A simple way is to calculate the equilibrium temperatures at steady state. the solar radiation is partly reflected and absorbed by the plastic sheet, of which reflexion and absorption coefficients should be known, and partly reflected and absorbed by the absorber. This provide the heat flow rate (in W/m²) for both. On the other way, both loose heat. the plastic sheet loses heat to the surrounding air, depending on its temperature and on the wind velocity. Usually, a heat transfer coefficient is either calculated or an average value is assumed (e.g. at 25 W/m²K). This heat loss is proportional to the heat loss coefficient multiplied by the temperature difference between the sheet (unknown) and the air (assumed known)

The absorber provides heat to the user and loose heat to the surrounding environment. The calculation of the latter is similar to that for the plastic sheet, but for its both surfaces: heat loss towards the plastic sheet, and heat loss on its backside. The provided heat is the product of the fluid flow rate by the inlet-outlet temperature difference, multiplied by the specific heat of the fluid used to transport the heat. to the user. Equating the l heat losses of each sheet to the absorbed solar intensity provides two equations , from which the temperatures can be obtained.

Thank You. I appreciate your thorough answer. Kirk Rensmeyer

The problem as defined is a simple conduction problem: if the heat flux is prescribed then the temperature field depends on the conductivities of the materials and probably the method of build. The sink temperature is the melting point of polyethylene. The full solution, as described by C-A.R above is much more complex. If it is needed, reflection is significant at low angles of incidence: it seems to me that a simple constant heat flux based approach is appropriate.

Thanks Jack,

It is useful to have several ways of viewing this problem. Your approach gives me new ideas. I need to do some calculations to determine what model is the best fit. Regards,

Kirk Rensmeyer

I have done several thermal calculations (simple and complex) and compared the results with experiments. I was always amazed ho the both fit!

RESEARCH ARTICLE | DECEMBER 20 2018

Numerical study on energy performance of sheet and tube

type photovoltaic thermal solar system 

O. Tata; M. Feddaoui; Y. Belkassmi

AIP Conf. Proc. 2056, 020021 (2018)

https://doi.org/10.1063/1.5084994

Numerical Study on Energy Performance of Sheet and Tube

Type Photovoltaic Thermal Solar System.

O. Tata1, a), M. Feddaoui1) and Y. Belkassmi2)

1 Ibn Zohr University, GEMS Laboratory, ENSA, B.P. 1136 Agadir, Morocco.

2 Ibn Zohr University, ERMAM, FPO, Ouarzazate, Morocco.

a) [email protected]

Abstract. Increasing the temperature of the photovoltaic module causes a reduction in its electrical efficiency.

Photovoltaic Thermal systems (PV-T) are used to minimize this undesirable effect by recovering residual energy. The

heat extracted from the PV modules causes the cooling of the photovoltaic cells and stabilizes its performances. These

systems produce both electricity and thermal energy at the same time. In this work, a photovoltaic/thermal sheet and tube

collector has been numerically investigated. A mathematical model has been developed to determine the dynamic

behavior of the collector. The heat transfer modeling is carried out in transient mode, on the basis of energy balance in

the principal components of the collector (glazing, PV module, absorber plate, liquid circulation tubes, liquid and

insulating). The model has been validated by comparing the obtained simulation results with experimental results

available in literature, where good agreement has been noted. Using our developed model, the thermal and electrical

behavior of sheet and tube collector has been analyzed. The effect of solar radiation, wind velocity, ambient temperature,

the inlet water temperature and fluid flow rate has been involved to identify their influence on the thermal and electrical

efficiencies. This model will be applied to optimize the performance of the hybrid systems under (PV-T) Moroccan

meteorological conditions.

INTRODUCTION

Photovoltaic conversion, both at the research level and at the industry level in recent years, there has been a

profound change associated with the growing interest in this energy. It represents a promising solution to solve some

most urgent problems which are currently facing the world, like climate change and energy security [1].

In fact, despite the great efforts made around the world, the performance of photovoltaic panels remains low and

the costs are very high. Indeed, the majority of the energy incident on the surface of the photovoltaic module is

dissipated by Joule effect [2].

This effect has been identified as hazardous to the functioning of the cells, because it causes an increase in the

temperature of the PV cells. It manifests itself by a significant decrease in the electrical efficiency of the PV

module.

In order to stabilize the operating temperature of the PV cells and improve their performance, a lot of research

has been conducted. The hybrid photovoltaic-thermal collector (PV-T) is proposed as a solution. This measure

allows at the same time the generation of electrical energy and the recovery of residual heat. It is, in principle, one of

the most effective ways of using solar energy to satisfy both the electrical and thermal energy needs [3]. In addition,

research in these hybrid technologies started in the 70s and flourished in the 1980s [4]. Several configurations of

hybrid collectors using air or water as coolant are studied experimentally and analytically [5].

1st International Congress on Solar Energy Research, Technology and Applications (ICSERTA 2018)

AIP Conf. Proc. 2056, 020021-1–020021-10; https://doi.org/10.1063/1.5084994

Published by AIP Publishing. 978-0-7354-1784-7/$30.00

020021-1

08 June 2024 23:33:55

Nomenclature

A

C

Di

Do

Eel

G

Gr

h

hc

hr

Hp

K

L

M

m

Nu

Pr

Q

Ra

Rc

Ti

Tam

U

Area, m2

Specific heat (J/kg.K)

Inner diameter of tube (m)

Outer diameter of tube (m)

Electrical energy (J)

Global incident irradiation (W/m²)

Grashoff number

Convective Transfer coefficient (W/m².K)

Conductive transfer coefficient(W/m².K)

Irradiative transfer coefficient(W/m².K)

Heat transferred to the fluid (J)

Thermal conductivity (W/m K)

Tube length, (m)

Mass (Kg)

Mass flow rate of the fluid (kg / s)

Nusselt number

Prandtl number

Absorbed heat (J)

Rayleigh number

Illuminated area ratio

Temperature at (i) node in(°C)

Ambient air temperature, (° C)

water velocity in the tube (m / s)

α

β

ԑ

η

θ1

θ2

ᴧ

σ

δ

τ

Subscripts

a

ab

is

PV

ad

t

cel

e

el

g

th

f

Absorbance

Temperature coefficient

The study of hybrid water sensors is well detailed in the literature [6]. In this technology, PV cells are bonded on

a metal plate, and cooled by a circulation of water, mainly, in copper tubes located at the back.

In 1997, Fujisawa and Tani [9] designed and built a hybrid solar collector PV-T with water and glass and plan

absorber in non-selective aluminum, and PV modules of mono-crystalline silicon. They found that this glass sensor

produces almost as much thermal and electrical energy as a PV solar collector and a flat solar thermal collector

together. In 2002 Sandnes and Rekstad [8] conducted a study on a collector composed of mono-crystalline silicon

based PV cells. The cells are bonded through a 0.5 mm thick adhesive to a black plastic absorber with water

circulation channels on the underside. In 2003, Tin tai Chow [10] proposed a detailed study of an explicit dynamic

model allowing the prediction of the performances of collector. His model based on the work of Bergene and Lovvik

[11]. In another study, Kalogirou and Tripanagnostopoulos [12] simulated the behavior of PV-T solar collectors with

water, based on polycrystalline silicon or amorphous silicon photovoltaic cells, insulated at the back side with a 5

cm layer of polyurethane, and integrated into industrial buildings. They noticed that the electrical production of a PV

solar collector is 25% higher than that of the hybrid component.

Shan et al. [13] developed a numerical model for performance prediction a PV-T collector with production of hot

water. Their results showed improved performance by increasing water flow and reducing the number of PV

modules connected. In 2005, Zondag [14] presented a state of the art on hybrid PV / T solar collectors, based on the

report of the European PV-catapult project Tripanagnostopoulos . He [15] also conducted an annual analysis of heat

pipe PV/T system under three different climate areas of China. Tripanagnostopoulos [16] conducted a

comprehensive study of PVT hybrid solar collectors, in order to reduce the operating temperature of the PV modules

and the heat losses through the insulator on the underside of the component to improve the performance of the

system. He introduced a new type of PV collector with a dual heat extraction function, either with water or with the

air circulation.

The system is suitable for integration into the building, and allows the supply of hot water or air depending on

the season and the thermal needs of the building. Touafek et al.[17] studied theoretically and experimentally a

thermal photovoltaic hybrid collector using a tube absorber and a galvanized steel sheet, and established by

numerical simulation the thermal behavior of the PVT collector and the temperature distribution. In the different

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08 June 2024 23:33:55

layers of the hybrid collector. S. Bhattarai, et al. [18] have studied experimentally a hybrid photovoltaic sensor

connected to a storage tank and compared its performance to that of a conventional sensor. Osama Rejeb et al. [19]

presented a numerical study based on the finite volume method, with the intention of identifying a configuration

ensuring the generation of optimal electrical and thermal efficiencies. And highlighted the influence of different

parameters on sensor performance, including meteorological parameters and the operating parameters.

This current study analyzes the performance of a hybrid sensor and identifies the most favorable configuration

for domestic and industrial applications in Morocco weather conditions.

MODELING

Outline of the PV/T Collector

Fig. 1 shows the front view of the PV/T sheet and tube considered in the current study. It consists of glazing, a

PV module for converting sunlight into electrical energy, a copper plate that absorbs residual heat, ten tubes in

which a fluid circulates to evacuate the heat transmitted by the absorber plate and a layer of glass wool used to

minimize losses to the bottom of the collector. The front glass cover is separated from the PV plate by an air gap.

The PV plate is fixed on to the absorber plate through a thin adhesive layer.

Figure 1. The front view of the PV/T sheet and tube considered in the current study.

The tubes are boned to the absorber plate and arranged at equal spacing throughout the panel width. The edges

and back surface of the PV-T collector were covered with insulation layer to reduce heat loss.

Assumptions

In order to simplify the simulation process, the 1D steady state model was used for the simulation. This model

performed almost as good as the 1D and 2D models [5]. In this explicit model, the following assumptions are

adopted:

1. For a compact and thin panel design, the losses of the absorbed solar energy to the surrounding are mainly

through the front and back panel surfaces; the edge loss is negligible.

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08 June 2024 23:33:55

2. The temperature at each layer of PV-T collector was well distributed and the geometrical center was

selected to be the representative node for each component.

3. Temperature gradient along the X-direction will not affect the temperature distribution in the Y-direction,

and one nodal temperature is used.

4. The water pressure drop through the system and the heat storage of the components has been negligent ( are

very small ).

5. The contact resistance between each layer has been neglected.

6. There is the identical water flow in all tubes, the mid-distance between any two adjacent water tubes is

thermally a symmetry plane; there will be no heat flow across this plane.

Mathematical Model

Mathematic models were developed Based on the energy balance analysis of the main components of the

collector (glass, PV module, absorber, tube, heat transfer fluid and insulator), in transient mode, using the nodal

approach. Some of the equations given by Chow [10] for the sheet and tube type PV/T system were employed and

modified. The energy exchange between the different components was predicted considering their average

temperatures. The PV/T collector described above was represented by six nodes which the heat balance is governed

by a differential equation. For the energy balance in the portion of the collector shown in Fig. 1(a) with surface area

a, length L and spacing W, the energy balance equations for the glass, PV plate, absorber plate, tube, and water are

given below:

For the Glass cover

, , , . , g ( ) ( ) ( )

g g g a a g a g g pv pv g

Thank You Suresh, I will review this paper. It looks interesting. Do you know of anyone working with Fresnel lens systems? They give you a higher Incident Solar Flux but tracking has to be done carefully.

Kirk Rensmeyer