladding arrangement. The predicted mass flow rates were in excellent agreement with the measured ones and therefore, the hypothesis was proved. A generalised PV model was also derived to describe the thermal behaviour of ventilated PV cooling ducts for both design and validation exercises.

Brinkworth also set out a practical and convenient procedure for determining the flow and convective heat transfer in PV cooling ducts.³⁵ This method covered the cases of free convection induced by the buoyancy effect, forced convection induced by the wind effect, and mixed convection induced by both buoyancy and wind effects. With an initial assumption of the relevant input heat flux and a prescribed duct geometry, the wall heat transfer coefficients were derived, leading to a better estimate of the input heat flux and ultimately converged to the solution. Generalised solutions were given for a representative case to illustrate how the flow and heat transfer characteristics were affected by the operating conditions and the duct geometries.

In practical situations, the flow in the duct might be obstructed by obstructions at the inlet and the outlet, or by support structures across the ducts. Brinkworth and Sandberg developed a procedure to predict the buoyancy-induced flow in PV cooling ducts, considering various pressure losses.⁵⁹ The hypothesis was that the pressure remained at the value where the expansion or contraction started. This procedure was validated by the measured flow rate in a duct heated from one side, with and without obstructions and support structures. Satisfactory agreement indicated that this procedure was adequate for practical application.

A design procedure for PV cooling ducts to minimise the PV conversion efficiency loss due to the temperature rise was put forward by Brinkworth and Sandberg.⁶⁰ It was found that there was an optimum depth of the PV cooling duct when the PV module temperature was the highest and the PV conversion efficiency was most affected. For a duct whose length was long enough for the flow to become fully-developed, the optimum ratio (the length to the hydraulic diameter) was found to be about 20. The results agreed reasonably well with the measurements on a full-size test rig. The optimum depth was also confirmed by a first-order theoretical foundation developed by Brinkworth.⁶¹

Sandberg and Moshfegh investigated the effects of the air gap geometry and the PV module location on the air flow in PV facades using lumped parameter analysis.⁶² The velocity and the temperature were assumed to be uniform across the air gap and only a function of height. Only buoyancy-induced flow was considered and the amount of heat transferred to the air gap was assumed to be known. The derived expressions were verified against measurements by varying outlet openings, aspect ratios and PV module positions.

Brinkworth pointed out that the convective and radiative heat transfer were intimately coupled together and should be treated in combination. A method for fully representing the coupling between the convective and radiative heat transfer in PV cooling ducts was then developed.⁶³ This method, in which the radiative heat transfer was represented in terms of local wall temperatures, was validated by comparison with other published work. This method does not need iteration and is applicable for both laminar and turbulent flows. Finally, the incorporation of duct heat transfer within thermal models of PV installation was given for a practical application.

4.3 Numerical studies

Air flow and heat transfer are governed by partial differential equations (PDEs) which represent conservation laws for the mass, momentum and energy, as shown below.⁶⁴

Conservation of mass

Conservation of momentum

Conservation of energy

Numerical studies are usually required because these PDEs are too complex to provide analytical solutions. Three classical numerical methods for solving PDEs are the finite difference method (FDM), the finite element method (FEM) and the finite volume method (FVM).⁶⁵ Computational fluid dynamics (CFD) is one of the most useful numerical techniques to study the fluid flow and heat transfer.⁶⁶

Moshfegh and Sandberg investigated the air flow and heat transfer characteristics of buoyancy-induced convection between a heated wall and an insulated wall in parallel, using a steady-state two-dimensional numerical model.⁶⁷ Both convective and radiative heat exchanges were taken into account as the flow and heat transfer mechanisms. The governing equation was solved by the FEM using FIDAP. Velocity and temperature profiles of the air at the outlet of the channel, and surface temperature profiles of the heated and the insulated walls were derived for various input heat fluxes and aspect ratios. It was found that for a given aspect ratio, the outlet air velocity and temperature increased with the increase of the input heat flux, while for a given heat flux, the outlet air velocity decreased while the outlet air temperature increased with the increase of the aspect ratio. The effect of surface emissivity on flow and heat transfer was reported in their subsequent study.⁵⁷ This study revealed the importance of radiative heat transfer in the heat transfer mechanisms in the air channel.

Liao et al. presented a CFD study of the air flow and heat transfer in a BIPV/T system using FLUENT.⁶⁴ The realizable k–ε viscous model was used to simulate the turbulent air flow and convective heat transfer in the cavity, and the surface to surface (S2S) radiation model was used to simulate the radiative heat transfer between boundary surfaces. The convective heat transfer coefficient was generated with the CFD model using experimental data as boundary conditions. The air velocity profiles from the CFD model were in good agreement with the ones from particle image velocimetry (PIV) experimental data. The computed heat transfer coefficients could be utilized in simple lumped parameter models for the design and analysis of BIPV/T systems. Convective heat transfer coefficient correlations were finally developed as a function of dimensionless characteristic numbers.

The CFD technique was also used to predict the optimum design of PV-DSFs, owing to its ability to provide information about flow and temperature fields. Usually, the length and the width of a PV-DSF are determined by the PV array dimension. The depth is then one of the most important variables in the design of a PV-DSF because the air gap size would influence the air circulation for cooling and therefore the energy conversion efficiency of PV panels. Many studies have been devoted to the determinations of the optimum depths for PV-DSFs. Gan utilized FLUENT to determine the adequate air gap on the power performance of PV modules mounted on pitched roofs and vertical facades.^68,69 The simulation was performed for realistic PV modules including module frames under bright sunshine and no wind when overheating of PV modules would be most likely to occur. The renormalization group (RNG) k–ε viscous model and the discrete ordinates (DO) radiation model were employed for modelling turbulent and radiative heat transfer, respectively. It was found that the air velocity generally increased with pitch angles under the constant solar heat gain, while the air velocity peaked at pitch angles of around 60 degrees for a certain location where the solar heat gain varied with inclination. The maximum PV temperature decreased with the increase in pitch angles and air gap depths, but increased with the increase in panel lengths in general. Based on CFD modelling, the minimum air gap depths for single and multiple PV module installations were given to reduce the possible overheating of PV modules.

Traditional numerical studies on PV-DSF are usually based on approximations or simplifications of boundary and initial conditions. However, more precise estimations are still required to simulate the performance of PV-DSFs. Grey-box modelling, based on a combination of prior physical knowledge and statistics, is a promising method for describing the heat dynamics of PV-DSFs and can be applied for simulation and prediction. Jiménez et al. found that the method for modelling non-linear stochastic systems using continuous-discrete stochastic state space models was suitable to describe the PV-DSF system.⁷⁰ However, more detailed measurements were needed to estimate the unknown physical parameters. This model was then applied to study the influence of forced ventilation where fins were placed in the air gap.⁷¹ The results showed that the heat transfer was increased with fins and a high forced velocity in the air gap.

4.4 Experimental studies

In addition to analytical and numerical studies, experimental studies are required to better understand and evaluate the air flow and heat transfer process and to provide useful data that might be used to validate the analytical and numerical models. Hot Wire Anemometry (HWA), Laser Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV) are the most commonly used diagnostic techniques to measure the fluid flow velocity. Both HWA and LDA are point measurement techniques, which offer good spatial and temporal response, but LDA offers a significant improvement over HWA at low fluid velocities. The PIV technique can measure fluid flow velocity at several locations simultaneously, so it can be used to measure three-dimensional transient fluid flow.⁷²

In many studies, the thermal behaviour of PV panels are usually mimicked with heating foils. Sandberg and Moshfesh carried out an experimental study on the air flow and heat transfer in a vertical channel between two surfaces.⁷³ A mock-up of a PV facade with one surface heated by heating foils was built in the laboratory. Tests were carried out using a channel with a rain protection at the top and a channel with both ends open. This is because the flow was constrained and expected to be laminar in the channel with a rain protection at the top, whereas in the channel with both ends open, the flow was expected to transition from laminar to turbulent. Air and surface temperatures were recorded and the flow rate was measured using the tracer gas technique. The results showed that 40% of the heat supplied by heating foils was transferred to the unheated surface by radiative heat transfer, and that the relation between the air flow rate and the input heat flux followed a power law relationship. Similar experiments were also conducted to investigate the air flow and heat transfer in ventilated solar roof.⁷⁴

Another experimental study was performed by Fossa et al. to investigate the natural convection in an open channel by changing the geometrical configurations of heat sources.⁷⁵ Surface temperatures were measured using thermocouples in order to infer information on the best cooling configurations for PV-DSF applications. The results indicated that the proper selection of the wall distance and the heating configuration could remarkably reduce the surface temperature and hence increase the PV conversion efficiency.

A testing device was specially designed by Zogou and Stapountzis to investigate the transient thermal behaviour of a PV-DSF in real insolation conditions in Volos, Greece.⁷⁶ K-type thermocouples were used to measure the inlet and outlet air temperatures and the PV panel back surface temperatures. An air velocity transducer was used to measure the outlet air velocity. Three operating modes were tested, including natural convection and forced convection with fans at two different nominal flow rates (110 m³ h⁻¹ and 190 m³ h⁻¹ with power consumption of 20 W and 22 W respectively). It was found that the use of fans, especially for the one with higher capacity, contributed to a significant decrease in the mean PV panel temperature and therefore an increase in the PV conversion efficiency. The experimental results also revealed the complexity of the air flow field inside the PV-DSF channel. Based on these findings, a further experimental investigation was carried out using flow visualization and HWA measurements.⁷⁷ The results were combined with CFD modelling to determine the wall heat transfer coefficients for building energy simulation. The results indicated that the air flow rates and heat transfer coefficients were critical to the performance of PV-DSF.

Kaiser et al. carried out an experimental study to investigate the impact of the channel aspect ratio and the induced air velocity on the PV module temperature for various incident solar radiations and ambient temperatures.⁷⁸ Resistance temperature detectors were attached to measure the PV module back surface temperature. The temperature sensors and wind speed sensors with hot film anemometers were used to determine the air conditions. The results indicated that higher aspect ratios resulted in lower PV module temperatures. The optimal aspect ratio to minimize the overheating of PV modules under natural convection ventilation was found to be 0.11. In addition, induced air velocity in the channel significantly affected the cooling effect. Lower aspect ratios could be used for achieving the same cooling effect if the induced air velocity was higher than that under the corresponding natural convection ventilation. Semi-empirical correlations were proposed for predicting the thermal behaviour of the PV-DSF.

4.5 Heat transfer analysis

Although the heat transfer process in the ventilated air cavity can be evaluated using experimental and numerical studies, the heat transfer correlations given in terms of dimensionless numbers are still indispensable for routine and prediction models; therefore, determining the most appropriate heat transfer correlations in PV-DSFs is another research focus.

An overwhelming amount of research has been done in natural convection in vertical channels with various boundary conditions. The most popular natural convection correlations for symmetric or asymmetric, isothermal or isoflux boundary conditions were developed by Bar-Cohen and Rohsenow.⁷⁹ The symmetric boundary conditions represent that the two vertical parallel plates are under the same conditions, either isothermal or isoflux, and the asymmetric boundary conditions represent that one vertical plate is isothermal or isoflux, while the other is insulated. The asymmetric isoflux condition is better for representing the boundary condition for opaque PV-DSFs, since the PV panel as the external skin is heated by the constant solar radiation, whereas the wall as the internal skin can be considered as adiabatic due to its thickness. However, for semi-transparent PV-DSFs, the shortwave solar radiation passes through the external semi-transparent PV panel and heats the internal skin, resulting in a more complex asymmetric boundary condition.⁸⁰

Despite the fact that various heat transfer correlations have been given in the literature, few correlations can be applied to natural convection in PV-DSFs. Al-Kayiem and Yassen argued that the application of heat transfer correlations suggested by Hollands⁸¹ in many studies was incorrect because these correlations were developed for a closed cavity.⁸² They therefore carried out an experiment using a rectangular passage solar air heater and then compared the experimental results with three widely used natural convection correlations – Hollands correlation,⁸¹ Bar-Cohen and Rohsenow correlation⁷⁹ and Tiwari correlation.⁸³ It was found that the Nusselt number was underestimated in the Hollands and Bar-Cohen correlations, but overestimated in the Tiwari correlation for the range of tested Rayleigh numbers. Agathokleous and Kalogirou also indicated that the Nusselt number correlation from Hollands cannot be used in an open channel, although the range of Nusselt numbers from Hollands et al. was the same as those from Bar-Cohen and Rohesnow for isothermal plates.³⁶ Cipriano et al. evaluated the accuracy of the existing heat transfer correlations for the average Nusselt number and air mass flow rate in PV-DSFs using Alya, a CFD code based on FEM.⁸⁰ The most appropriate correlations for natural convective PV-DSFs were obtained, as shown in Table 2.

Table 2 The most appropriate correlations for natural convection in PV-DSFs⁸⁰

Authors	Correlations	Notes
Symmetric, isothermal plates
Olsson^84	Nus = [(Nufd)^−1.3 + (Nuplate)^−1.3]^−1.3	Ra′ ≤ 10^5
	Nuplate = cC̄l(Ra′)^1/4f
	f = 1 + (Ra′)^−0.4
Asymmetric, isothermal and adiabatic plates
Bar-Cohen and Rohsenow^79		Ra′ ≤ 10^5
Symmetric, isoflux plates
Olsson^84	Nu = [(Nufd)^−3.5 + (Nuplate)^−3.5]^−1/3.5
	Nufd = 0.29(Ra′′)^1/2
	Nuplate = cH̄1(Ra′′)^1/5
Bar-Cohen and Rohsenow^79
Asymmetric, isoflux and adiabatic plates
Bar-Cohen and Rohsenow^79

---

Heat transfer analysis in naturally ventilated PV-DSFs is complex because the parameters and conditions are difficult to determine. The more accurate the boundary and initial conditions, the more reasonable the heat transfer coefficients. Compared to the natural convection, the forced convection is the controlled flow and has more known parameters.^85–88 Heat transfer coefficients for forced convection are much higher than those for natural convection.³⁶

5. Outlook for future research

Although much work has already been done regarding the energy performance and heat transfer characteristics of PV-DSFs, more efforts are still required for the further development of this technology. Future research opportunities are outlined as follows.

5.1 Further investigation on heat transfer characteristics

The air flow and heat transfer characteristics in PV-DSFs are affected by many factors, including the solar radiation intensity, the ambient air temperature, the air flow rate and the geometrical properties of the air cavity, etc. Although a number of studies have been devoted to the heat transfer characteristics in PV-DSFs, some considered assumptions or approximations cannot represent the real conditions. Therefore, further investigation should be conducted regarding the heat transfer mechanisms of real PV-DSF cases. Additionally, the radiative heat transfer is of great importance to the thermal behaviour of PV-DSFs. However, the convective and radiative heat transfer are usually assumed to take place independently in many studies. On the other hand, semi-transparent PV-DSFs, which can be integrated with different types of glazing, have been adopted and constructed in many buildings. The coupled convective and radiative heat transfer characteristics of a semi-transparent PV-DSF should be investigated.

5.2 Development and optimization of system configurations

The PV-DSF system is a feasible scheme to promote BIPV technologies. With proper designs, the PV-DSF system could be switched between passive cooling mode in hot seasons and heat recovery mode in cold seasons. In addition, the heat dissipated from PV panels can also be utilized for other use, such as space heating, hot water and heat pump. Future work should focus on the development and optimization of the configuration of PV-DSF for better balance between energy production from PV-DSFs and energy needs of buildings. The strategies for balancing the indoor thermal comfort and building energy use should also be proposed.

5.3 Evaluation of long term dynamic performance

Based on the literature review, very few experiments have been carried out to investigate the long term dynamic performance of PV-DSF in real buildings. On the other hand, the long term performance of the PV-DSF with emerging thin film PV technologies, such as CdTe, CIGS and dye-sensitized solar cells, has not yet been evaluated. Therefore, long term, real-time tests regarding the dynamic energy performance of PV-DSFs should be carried out in real buildings. The influence of weather conditions in different climate zones might also be considered. The long term tests can reflect the long-term energy behaviour of PV-DSF under real conditions, as well as help us to formulate the optimum operation schemes under different weather conditions. The adaptability of PV-DSF technology in different regions can also be obtained based on the results.

5.4 Assessment of economic and environmental benefits

Economic and environmental assessment should be conducted in order to evaluate the feasibility of PV-DSFs. Economic assessment is an approach to determine whether the opportunity costs of PV-DSFs are outweighed by additional energy saving. Environmental assessment is conducted to evaluate their energy requirement during the life cycle, in which the energy payback time and the greenhouse gases emission rates are usually used as environmental indicators.

6. Conclusions

The increasing demand for sustainable buildings has made the PV-DSF a promising building envelope solution in recent years. This paper presents a comprehensive literature review of previous studies on PV-DSF technology in terms of both energy performance and heat transfer characteristics. The energy performance is one of the most important considerations in the design and evaluation of PV-DSFs. Both the energy supply from the PV systems and the energy demand for HVAC and lighting affect the energy performance of PV-DSFs. The air flow and heat transfer characteristics in PV-DSFs play a vital role in the thermal behaviour of PV-DSFs. The heat transfer in naturally ventilated PV-DSFs is more complex than that in mechanically ventilated PV-DSFs since there are more unknown parameters. Although a lot of pioneer work has been done on PV-DSFs, there are still many problems and issues to be solved and addressed. Follow-up studies relating to this technology should be carried out regarding the work outlined above.

Acknowledgements

The work described in this paper was financially supported by the Hong Kong Polytechnic University through research project 8-ZG2L.

References

1. B. Prindle, M. Eldridge, M. Eckhardt and A. Frederick, The twin pillars of sustainable energy: synergies between energy efficiency and renewable energy technology and policy, American Council for an Energy-Efficient Economy, Washington, DC, 2007.
2. IEA, Transition to sustainable buildings: strategies and opportunities to 2050, International Energy Agency (IEA), 2013, http://www.iea.org/publications/freepublications/publication/Building2013_free.pdf.
3. L. Yang, H. Yan and J. C. Lam, Thermal comfort and building energy consumption implications–a review, Appl. Energy, 2014, 115, 164–173.
4. DOE, Quadrennial technology review: an assessment of energy technologies and research opportunities, U.S. Department of Energy (DOE), 2015, http://energy.gov/sites/prod/files/2015/09/f26/QTR2015-05-Buildings.pdf.
5. A. Ghaffarianhoseini, A. Ghaffarianhoseini, U. Berardi, J. Tookey, D. H. W. Li and S. Kariminia, Exploring the advantages and challenges of double-skin façades (DSFs), Renewable Sustainable Energy Rev., 2016, 60, 1052–1065.
6. M. A. Shameri, M. A. Alghoul, K. Sopian, M. F. M. Zain and O. Elayeb, Perspectives of double skin façade systems in buildings and energy saving, Renewable Sustainable Energy Rev., 2011, 15, 1468–1475.
7. T. E. Jiru and F. Haghighat, Modeling ventilated double skin facade—A zonal approach, Energ Build, 2008, 40, 1567–1576.
8. T. Ma, H. Yang and L. Lu, Solar photovoltaic system modelling and performance prediction, Renewable Sustainable Energy Rev., 2014, 36, 304–315.
9. C. Peng, Y. Huang and Z. Wu, Building-integrated photovoltaics (BIPV) in architectural design in China, Energ Build, 2011, 43, 3592–3598.
10. L. V. Mercaldo, M. L. Addonizio, M. D. Noce, P. D. Veneri, A. Scognamiglio and C. Privato, Thin film silicon photovoltaics: Architectural perspectives and technological issues, Appl. Energy, 2009, 86, 1836–1844.
11. M. Pagliaro, R. Ciriminna and G. Palmisano, BIPV: merging the photovoltaic with the construction industry, Prog. Photovoltaics, 2010, 18, 61–72.
12. T. Ma, H. Yang, Y. Zhang, L. Lu and X. Wang, Using phase change materials in photovoltaic systems for thermal regulation and electrical efficiency improvement: A review and outlook, Renewable Sustainable Energy Rev., 2015, 43, 1273–1284.
13. B. J. Brinkworth, B. M. Cross, R. H. Marshall and H. Yang, Thermal regulation of photovoltaic cladding, Sol. Energy, 1997, 61, 169–178.
14. B. Norton, P. C. Eames, T. K. Mallick, M. J. Huang, S. J. McCormack, J. D. Mondol and Y. G. Yohanis, Enhancing the performance of building integrated photovoltaics, Sol. Energy, 2011, 85, 1629–1664.
15. T. Zhang, Y. Tan, H. Yang and X. Zhang, The application of air layers in building envelopes: a review, Appl. Energy, 2016, 165, 707–734.
16. T. Miyazaki, A. Akisawa and T. Kashiwagi, Energy savings of office buildings by the use of semi-transparent solar cells for windows, Renewable Energy, 2005, 30, 281–304.
17. T. Y. Fung and H. Yang, Study on thermal performance of semi-transparent building-integrated photovoltaic glazings, Energ Build, 2008, 40, 341–350.
18. P. W. Wong, Y. Shimoda, M. Nonaka, M. Inoue and M. Mizuno, Semi-transparent PV: thermal performance, power generation, daylight modelling and energy saving potential in a residential application, Renewable Energy, 2008, 33, 1024–1036.
19. J. H. Song, Y. S. An, S. G. Kim, S. J. Lee, J. H. Yoon and Y. K. Choung, Power output analysis of transparent thin-film module in building integrated photovoltaic system (BIPV), Energ Build, 2008, 40, 2067–2075.
20. D. H. W. Li, T. N. T. Lam, W. W. H. Chan and A. H. L. Mak, Energy and cost analysis of semi-transparent photovoltaic in office buildings, Appl. Energy, 2009, 86, 722–729.
21. K. E. Park, G. H. Kang, H. I. Kim, G. J. Yu and J. T. Kim, Analysis of thermal and electrical performance of semi-transparent photovoltaic (PV) module, Energy, 2010, 35, 2681–2687.
22. J. H. Yoon, J. Song and S. J. Lee, Practical application of building integrated photovoltaic (BIPV) system using transparent amorphous silicon thin-film PV module, Sol. Energy, 2011, 85, 723–733.
23. L. Lu and K. M. Law, Overall energy performance of semi-transparent single-glazed photovoltaic (PV) window for a typical office in Hong Kong, Renewable Energy, 2013, 49, 250–254.
24. P. K. Ng, N. Mithraratne and H. W. Kua, Energy analysis of semi-transparent BIPV in Singapore buildings, Energ Build, 2013, 66, 274–281.
25. E. L. Didoné and A. Wagner, Semi-transparent PV windows: a study for office buildings in Brazil, Energ Build, 2013, 67, 136–142.
26. L. Olivieri, E. Caamaño-Martín, F. J. Moralejo-Vázquez, N. Martín-Chivelet, F. Olivieri and F. J. Neila-Gonzalez, Energy saving potential of semi-transparent photovoltaic elements for building integration, Energy, 2014, 76, 572–583.
27. L. Olivieri, E. Caamaño-Martin, F. Olivieri and J. Neila, Integral energy performance characterization of semi-transparent photovoltaic elements for building integration under real operation conditions, Energ Build, 2014, 68, 280–291.
28. W. Liao and S. Xu, Energy performance comparison among see-through amorphous-silicon PV (photovoltaic) glazings and traditional glazings under different architectural conditions in China, Energy, 2015, 83, 267–275.
29. W. Zhang, L. Lu, J. Peng and A. Song, Comparison of the overall energy performance of semi-transparent photovoltaic windows and common energy-efficient windows in Hong Kong, Energ Build, 2016, 128, 511–518.
30. M. Wang, J. Peng, N. Li, L. Lu, T. Ma and H. Yang, Assessment of energy performance of semi-transparent PV insulating glass units using a validated simulation model, Energy, 2016, 112, 538–548.
31. E. Bándy, Á. Földváry and J. Mizsei, Semitransparent monocrystalline solar cells manufactured by laser cutting and anisotropic etching, Microsyst. Technol., 2013, 19, 837–844.
32. L. M. Gonçalves, V. de Zea Bermudez, H. A. Ribeiro and A. M. Mendes, Dye-sensitized solar cells: a safe bet for the future, Energy Environ. Sci., 2008, 1, 655–667.
33. J. Peng, L. Lu, H. Yang and J. Han, Investigation on the annual thermal performance of a photovoltaic wall mounted on a multi-layer façade, Appl. Energy, 2013, 112, 646–656.
34. J. Peng, L. Lu, H. Yang and T. Ma, Comparative study of the thermal and power performances of a semi-transparent photovoltaic façade under different ventilation modes, Appl. Energy, 2015, 138, 572–583.
35. B. J. Brinkworth, Estimation of flow and heat transfer for the design of PV cooling ducts, Sol. Energy, 2000, 69, 413–420.
36. R. A. Agathokleous and S. A. Kalogirou, Double skin facades (DSF) and building integrated photovoltaics (BIPV): A review of configurations and heat transfer characteristics, Renewable Energy, 2016, 89, 743–756.
37. H. Yang, J. Burnett and J. Ji, Simple approach to cooling load component calculation through PV walls, Energ Build, 2000, 3, 285–290.
38. Y. Wang, W. Tian, J. Ren, L. Zhu and Q. Wang, Influence of a building's integrated-photovoltaics on heating and cooling loads, Appl. Energy, 2006, 83, 989–1003.
39. T. T. Chow, K. F. Fong, W. He, Z. Lin and L. S. Chan, Performance evaluation of a PV ventilated window applying to office building of Hong Kong, Energ Build, 2007, 39, 643–650.
40. T. T. Chow, G. Pei, L. S. Chan, Z. Lin and K. F. Fong, A comparative study of PV glazing performance in warm climate, Indoor Built Environ., 2009, 18, 32–40.
41. T. T. Chow, Z. Qiu and C. Li, Potential application of “see-through” solar cells in ventilated glazing in Hong Kong, Sol. Energy Mater. Sol. Cells, 2009, 93, 230–238.
42. W. He, Y. Zhang, W. Sun, J. Hou, Q. Jiang and J. Ji, Experimental and numerical investigation on the performance of amorphous silicon photovoltaics window in East China, Build. Environ., 2011, 46, 363–369.
43. J. Han, L. Lu, J. Peng and H. Yang, Performance of ventilated double-sided PV façade compared with conventional clear glass façade, Energ Build, 2013, 56, 204–209.
44. J. Peng, L. Lu and H. Yang, An experimental study of the thermal performance of a novel photovoltaic double-skin facade in Hong Kong, Sol. Energy, 2013, 97, 293–304.
45. J. Peng, D. C. Curcija, L. Lu, S. E. Selkowitz, H. Yang and R. Mitchell, Developing a method and simulation model for evaluating the overall energy performance of a ventilated semi-transparent photovoltaic double-skin facade, Prog. Photovoltaics, 2016, 24, 781–799.
46. J. Peng, D. C. Curcija, L. Lu, S. E. Selkowitz, H. Yang and W. Zhang, Numerical investigation of the energy saving potential of a semi-transparent photovoltaic double-skin facade in a cool-summer Mediterranean climate, Appl. Energy, 2016, 165, 345–356.
47. M. Wang, J. Peng, N. Li, H. Yang, C. Wang, X. Li and T. Lu, Comparison of energy performance between PV double skin facades and PV insulating glass units, Appl. Energy, 2017, 194, 148–160.
48. L. Gaillard, S. Giroux-Julien, C. Ménézo and H. Pabiou, Experimental evaluation of a naturally ventilated PV double-skin building envelope in real operating conditions, Sol. Energy, 2014, 103, 223–241.
49. S. Saadon, L. Gaillard, S. Giroux-Julien and C. Ménézo, Simulation study of a naturally-ventilated building integrated photovoltaic/thermal (BIPV/T) envelope, Renewable Energy, 2016, 87, 517–531.
50. M. Shahrestani, R. Yao, E. Essah, L. Shao, A. C. Oliveira, A. Hepbasli, E. Biyik, T. D. Caño, E. Rico and J. L. Lechón, Experimental and numerical studies to assess the energy performance of naturally ventilated PV façade systems, Sol. Energy, 2017, 147, 37–51.
51. L. Mei, D. Infield, U. Eicker and V. Fux, Thermal modelling of a building with an integrated ventilated PV façade, Energ Build, 2003, 35, 605–617.
52. D. Infield, L. Mei and U. Eicker, Thermal performance estimation for ventilated PV facades, Sol. Energy, 2004, 76, 93–98.
53. D. Infield, U. Eicker, V. Fux and J. Schumacher, A simplified approach to thermal performance calculation for building integrated mechanically ventilated PV facades, Build. Environ., 2006, 41, 893–901.
54. G. Y. Yun, M. McEvoy and K. Steemers, Design and overall energy performance of a ventilated photovoltaic façade, Sol. Energy, 2007, 81, 383–394.
55. O. Zogou and H. Stapountzis, Energy analysis of an improved concept of integrated PV panels in an office building in central Greece, Appl. Energy, 2011, 88, 853–866.
56. L. Mei, D. Infield, U. Eicker, D. Loveday and V. Fux, Cooling potential of ventilated PV façade and solar air heaters combined with a desiccant cooling machine, Renewable Energy, 2006, 31, 1265–1278.
57. B. Moshfegh and M. Sandberg, Flow and heat transfer in the air gap behind photovoltaic panels, Renewable Sustainable Energy Rev., 1998, 2, 287–301.
58. B. J. Brinkworth, R. H. Marshall and Z. Ibarahim, A validated model of naturally ventilated PV cladding, Sol. Energy, 2000, 69, 67–81.
59. B. J. Brinkworth and M. Sandberg, A validated procedure for determining the buoyancy-induced flow in ducts, Build. Serv. Eng. Res. Technol., 2005, 26, 35–48.
60. B. J. Brinkworth and M. Sandberg, Design procedure for cooling ducts to minimise efficiency loss due to temperature rise in PV arrays, Sol. Energy, 2006, 80, 89–103.
61. B. J. Brinkworth, Optimum depth for PV cooling ducts, Sol. Energy, 2006, 80, 1131–1134.
62. M. Sandberg and B. Moshfegh, Buoyancy-induced air flow in photovoltaic facades: Effect of geometry of the air gap and location of solar cell modules, Build. Environ., 2002, 37, 211–218.
63. B. J. Brinkworth, Coupling of convective and radiative heat transfer in PV cooling ducts, J. Sol. Energy Eng., 2002, 124, 250–255.
64. L. Liao, A. K. Athienitis, L. Candanedo, K. W. Park, Y. Poissant and M. Collins, Numerical and experimental study of heat transfer in a BIPV-thermal system, J. Sol. Energy Eng., 2007, 129, 423–430.
65. A. De Gracia, A. Castell, L. Navarro, E. Oró and L. F. Cabeza, Numerical modelling of ventilated facades: A review, Renewable Sustainable Energy Rev., 2013, 22, 539–549.
66. Z. Zhai, Q. Chen, P. Haves and J. H. Klems, On approaches to couple energy simulation and computational fluid dynamics programs, Build. Environ., 2002, 37, 857–864.
67. B. Moshfegh and M. Sandberg, Investigation of fluid flow and heat transfer in a vertical channel heated from one side by PV elements, part I-Numerical Study, Renewable Energy, 1996, 8, 248–253.
68. G. Gan, Numerical determination of adequate air gaps for building-integrated photovoltaics, Sol. Energy, 2009, 83, 1253–1273.
69. G. Gan, Effect of air gap on the performance of building-integrated photovoltaics, Energy, 2009, 34, 913–921.
70. M. J. Jiménez, H. Madsen, J. J. Bloem and B. Dammann, Estimation of non-linear continuous time models for the heat exchange dynamics of building integrated photovoltaic modules, Energ Build, 2008, 40, 157–167.
71. N. Friling, M. J. Jiménez, H. Bloem and H. Madsen, Modelling the heat dynamics of building integrated and ventilated photovoltaic modules, Energ Build, 2009, 41, 1051–1057.
72. K. D. Jensen, Flow measurements, J. Braz. Soc. Mech. Sci. Eng., 2004, 26, 400–419.
73. M. Sandberg and B. Moshfegh, Investigation of fluid flow and heat transfer in a vertical channel heated from one side by PV elements, part II-Experimental study, Renewable Energy, 1996, 8, 254–258.
74. M. Sandberg and B. Moshfegh, Ventilated-solar roof air flow and heat transfer investigation, Renewable Energy, 1998, 15, 287–292.
75. M. Fossa, C. Ménézo and E. Leonardi, Experimental natural convection on vertical surfaces for building integrated photovoltaic (BIPV) applications, Exp. Therm. Fluid Sci., 2008, 32, 980–990.
76. O. Zogou and H. Stapountzis, Experimental validation of an improved concept of building integrated photovoltaic panels, Renewable Energy, 2011, 36, 3488–3498.
77. O. Zogou and H. Stapountzis, Flow and heat transfer inside a PV/T collector for building application, Appl. Energy, 2012, 91, 103–115.
78. A. S. Kaiser, B. Zamora, R. Mazón, J. R. García and F. Vera, Experimental study of cooling BIPV modules by forced convection in the air channel, Appl. Energy, 2014, 135, 88–97.
79. A. Bar-Cohen and W. M. Rohsenow, Thermally Optimum Spacing of Vertical, Natural Convection Cooled, Parallel Plates, J. Heat Transfer, 1984, 106, 116–123.
80. J. Cipriano, G. Houzeaux, D. Chemisana, C. Lodi and J. Martí-Herrero, Numerical analysis of the most appropriate heat transfer correlations for free ventilated double skin photovoltaic façades, Appl. Therm. Eng., 2013, 57, 57–68.
81. K. G. T. Hollands, T. E. Unny, G. D. Raithby and L. Konicek, Free convective heat transfer across inclined air layers, J. Heat Transfer, 1976, 98, 189–193.
82. H. H. Al-Kayiem and T. A. Yassen, On the natural convection heat transfer in a rectangular passage solar air heater, Sol. Energy, 2015, 112, 310–318.
83. G. N. Tiwari, Solar energy: fundamentals, design, modelling and applications, Alpha Science Int’l Ltd., 2002.
84. C. O. Olsson, Prediction of Nusselt number and flow rate of buoyancy driven flow between vertical parallel plates, J. Heat Transfer, 2004, 126, 97–104.
85. H. M. Tan and W. W. S. Charters, An experimental investigation of forced-convective heat transfer for fully-developed turbulent flow in a rectangular duct with asymmetric heating, Sol. Energy, 1970, 13, 121–125.
86. A. Zöllner, E. R. F. Winter and R. Viskanta, Experimental studies of combined heat transfer in turbulent mixed convection fluid flows in double-skin-facades, Int. J. Heat Mass Transfer, 2002, 45, 4401–4408.
87. L. M. Candanedo, A. K. Athienitis, J. A. Candanedo, W. O'Brien and Y. Chen, Transient and Steady State Models for Open-Loop Air-Based BIPV/T Systems, ASHRAE Trans., 2010, 116, 600–612.
88. L. M. Candanedo, A. Athienitis and K. W. Park, Convective heat transfer coefficients in a building-integrated photovoltaic/thermal system, J. Sol. Energy Eng., 2011, 133, 0210021.

---