Mathematical Modeling of Photovoltaic Thermal- Thermoelectric (PVT-TE) Air Collector

Received Dec 20, 2017 Revised Jan 18, 2018 Accepted Jan 31, 2018 Photovoltaic (PV) cell from solar energy is one of the most widely adopted renewable energy source and commercially available system that can be used in various applications. More appealing application of PV arrays used in thermoelectric (TE) device was it can convert solar thermal energy from temperature difference into electric energy to act as power generators. In this study, a theoretical model is developed by using conducting steady state energy analysis of a PVT-TE air collector. The matrix inversion method is used to obtain energy balance equation. The effect of various parameters also investigated. The mass flow rate of range 0.01 kg/s to 0.05 kg/s and solar intensity of 400 W/m, 600 W/m and 800 W/m was used to obtain outlet temperature, To in the range about 28.9 C to 43.7C and PV temperature, Tp about 35.3C to 60C. Keyword:


INTRODUCTION
Solar energy is becoming increasingly attractive. It is an alternative and renewable energy resource, comes from the energy of the sun and serves as one of the most abundant permanent energy sources. Solar energy is free, clean, secure, and available on earth throughout the year. This form of clean energy is important to the world, especially during these times of high fossil fuel costs and environmental concerns arising from fossil fuel applications [1], [2], [3], [4], [5]. Furthermore, solar energy can be used in various applications such as thermal management using thermal collectors or electricity generation through photovoltaic (PV) cells. PV cell are semiconductor devices used to convert solar energy into electricity [6], [7], [8], [9], [10], [11]. To overcome the limitation of conversion efficiency of PV cell, photovoltaic thermal (PVT) was introduced which is the most commonly used method for active cooling that provide both thermal and electricity simultaneously [12], [13]. Beside that, by modifying the nonlinear I-V calculation which includes open circuit, extreme power and short circuit, the theoretical and simulation approach of the photovoltaic cell by Matlab-Simulink Situation can be evaluated to get a better performance [14], [15].
In addition to alternative sources, thermoelectric (TE) devices have been arise as other encouraging environmental friendly applications for heat pump and power generators [16]. Thermoelectric generator (TEG) have benefits such as compressed in size, mild in weight, high dependability, no working fluid and no mechanical moving parts. Furthermore, direct current (DC) electric sources such as fuel cells, car DC electric sources and PV can be used for powered the thermoelectric [17].
A contemporary idea of conversion of thermal energy into electricity directly using TE has been present several years ago. The integration of TEs with PV systems allows used of the PV by-product heat to generate additional electricity, therefore improving the power generation of the system [18]. Mojumder et al. [19] proposed single pass PVT air collector system where a number of thin rectangular fins was establish for heat dissipation. The energy balance equation was analytically derived for each component of the design and the thermal and electrical efficiency of PVT system were calculate by conducting measurement of different number of fins (0-4), mass flow rate (0.02-0.14 kg/s) and solar radiation (200-700W/m 2 ). The result show that by using four fins at mass flow rate 0.14 kg/s and 700 W/m 2 of solar radiation, the maximum PV efficiency and thermal efficiency acquired of 13.75% and 56.19% respectively. A mathematical model was develop by Khelifa et al. [20] with a thermal system for water heating. This study also includes theoretically and experimentally the hybrid PVT collector. The energy balances of the model and the coupled differential equations obtained are solved using finite differential method. Different parameters used different method to analysis the data in hybrid PVT collector such as fluid flow, heat transfer in the module, heat transfer between the photovoltaic and coolant, and effect of radiation. Kossyvakis et al. [21] examined experimentally the performance of a tandem PV-TEG hybrid utilize poly-Si as well as dye-sensitized solar cells. The performance effect is tested using different thermoelement geometry which the shorter thermoelements increases the power output levels when considered the conditions of actual operation. Zhu et al. [22] build a combination of PV-TE technologies which effectively increase the total power output by delivered a large temperature difference across the TE module with controlled heat flow. The theoretically and numerically temperature distribution was calculated for design PV-TE hybrid system. An advance of theoretical model was studied by Zhang et al. [23] for evaluating the efficiency of concentrating PV-TE hybrid system by using different type of PV cell. Rezania & Rosendahl [24] studied on CPV system integrated with TEGs. They investigate feasibility of hybrid system of concentrated photovoltaic-thermoelectric (CPV/TEG) system over wide range of solar concentration and different type of heat sinks. They reported that the efficiency of CPVonly system is lower than the CPV/TEG system that consists of TE materials ZT≈1.
From previous studies, most theoretical studies only use the common equation of the Hottel-Whiller equation. Therefore, the aim of this study is to propose a new theory approach by using the equilibrium equation in the mathematical model to predict the temperature and output temperature of the PV. Furthermore, this new theory also can minimize the error in this theoretical study. According to author's knowledge, it can be concluded that the study of thermal equilibrium on the PVT system is limited and studies on PVT-TE hybrids have not been studied by any previous researchers.

MATHEMATICAL MODELING
The cross-sectional view of PVT-TE air collector are arranged as shown in Fig. 1 which included air channels frequently present at the back of a PV laminate allowing naturally or forced open air to flow and extract accumulated heat over convective heat transfer. A series of analytical solutions were deliberated based on the flow model and thermal distribution in the energy balance equations for each component of the PVT systems. The following assumptions based on [25], [26], [27].

Figure 1. Schematic of Heat Transfer Coefficients in a PVT-TE Air Collector
The energy balance equations at steady state for PVT-TE air collector is given as For the PV is For the air flow channel is For the back plate is   (14) where, Re and Pr are the Reynolds and Prandtl number given as:  (15) k C   Pr (16) The mean air temperature as follow: The physical properties of air are given as [24], [25], [26], [27]: thermal conductivity Heat transfer coefficients are calculated corresponding to the initially guessed temperature values. In this study, the air, ambient, PV and back plate temperatures of the first section were initially predicted and specified, except those of the PV, which was set to 30°C above the ambient temperature. For back plate and air temperature in channel were set 20°C and 10°C above the ambient temperature. In order to fulfill the complete process, the major design parameters are given as L = 0.54 m, W = 0.53 m, α= 0.9, τ= 0.92, ε p = 0.7, ε b = 0.9, T a = T i = 27 o C and V = 1 m/s. For simplicity, Eq. (1) to (3) can be presented in a 3×3 matrix form.
) ( Referring to Eq. (22), the temperature vector can be calculated using matrix inversion form by Excel In this study, an adequate accumulation for T p , T f , and T b was attained in three to four iterations after outlet temperature resolved using Equation (17).

RESULT AND DISCUSSION
The result of this study show the effect of changing mass flow rate and variable solar radiations on the outlet temperature, T o and PV temperature, T p on the performance of PVT-TE air collector system. The comparison of theoretical result between T o and T p was established shown in Figure 2.

. Variation Solar Intensity of T p Versus Mass Flow Rate
A theoretical prediction was obtained represented in Fig. 3 and 4 by substituting the specified value of collector inlet temperature (T i ), ambient temperature (T a ), and other parameters in the information above into the suitable equations developed for T o and T f . The value ranges from 28.9 o C to 43.7 o C for the system output temperature. It show that the gain in produced thermal energy.
T o and T p obtain at higher solar radiation was due to more amount of incident solar energy converted into heat. The energetic behaviour of PVT also affect by solar radiations which is the most important external parameter for TE solar systems. At the highest air velocity in channel makes a higher heat convection effect, which offers the maximum heat gain. The maximum To and Tp were obtained about 43.7ºC and 60ºC respectively for 90 number of thermoelectric at 0.01kg/s of mass flow rate and 800W/m 2 of solar radiation. Thermoelectric used as fins has better electrical and thermal efficiency compared to the design without fins. In addition, PV top, rear surface, collector back wall and outlet air temperature were significantly affected by fin numbers and mass flow rates.

CONCLUSIONS
The improvement of the overall generation efficiency of the PVT-TE air collector system was increased compared to that of single PV panel. A series of parameters on the PVT-TE air collector system of solar energy utilization have been analyzed and the effects towards the systems also studied. It can be conclude that temperature is the dominant factors among this parameter which affect the conversion efficiency of such hybrid systems. In addition, it also important to select suitable value of the convection heat transfer coefficient and concentrated ratio to maintain a larger temperature gradient of the TE module. In addition, the electrical output of the PV module at the initial operating temperature should be examined in order to provide more clear view on the feasibility of such system before establish the integration of the TE device.