Computational drying model for solar kiln with latent heat energy storage: Case studies of thermal application

Accepted Manuscript Computational drying model for solar kiln with latent heat energy storage: Case studies of thermal application

A. Khouya, A. Draoui PII:

S0960-1481(18)30742-0

DOI:

10.1016/j.renene.2018.06.090

Reference:

RENE 10246

To appear in:

Renewable Energy

Received Date:

30 October 2017

Accepted Date:

21 June 2018

Please cite this article as: A. Khouya, A. Draoui, Computational drying model for solar kiln with latent heat energy storage: Case studies of thermal application, Renewable Energy (2018), doi: 10.1016/j.renene.2018.06.090

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ACCEPTED MANUSCRIPT Computational drying model for solar kiln with latent heat energy storage: Case studies of thermal application. A. Khouyaa, A. Draouib aLaboratory

of Innovative Technologies, National School for Applied Sciences, Abdelmalek Essaâdi University, B.P. 1818 Tangier, Morocco. Email: [email protected] bEnergetic and heat Transfer Team, Faculty of Sciences and Techniques, Abdelmalek Essaâdi University, B.P. 416 Tangier, Morocco

Abstract: The use of solar energy in wood drying systems can reduce the often-heavy energy bill that manufacturers in this promising sector complain about. In this context, the study of solar kilns has received increasing attention and the work presented in this paper is a contribution for developing theoretical investigation during drying process of wood using solar energy. The system of drying consists of four units, solar air collector, cylindrical parabolic solar collector, drying and thermal storage unit. Two mathematical models of storage and drying are developed. The governing equations are solved by Newton Raphson’s method for storage and finite difference techniques for the drying model. The results show that the size of the latent storage unit increases when the temperature level is raised. The integration of thermal storage unit into the solar kiln has the effect of reducing the drying time up to about 26.5 %. The recovered heat process is efficient to improve markedly the amount of the energy supplied to the drying unit and reduce drying time up to about 47 %. The effect of choosing the phase change material on the thermal storage unit is significantly important in terms of increasing the evaporation capacity and drying efficiency.

Keywords: Solar kilns; Thermal storage; Drying time; Recovered heat; Drying efficiency.

1. INTRODUCTION The issue of energy efficiency is one of the main axes of the strategic vision of Morocco to reduce its energy dependence and constitutes the roadmap of the development model that Morocco wishes to set up to make the transition to a green economy. In the context of sustainable development, the national concern is the reduction of energy consumption and the improvement of the performance of energy production systems. In fact, the National Energy Strategy adopted in 2009 considers energy efficiency as a national priority aiming to achieve 12% energy savings by 2020 and 15% by 2030 [1]. Moreover, if we analyze for example an energy-intensive sector such as processes in the wood drying industry, it is generally considered that drying operations represent about 15 % of the total energy consumed by the industrial sector in developed countries [2]. This is an important part and it is necessary to find solutions to optimize the process of drying wood in an economic and ecological approach. The efficient use of renewables energies appears to be an ecological necessity but also to guarantee attractive prices in the regional and international energy markets. Solar drying, as a means of preserving wet products, has been considered the most widely used system of solar energy [3]. The wood drying industry is one of high energy consumers during processing. From an economic point of view, this activity leads to a reduction in transport costs and an increase in the sales value of the dry product. Traditionally, there are several techniques for drying wood, among the most used we can mention: conventional drying, microwave drying, vacuum drying and outdoor drying. Conventional dryers with a very high heating power are useful, however their energy consumption remains too high [4]. Drying in the open air is characterized by long drying periods and the use of large areas of land. However, constraints related to large scale supply and demand limit the use of normal outdoor drying of the sun. Solar drying techniques can alleviate the disadvantages of open drying and improve the quality of dried wood species.

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ACCEPTED MANUSCRIPT Nomenclature Symbols A Cp Dm I F h L M R t T Th U V X W

Surface of wood segment (m2) Specific heat (KJ/kg.°C) Mass flow rate of air (kg/s) Solar intensity (W/m2) Frozen fraction [-] Heat coefficient transfer (W/m2.°C) Length (m) Mass of wood (kg) Radius of tube (m) Time (s) Temperature (°C) Thickness of the board (m) Air velocity Volume (m3) Moisture content (kg water/ kg dry matter) Absolute humidity (kg water/kg dry air)

Greek letters ΔH Δt ε η

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Latent heat (KJ/kg) Time step (s) Effectiveness [-] Drying efficiency (%)

Thermal conductivity (W/m2.°C) Density (kg/m3) Dimensionless time [-] Relative humidity [-]

λ ρ τ φ Indices a c dr eq f fi i in max me min o PCM s w wv

Air Collector Drying Equilibrium Fluid Final Inlet Initial Maximal Melting point Minimal Outlet Phase change material Surface of the tube Wood Water vapor

Some distinguishing features of the drying systems are the variation in the product size and shape, variety of methods and drying media used and the large range of drying times [5, 6]. The essential mechanisms involved with the wood drying are the bound moisture diffusion and mass transfer of bulk water which depends on the applied temperature. Mathematical models have proved to be useful for describing heat and moisture transfer in wood stack and predict the influence of weather conditions on its characteristics during drying process. Most of the previous mathematical models have applied finite difference techniques and the finite-volume method to solve the governing equations that describe heat and moisture transfer during drying of wood [7-11]. A numerical and experimental study on drying process of wood has been conducted at Wood Research Institute of Munich, in Germany [12]. The governing equations of heat and mass transfer in wood stack are solved using finite elements method. For verification, the drying model is executed within the TRNSYS program with experimental data of wood drying experiments. Under transient condition, the numerical results show considerable agreement with previous experimental and theoretical works. The mass transfer coefficient had significant effects on the predicted drying rate of wood. The drying rate can be represented by a phenomenological model based on an overall mass transfer coefficient to predict the drying kinetic of wood at low temperature [13]. The overall mass transfer coefficient is depending on the four influential parameters: drying air temperature, wood thickness, velocity and relative humidity of air. The model suitably described conventional drying curves of Canelo wood by a constant mass transfer coefficient and then has been successfully tested for the optimization of convective drying process of different wood species under transient conditions at industrial scale [14]. It has been reported that the global mass transfer coefficient decreases as the thickness of wood boards increases and the drying time increases with thickness. A numerical and experimental investigation under different drying conditions was performed to determine the characteristic curves and evaporative drying capacities of three wood species: Beech, Red pine and Spruce [15]. The characteristic drying curves were modeled as a third degree polynomial function. This study showed that there is a linear relationship between evaporative capacity and maximum mass transfer flux. This relationship indicates that most of the drying rate occurs when extragranular resistances at the air-wood interface are predominant. Calculated evaporative capacities are greater for Spruce and Beech than Red pine, indicating that larger dryers will be required for Red pine drying. The reduced drying rate curves calculated for these three wood species make it possible to extract as much information as possible on the drying conditions regardless of the proposed drying environment. The sorption isotherms during convective drying of Red pine, Spruce and Beech wood have been also established for rang relative humidity between 0 and 100 %. Results have shown that sorption isotherms are affected by the temperature and relative humidity of air and that the drying air temperature is the main factor in controlling the product drying rate [16].

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ACCEPTED MANUSCRIPT Drying wood using solar energy is not very common, but could be a complement to conventional convective drying in order to reduce drying time, consumption energy and preserved the quality of wood. Several drying methods have been suggested in order to rationalize the input thermal energy in solar kiln, as well as to improve its thermal efficiency during drying process. It has been shown that the sensible energy storage can be reduced the drying time in solar kiln compared to an operation of drying without storage [17]. Moreover, the judicious integration of thermal storage and air renewal in the drying unit can be used to assess the effectiveness of continuous solar dryer and produced a better quality of wood. One disadvantages of the use and development of renewable energies is their intermittent and variable nature as they are governed by climatic conditions and geographic locations. The thermal performances of the two solar drying system of wood (Oxford and Boral kilns) have been compared by using the climatic and geographical conditions of Brisbane in Australia [18, 20]. The Oxford design is likely to produce faster drying rates and relatively smaller energy losses than those for the Boral kiln. There is no significant difference predicted in the timber quality between the two designs. The Oxford design was also predicted to receive a relatively larger amount of solar energy (compared to Boral kiln) for a given geographical location. The Oxford kiln was generally found to be more productive than the Boral kiln for hardwood drying in Australia. The technique of measuring the drying efficiency of solar kiln based on the total life-cycle (LC) energy effectiveness was efficient to overcome the shortcomings and inadequacies of the traditional practices for assessing the performance of solar dryers. Results found that the drying efficiency of the Oxford kiln was 55 % and that of Boral 40 %. The net present energy value (NPEV) for drying one cubic metre of timber were positive for both the Oxford and Boral kilns, which imply that both the kilns were feasible for drying purposes in energy terms. However, the NPEV for the Oxford kiln (657 MJ = 182.5 KWh) has been larger (37 %) than that for the Boral kiln (113.33 KWh). Recalling that, the net energy values have been calculated by subtracting the energy consumption values, together with the energy‐loss values, from the input solar energy. Thus, the larger NPEV for the Oxford kiln indicates that the Oxford kiln is more desirable than the Boral kiln over the analysis period of 20 years. Analytic Hierarchy Process (AHP) constructed model for assessing the performance quality of drying was also proposed in order to define the effective criteria of site selection for solar drying units of wood [21]. The model is structured around three procedures: in the first, the experts of solar dryers were interviewed for preliminary investigation, in the second, the performances criteria were evaluated by Analytic Hierarchy Process. Finally, the model determines the provinces and locations which are able to shelter with potential for greater energy efficiency the solar dryers of wood. Results from the interview with the experts indicated that the maximum solar intensity throughout the year in a given region is the most important parameter for site selection of solar kiln and that Qom province (in Iran) is better classified for receiving solar wood drying facilities. Modeling and simulation of an industrial indirect solar dryer for Iroko have been conducted, in a tropical Cameroonian climate [22]. The model is based on heat and mass transfer equations established at different levels of the solar dryer (walls, black body, wood stack and drying air). It has been found that the drying kinetic is fast when the initial moisture content of wood is important. The drying quality can be improved if the initial water content and thickness of wood before drying are homogenized in the stack. The theoretical variations of the relative humidity and temperature of the air inside the drying chamber were computed and the analyses gave satisfactory physical meanings. Using the solar collector, the drying rate is a little faster and the final moisture content of the wood stack of Iroko species (Chlorophora excelsa) is lower than the one obtained without utilization of the solar collector [23]. It was suggested to optimize the energy power consumed by the blowers especially at night, keep the door of the dryer opened when inside air reaches the saturation state. The mathematical model can be used to design a performing dryer in order to build in tropical regions many indirect solar kilns at moderate prices. A review about the methods of reducing the consumption of energy on wood drying kilns has been investigated by the Forestry Commission in UK [24]. This review identifies cases where possible energy savings can be made during the wood drying process. These include energy recovery systems specifically designed for wood dryers (systems that recover heat from humid / hot air during drying), use of variable frequency drives on fans, maintenance general and insulation. There is great potential for energy saving systems to be incorporated into UK dry kilns, not only for costs, but to help the environment and anticipate government guidelines on energy consumption. Based on the data reviewed, the main conclusions of this review recommend to achieve significant savings by using the heat recovery systems on wood drying operations in the UK. When minimizing running costs of drying kilns, efforts should be made to improve energy efficiency and avoid processing defects of dried wood. The energy requirements and greenhouse gas emissions have been estimated for drying wood chips [25]. It has been shown that increasing temperature will decrease drying time and increase throughput but not necessarily decrease the drying cost. This is due to higher energy use and higher cost of capital inputs such as loading/unloading and supplied heat in drying systems. Thus, low drying air temperature can be used if throughput is not a key issue for an operation of drying process. A company based in Germany called Barr-Rosin under the Gesellschaft für Entstaubungsanlagen (GEA) Group of Companies has developed a commercial drying system for biomass such as sawdust and wood chips using superheated steam. The capital cost and evaporation capacity of this dryer unit are respectively AU$15M and 20 tonne of evaporated water per hour [26]. The operating cost in Europe was estimated to be around AU$31/tonne of water evaporated. The re-constructed financial model based on Barr-Rosin data found that the operating

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ACCEPTED MANUSCRIPT cost was AU$35/tonne dry product or AU$54/tonne water evaporated. In terms of less expensive drying, ambient air and solar drying can be considered when the throughput, control and quality requirements of the dry product are not so demanding. The likely cost of solar drying would be about AU$15/tonne of wet biomass, as reported by one equipment supplier. This translates to approximately AU$47/tonne evaporated water. The typical cost of drying wood at high temperatures is about AU$50/tonne of wood. Thermal energy storage is very important to eradicate the gap between energy supply and energy demand and to improve the energy efficiency of solar energy systems. Thermal energy storage can be stored as a change in the internal energy of a material such as sensible heat, latent and thermochemical heat, or a combination thereof. Latent heat thermal energy storage is more useful than sensible energy storage due to the high storage capacity per unit volume/mass at nearly constant temperatures. Thermal energy storage plays an important role in the efficient use of thermal energy and can be used in various fields, such as heating or cooling systems, solar collectors, electrical and industrial heat recovery [27]. Solar energy is available only during the day, and its application requires efficient storage of thermal energy so that excess heat collected during the hours of sunshine can be stored for later use during the night [28]. Over the last two decades, many scientists, international and community ecologists have made considerable efforts to promote the energy efficiency and sustainability of industrial systems, which have resulted in a number of promising energy storage technologies and green strategies [29, 30]. To select an appropriate phase change material (PCM) for a specific application, the first criterion to be considered is the operational temperature range required by the solar kiln. The melting point of the PCM to be used as thermal storage energy must match the operation range of application. For example, for drying applications the phase change melting temperature should be around 60 °C [31]. It has been shown that an interval of about 5 to 10 °C should be considered for many thermal storage systems, assuming that a temperature difference of about 10 °C can be used to charge the storage unit, the PCM melting point should be about 10 °C lower than the charging temperature [32]. The properties of the phase change materials to be used for latent heat storage were emphasized as the desired properties such as thermal melting, low volume change, low vapor pressure, high thermal conductivity, specific heat. specific and mass. chemical stability, non-corrosive, non-toxicity, non-fire risks, high reproducible nucleation capacity without segregation, non-subcooling, and finally low price and abundant supply [33]. A high heat of fusion and a precise melting point without subcooling are two primary requirements in the selection approach of an appropriate phase change material [34, 35]. A review of literature reveals very little empirical research and understanding of optimum designs on the study of solar dryers equipped with thermal storage tanks for different weather conditions and no common standards of comparison, specification and analyze between various drying models and solar kilns. The present work is therefore a contribution to the improvement of energy efficiency and the modeling of a solar dryer equipped with latent energy storage unit. This paper collects the results of the original research work carried out on the two themes that are solar drying and heat storage. It aims to facilitate studies on thermal drying application for a better use of solar energy in drying techniques on an industrial scale. This paper is structured as follows: First, we will present all the tools and methods used to study solar drying coupled to a thermal storage tank. Next, we will outline the approach and methodology adopted to size and analyze the thermal performance of a latent heat storage tank, after that, we will present the mathematical model of solar drying of wood. The equations of storage and drying model will be solved after having specified certain operating assumptions and the associated boundary conditions necessary for numerical resolution. Simulations and case studies will be carried out with reference to the climatic conditions of Tangier city (Morocco). The advantages of integrating the latent storage unit into the drying system will be discussed. The effect of certain physical parameters on the kinetics of solar drying, the strengths and limitations of the studied system will be presented in separate paragraphs. These investigations will enable us to define the optimal design and operating conditions of the solar kiln and estimate the criteria reducing drying time and improving the drying quality of wood before its use. We will conclude this research work with a conclusion gathering all the results and the statement of perspectives and recommendations for future works.

2. Material and method The performance of the solar kiln designs has been theoretically investigated, for the climatic conditions and geographical location of Tangier (latitude 35°46′02″ Norte, longitude: 5°47′59″ West). Fig. 1 presents the schematic diagram of the solar kiln and its principal components (solar air collector, parabolic solar collector, drying chamber and latent heat storage unit). The incoming air from the outside passes through a solar air collector where it heats up and then leads to the drying unit to dry wood. The air coming out at the wood stack is wet but still hot, reason why we thought of integrating a system for recycling hot air between the drying unit and the solar air collector. Integration of the thermal storage unit into the system is intended to ensure continuous drying during sunset (night). The storage is carried out during the daylight thanks to a parabolic solar collector which concentrates the solar radiation on an absorber in which passes a heat transfer fluid which circulates between the storage unit and the solar

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ACCEPTED MANUSCRIPT collector. As it warms up, this fluid loses some of its energy in favor of the storage unit and consequently the thermal storage process begins to appear in the MCP (Phase Change Material). The present solar dryer operates in forced convection (an indirect dryer) and defined according to the dimensions of wood. The recovered flow defines as the fraction of humid air that is released from the drying chamber and returned to be heated in the solar air collector during the diurnal period or in the heat storage unit during the nocturnal period. The solar air collector unit is defined by its characteristics such as the length Lc, width lc and area Ac (Table 1). The thermal storage unit consists of a hollow cylinder PCM with the HTF (Heat Transfer fluid) flowing through an interior tube for the purpose of heat exchange. It should be noted that the charging mode of the latent heat storage unit is not mentioned her, only the mode of discharge period is studied and modelled, therefore, the modelling of the cylinder parabolic solar collector is not also considered in this work. The mathematical model of solar air collector and thermal storage (discharge period) inspired from previous works have been translated into a subprogram and connected to drying model enables to simulate the distribution of moisture content and temperature during drying process [16, 32]. The selected wood specie for this study is Red pine (Pinus resinosa). It is commonly used in many fields such as design, building, furniture and industry.

Fig. 1. Schematic diagram of the Solar Kiln. Table 1 Specifications of the solar air collector. Parameters

Values

Length (m)

3

Larger (m)

3

Depth (m)

0.1

Area (m²)

9

Absorptivity of the glass cover

0.03

Transmissivity of the glass cover

0.95

Absorptivity of the absorber plate

0.9

Air velocity (m/s) Mass flow rate (kg/s)

16 17 18 19 20 21 22 23

1 Rang of 0.165 to 0.285

3. Thermal storage model during the discharge period In the field of solar wood drying, it appears that the average thermal storage technology of parabolic solar concentrators is the most economical and the most robust. By exploiting the direct solar radiation, considered as the main resource, which is very considerable on a planetary scale, this technology offers a real alternative to the consumption of the fossil resources as well as the possibility of the hybridization of these installations. This storage technology will allow continuous wood drying throughout the

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ACCEPTED MANUSCRIPT day, reduce drying time and the energy required for production without forgetting the positive impact of the project on the environment since it will use clean energy without emission of greenhouse gases. In this context, the work presented in this section is a contribution to the design and modeling of heat transfer in a thermal storage tank integrated into a solar wood dryer. It will aim to facilitate studies on latent heat storage systems for better use of solar energy in industrial scale drying techniques. In this section, we first present the approach undertaken to size the latent heat storage tank, then we will expose a calculation algorithm that allows to study and analyze the thermal performance of the thermal storage unit sized to satisfy the needs of solar drying of wood. 3.1 Sizing of the thermal storage unit The design of a latent heat energy storage system involves the selection of a storage material, design of a geometrical configuration of containment and a heat exchanger type. The selection of the phase change material is the most important part of a thermal storage design. The schematic diagram of the latent heat storage tube is shown in Fig. 3. This thermal storage unit is connected to the cylindrical parabolic solar collector (See Fig. 1) which will supply it with the thermal energy collected from the sun. It consists of a hollow cylinder PCM with the air flow passes through the inner tube for the purpose of heat transfer exchange. The air flow enters the tube at temperature Ti and pick up heat from the energy latent storage. This transfer process causes the solidification of some of PCM on the outside of the tube and the HFT temperature rises. The amount of thermal energy required to heat fluid is proportional to the mass of PCM incorporated in the tube and its latent heat of solidification. In addition, heat transfer performance in the exchanger is depended on the thermophysical properties of PCM and tube. The principal design parameters for a latent heat storage unit are: Effectiveness ε and the Number of Transfer Units (NTU). An efficient latent heat storage is characterized by a higher effectiveness and /or a little variation of effectiveness as possible as the PCM continues to solidify. The thermal model approach for the prediction of heat transfer during the discharge phase has been primarily based on the method proposed by Basakayi [32]. The following simplifying assumptions were considered:

Dm

Ti

Tube

Tf (x,t)

PCM

rm Ri PCM

25 26 27 28 29 30 31 32 33 34 35

Ro

Fig. 2. Schematic diagram of the latent heat exchanger.

- The thermal conductivity and specific heat in each phase of MCP are constant; - The heat exchanger tube has a length greater than its diameter; - The density difference between solid and liquid phases is negligible; - The heat transfer by convection is fully uniform and developed over the tube; - The flow is laminar. Given these hypotheses, the heat transfer equations in the tube can be presented in the following way: The rate of heat transfer per unit length of tube can be expressed as:

6

.

ACCEPTED MANUSCRIPT

Tme  Ts 

1

  2 PCM

2 3

The rate of convective heat transfer between surface and air fluid is given by:

4

  2Ri

5 6

The energy released from the PCM is provided by:

7



8 9

The heat transfer rate per unit length of tube supplied to the HFT is given by:

T

.

.

r ln m  Ro

s

 Tf

  



(2)

1 Ri  Ro   ln  h  s  Ri 

  rm2  Ro2  PCM H  t

.

(3)

T f

10

  Dm.C pa

11

The heat exchanger effectiveness ε is given by:

12



13 14

The Number of Transfer Units (NTU) for heat exchanger is expressed as follows:

15

NTU x 

16 17 18 19 20 21 22 23 24 25 26 27

Initial conditions: At the initial time: the PCM was in the liquid state and at melting temperature Tme At the initial time: the front solidification is equal to outer radius (rm (x, t = 0) = Ro).

28 29

T f  Ti Tme  Ti

(4)

x

 1

(1)

F Fi

(5)

2Ri hx Dm.C pa

(6)

Boundary conditions: At the beginning of the heat recovery process, the total volume of PCM is assumed to be in liquid state and at freezing temperature Tme The inlet temperature of HFT in the heat exchanger is Ti (Tf (x = 0, t) = Ti). The variables of the system are: the solidification front radius rm(x, t), the HFT temperature Tf (x, t) and the effectiveness of heat exchanger ε (x, t). The solution is found by introducing the following dimensionless parameters [32]:

r The frozen fraction : F   m R  o

2

   1 

(7)

The dimensionless time:

  PCM  Tme  T f dt     2   HR o  0  PCM t

30 31 32 33

(8)

The dimensionless heat power:

.

  / 2Ri hTme  T f 



The dimensionless space (axial position): 

(9) h

 2Ri / Dm.C pa  hdx

(10)

0

34 35 36

By rearranging Eq. (1) to (6) and using the defined dimensionless variables (Eq. (7) to (10)), the corresponding values of the solidified fraction Fi of PCM at inlet of the heat exchanger and the frozen fraction F at the axial position x are found by the implicit equations [32]:

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ACCEPTED MANUSCRIPT 2Ri hx  F  F  R    ln i    . PCM . ln i  ln o   [ g1 ( Fi )  g1 ( F )] Dm.C pa s F  F   Ri  2

1

  NTU x 

2



3 4

g (F) and g1 (F) are the auxiliary functions expressed as [32]:

5

6 7 8 9 10

R  Fi 1 F   g 0 ( Fi )  i PCM ln o  2 4 2 s  Ri 

(11)

(12)

g 0 ( F )  1  F ) ln(1  F )  F

(13)

  17 z 2     z 1   450  z 2    g1 ( F )     4 z2    1     100   hRi where :   ; z  ln(1  F )  PCM

(14)

The results (Equations (11) and (12) are given in terms of the fraction of frozen layer F as the primary variable and they are used in the design and the evaluation of the performance of the LHS. The parameter Fi in equations (11) can be founded by a Newton Raphson method. From the estimation of Fi and the dimensionless time τ, the outside radius of the tube heat exchanger is calculated as: 1/ 2

11

 (T  Ti ).t   Ro   PCM me   PCM H 

12

The number of tubes Ntube in heat exchanger depends on mass flow rate and is obtained from [32]:

13

N tube 

14 15 16 17

NTU provides a measure of the size of a heat exchanger and its ability to transfer heat between two fluids at different temperatures. In order to ensure a better effectiveness for the heat fluid transfer, it must be ensured that [30]: (17) 0.5  NTU  5

The thermal storage tank diameter DT is given by the expression [32]:

18

DT  d 2 N tube

19 20

d is the shortest distance between two adjacent tubes given by: d  2 Ro 1  Fi

21 22 23

The volume of phase change material VPCM required to store thermal energy for a given storage period is evaluated From [32]:

(15)

Dm.C pa .NTU

(16)

2Ri h.L

3

(18)



(19)

V PCM  VT  V f  Vtube

(20)

2

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

D  where: VT    T  L ; V f  N tube L( Ri ) 2 ; Vtube   ( Ro  Ri ) N tube L( Ro  Ri )  2  The final step is the evaluation of the amount of the PCM. With the volume of PCM calculated in the previous step, the mass of phase change material MPCM is calculated as:

M PCM   PCM .V PCM

(21)

Fig. 3 presents a flowchart that shows the different steps to follow in determining the sizing of thermal storage unit. The flowchart helps identify problem variables and required results. The computer program code was written using C ++ software. This program calculates different thermal parameters of the latent heat storage, depending on the properties of the PCM (melting point, heat of fusion, thermal conductivity and density), the desired minimum and maximum outlet temperature of HFT at the heat exchanger, the properties of the selected HTF and the discharge period. The dimensions of the shell and the tube of the thermal storage were determined according to the diameter of the shell, the inner and outer radius of the heat exchanger, the length and number of the tubes and the volume of PCM. 3.2 Determination of the thermal parameters of the LHS

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14

ACCEPTED MANUSCRIPT The thermal storage tank studied in this work was modeled to ensure the feeding of the drying unit with hot air during the night. To do this, we have assumed that the phase change material in the storage unit is initially at a constant temperature which is equal to its melting point. As a reminder, only the phase of discharge of the storage tank during the night was evoked in this research work. In addition, the study of the parabolic solar collector which normally must load this storage unit during the day (period of sunshine) is not considered in this investigation. Regarding the results, all the numerical values relating to the sizing of the storage unit and which will be presented in section 5.1 of this document are calculated for a 12 hours discharge period of the storage unit. This wise choice is justified by the fact that the drying of the wood at low temperature requires a drying time of a few days or even weeks to reach the equilibrium moisture content desirable for the exploitation of wood. After sizing the shell-and-tube latent heat exchanger storage, the instantaneous outlet temperature of the HTF during the discharge period, front solidification and heat transfer rate were then evaluated. Results of the thermal storage unit were obtained in the following steps: Step 1: Since the total discharge period was 12 hours, for various instants: tk = 0, 2, 4, 6, 8, 10 and 12 h, the corresponding dimensionless time τik is calculated as:  (T  Ti ).t k Ro   PCM me   ik  PCM H

  

1/ 2

(22)

15

Step 2: Secondly, the fraction of solidified PCM Fik at inlet of heat exchanger is determined using the implicit equation:

16

 ik 

17

Step 3: The effectiveness ε is obtained from the implicit equation:

18

  NTU x 

R  Fik 1 F   G0 ( Fik )  ik PCM ln o  2 4 2 s  Ri 

(23)

R 2Ri hx   ln 1      . PCM . ln 1    ln o Dm.C pa s  Ri

    [G1 ( Fik )  G1 ( F )]  2

(24)

19 Physical properties of the problem: λPCM, λs, ρPCM, L, ΔH, Cpa, h, Dm, Tme,

20 21 22 23

Specification of Tf, min and Tf, max

24 25

Calculate of ε and NTU

26 27 28 29 30

0.5 < NTU < 5 No

Yes Find the value of Fi and τ

31 32 33

Calculate the value of Ri, Ro, Mpcm, Vpcm, Ntube, DT

34 35

END

36 37 38 39 40 41

Fig. 3: Flow chart for sizing the thermal storage unit. Step 4: The axial distance from the inlet of the heat exchanger varies from j =0 to j = L, where L is the length of the tube, therefore, the corresponding value of Fj can be determined as:

9

T f  Ti

ACCEPTED MANUSCRIPT

Fj

1

j 

2

Step 5: The last step is about the calculation of solidification front radius of the PCM. It is given by:

3

rm  Ri F j  1

4 5 6 7

The governing equations in step 2 and 3 are resolved using a Newton Raphson method.

4. Global model of the drying unit

8

4.1. Assumptions

 1

Tme  Ti

(25)

Fik

(26)

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

The mathematical model is based on the following assumptions: - The heat transfer between the wood boards and the drying air is carried out only by convection; - The air velocity is uniform along the boards; - The drying walls are adiabatic; - The shrinkage is negligible; - The mass flow rate is distributed equitably between all wood boards column; - Each wood board is represented only by its position from the inlet of the stack in the direction of mass flow rate; - The gradient of temperature and moisture content is negligible in the boards. The last hypothesis is far from reality, but it may be possible to retain the idea that the maximum of drying is carried out on the surface of the material and that the mass transfers are controlled by extragranular resistances [15].

27

with

28

dM j t k   m0

29 30

where m0 is the dry mass of the jth wood segment, invariant with time and tk-1 = tk – Δt. The drying rate is defined by:

31

m   m0

32

MR is the reduced moisture content expressed as [15]:

33

MR 

34



In considering the above assumptions, the governing equations of heat and mass transfer in the wood stack on a macroscopic scale are expressed in sections 4.2 to 4.5: 4.2. Mass conservation for wood The mass balance Mj at actual time tk for the jth board of wood can be calculated as follows [17]:

M j t k   M j t k 1   dM j t k 

.

dX dt

dX j t k  dt

(27)

t k  t k 1 

dX dX   m0 . f ( MR) dt dt 1

(28)

X  X eq X in  X eq is the drying rate of the first period taken at the reduced water content of MR = 1 1

35 36 37

Globally, the polynomial or exponential functions can be used to represent the drying characteristic curves. In this study, the polynomial functions of degree 3 are considered and the drying rate can be expressed as:

38 39 40

X1, X2, and X3 are constants determined by test in the previous work [16]. For Red pine wood: The mass transfer coefficient hm is a function of the heat transfer coefficients ht and can be expressed as:

41

hm 

f ( MR)  X 1 MR  X 2 MR 2  X 3 MR 3

(29)

f ( MR)  2 MR  0.45MR 2  0.97 MR 3

h s

d C pa  a  0 dX .

(30)

10

2

ACCEPTED MANUSCRIPT  is referred to the sorption isotherm of wood expressed as: X X eq   s exp( . ln  . exp( ))

3

where

1

4 5 6 7 8 9 10 11 12

The term

(31)

 s  0,27  0,003Tw and   0,24  0,032Tw for Red pine[16].

4.3. Mass conservation for air drying The mass conservation of air can be represented as follows [17]:

 a .Va .

dW dX  m0 . dt dt

(32)

4.4. Energy conservation for air drying The energy rate balance of a drying air adjacent to the wood board can be represented as follows:

dT f

 hATw  T f 

13

 a .Va .C pa

14 15 16

4.5. Energy conservation for wood

17

m w .C pw

18 19 20

From a process point of view, it is advantageous to determine the evaporation capacity corresponding to a set of operating conditions. This criterion allows sizing and design the industrial dryers. The evaporation capacity Cevap is defined as the amount of water evaporated per unit of time and surface required to evaporate 90 % of water liquid initially presented in the wood stack [15]:

21

C evap 

22 23

The energy supplied (Qu) to the drying chamber is defined as the total energy transmitted to the wood stack during drying and is defined as follows: tdr

dt

(33)

The energy rate balance of a wood board can be represented as follows:



(34)

0,9.(min  m fi )

(35)

Aw .t dr





25 26

Dm.C pa T f ,o  T f ,i dt (36) 0 The thermal efficiency of drying is defined as the thermal energy required for the drying divided by the thermal energy available for the drying:

27



24

28 29 30 31 32 33 34 35 36 37

Qu 

dTw dX t k   hAT f  Tw   m0 .H . dt dt

m wv .H  m wv .C pw (T f ,o  T f ,i ) Qu

 100

(37)

4.6. Numerical method for solving drying model The mathematical equations of the drying model are discretized by the implicit finite difference numerical method already developed by several researchers in many publications and brilliantly exposed [7, 8, 10, 12, 16]. This choice is motivated on the one hand by the perfect adaptation of this method to the system resolution of coupled differential equations, and on the other hand, the implicit scheme is unconditionally stable. Fig.4 illustrates the numerical scheme adopted to discretize the drying model equations. The discretized heat and mass transfer equations are explained in sections 4.6.1 to 4.6.3.

11

ACCEPTED MANUSCRIPT

1 2 3 4 5 6

Fig 4. Temperature and mass rate balance on drying air and wood boards. 4.6.1. Mass conservation for air drying The mass rate balance of a drying air segment adjacent to the wood segment throughout the boards shown in Fig. 4 can be represented as follows:

Dm . W j 1 tk   W j tk 1   m0 .

dX j t k 

(38)

dt

7 8 9 10

4.6.2. Energy conservation for air drying

11 12 13

4.6.3. Energy conservation for wood

14

mw .C pw

15 16

The discretized equations (38), (39) and (40) can be written as: [A][X] =[B]

By the adoption of the scheme represented in Fig. 4, the energy conservation of air can be expressed as follows:

Dm . C pg T f , j t k   T f , j t k 1   hA T f , j t k   Tw, j t k   0

(39)

By the adoption of the scheme represented in Fig. 4, The energy conservation of wood boards can be formulated as follows:

Tw, j t k   Tw, j t k 1  t

 hA T f , j t k   Tw, j t k   m0 .H .

dX j t k 

(40)

dt

(41)

Surrounding meteorology Ta, φ, I

U

Cylindrical parabolic solar collector (CPSC)

Air solar collector (ASC) Dm To, f, ASC W To, f, DU

Dm To, f, DU

DCPSC To, f, CPSC

DCPSC To, f, TS

Dm To, f, DU Drying unit (DU)

dX/dt

17 18 19 20 21 22

U

Thermal storage (TS) Dm To, f, TS

Surrounding wood

Fig. 5. Flow chart for calculation scheme of the drying model. The algebraic system (41) is solved using Gauss Seidel Algorithm with a convergence criterion of 10−6. A time step of 100 s is used in the computation model. After each iteration, the coupling between the algebraic system (41) and equation (27) is performed in

12

1 2 3 4 5 6 7 8 9 10 11

ACCEPTED MANUSCRIPT order to find the instantaneous moisture content of wood, absolute humidity of air, the temperature of air and wood. A computer program is developed under C++ language enable to simulate the thermal performance of the solar kiln for different weather condition. Simulations are realized using the thermophysical properties of Red pine [16]. The input parameters such as weather conditions and sorption isotherm were brought into play stat variables. The minimum and maximum values of some drying conditions such as solar intensity, outlet air temperature at the collector and relative humidity of Tangier city have been reported in Table 2. The calculation scheme was constructed according to the flowchart shown in Fig 5. It should be noted that the modeling of the cylindrical parabolic solar collector and the description of the operation of the storage unit during the charging phase are not developed in this project. Only the operation of the thermal storage unit during the discharge process (operation during the night) is studied in this research work (see paragraph 3 of this document). The electrical energy consumption by the blowers to ensure the required air velocity in the stack of wood is not included in these calculations. Table 2 Some drying conditions for Tangier city. Month

13 14 15 16 17 18 19 20 21 22 23 24 25 26

27 28 29

Ta, min (°C)

Ta, max (°C)

φa, min (%)

Φa, max(%)

Imax (W/m2)

Tc_max(°C)

June

23

32

43

86

1000

68

September

18

27

45

90

900

54

December

9

18

54

96

500

40

March

15

20

50

90

600

46

4.7. Comparison of a present model with previous experimental and theoretical work In order to verify the present mathematical model for wood, we compare our results with the experimental and theoretical results performed by Awadalla et al., [12] at a constant drying air temperature of 75 °C and a drying air velocity ranging from 2.5 to 3 m/s. Experiment have been carried out on spruce boards with dimension of 0.5 m× 0.18 m × 0.09 m and initial moisture content of 0.4 kg water/kg dry matter. As indicated in Fig. 4, the present mathematical model does not reflect the drying behavior during the first hours because it did not take into account the first phase of drying which result in the increases of setting temperature at the product level. This is due to the fact that in the calculations, this first phase of drying is only considered a point that has been calculated at the reduced moisture content MR = 1 (section 4.2). The deviation of the present model from the previous experimental and theoretical work did not exceed 5 %. This discrepancy may be due to the physical properties of wood used in different models. We can conclude that the present model is enabling for the simulation of heat and moisture transfer during drying process of wood using solar energy as a renewable power generator.

Fig. 6. Comparison of present model with previous experimental and theoretical work.

5. Results and discussion 13

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

ACCEPTED MANUSCRIPT 5.1. Determination and analyze of the thermal storage parameters Three phase change materials are selected to study the performance of the mathematical thermal storage model for application in the wood drying field. These phase change materials (PCMs) are RT64 (Paraffin), RT82 (Paraffin) and Erythritol (Alcoholic sugar) [29, 32-35]. These three materials were considered for this study because of their physical properties during the phase change including their melting temperatures likely to cover solar wood drying applications as well as their latent heat, specific heats, and thermal conductivities more used for long-term storage of latent heat. These different advantages encourage us to test our calculation algorithm on the three phase change materials in order to study the strengths and weaknesses of their applications in the field of solar drying of wood. For the choice of heat transfer fluid, air was used to unload the storage tank because it is an essential fluid commonly used in drying operations. However, the approach and discussion applies equally well to any other fluid that can transmit heat to the solar dryer by means of a heat exchanger. With regard to the material constituting the tube of the heat exchanger, our choice focus on the use of the material Cooper, because of its important physical and mechanical characteristics to realize this project and its high thermal conductivity to facilitate the transfer of heat from the PCM to the air [32]. Tables 3, 4 and 5 indicate respectively the thermophysical properties of PCMs, HFT and tube used in the numerical simulations in order to partly size the latent heat storage tank likely to satisfy the energy demand of the drying unit and to analyze its thermal performances during the discharge process [28, 29]. The inner and outer radius of the tube are not shown in Table 5 as they will be estimated from the design of the thermal storage unit.

Table 3 Properties of the studied phase change materials. Properties

RT64

RT82

Erythritol

Melting point (°C)

64

78-82

118

Latent heat of fusion (KJ/kg)

240

170

339

Density (liquid phase) (kg/m3)

780

770

1300

880

880

1480

Specific heat (liquid/solid) (KJ/kg.°C)

2

2

2.765

Specific heat (liquid/solid) (KJ/kg.°C)

2

2

1.383

Thermal conductivity (liquid) (W/m.°C)

0.2

0.2

0.326

Thermal conductivity (solid) (W/m.°C)

0.2

0.2

0.733

Density (solid phase)

(kg/m3)

21 22 Table 4 Properties of the HFT (Air). Properties

Values

Density (kg/m3)

1.1

Specific heat (KJ/kg.°C)

1.007

Mass flow rate (kg/s)

0.225

Viscosity (kg/m.s)

0.000018

Thermal conductivity (W/m.°C)

0.0224

23 24 Table 5 Properties of the tube (Cooper). Properties Density

Values

(kg/m3)

8795

Thermal conductivity (W/m.°C)

386

Length of tube (m)

3

25 26 14

1 2 3 4 5 6 7 8

ACCEPTED MANUSCRIPT This study is carried out according to the four Scenarios set out in Table 6. Each Scenario is referred to a temperature range that can be obtained after properly dimensioning the thermal storage unit. For the discussions, we first present the parameters relating to the sizing of the storage unit for each Scenario, then we present the temporal and spatial variation of some thermal parameters of the storage unit. We will conclude this paragraph by analyzing parameters such as effectiveness, solidification front radius and thermal power on the performance of the storage unit during the discharge process.

Table 6 Scenarios adopted for the thermal performances analysis of the storage unit.

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Temperature

Scenario 1

Scenario 2

Scenario 3

Scenario 4

Tf, min (°C)

47

65

78

87

Tf, max(°C)

54

57

85

94

The storage tank is intended to store the thermal energy that has been generated by the solar collectors during the day for use during the night. It should be noted that a properly dimensioned storage tank is extremely important for a properly functioning and cost effective solar thermal system. There are two or three important factors that make sizing the storage tank important. If the storage tank is undersized, the energy requirements of the solar dryer overnight will not be met and the drying time will be very long. In contrast, if the storage tank is too big, there will be a waste of energy, more maintenance costs and operations will be very high. Various energy and economic criteria are evaluated for a range of thermal storage sizes. We can then choose a particular size that meets the drying needs, in terms of productivity, quality and storage time. In Morocco, this concept is still in development and the main question is how to find the optimal size of a thermal storage tank for a solar drying application of wood? In addition, how can the whole system work effectively? The purpose of this present work is to answer by a questionable contribution to these questions. The first section of this paragraph provides the results and a detailed analysis of the design methodology of the thermal storage unit according to the approach and steps described in section 3 of this work. It should be noted that the integration of the latent energy storage in a solar kiln is a novelty addressed in this field of research projects. Thus, we will show throughout the following sections the possibility of experimenting a solar drying system whose capacity could also be extended on an industrial scale and able to operate 24 hours a day thanks to solar energy and a robust storage system.

Table 7 Parameters for sizing and design of the thermal storage unit.

26 27 28 29 30 31 32 33

Materials

Ri(m)

Ro(m)

Masse of PCM (kg)

Volume of PCM(m3)

RT64 (Scenario 1)

0.0686

0.0789

2104

2.39

Tank diameter (m) 1.38

RT82 (Scenario 1) Erythritol (Scenario 1) RT82 (Scenario 2) Erythritol (Scenario 2) Erythritol (Scenario 3) Erythritol (Scenario 4)

0.134

0.154

2922

3.45

0.041

0.047

1126

0.13

0.15

0.054

Tank volume (m3)

Number of tube

Tube pitch (m)

4.45

36

0.22

1.85

8

19

0.4

0.69

0.62

0.91

11

0.185

4978

5.88

2.38

13.42

36

0.38

0.062

1842

1.13

0.85

1.7

15

0.2

0.058

0.067

3480

2.14

1.2

3.37

29

0.21

0.0541

0.0622

4432

2.72

1.31

4

37

0.2

The sizing of the thermal storage tank for different discharge Scenarios is shown in Tables 7. For Scenarios 1 and 2, all parameters such as PCM mass, PCM volume and the number of tubes required to ensure the imposed minimum and maximum temperatures for a better functioning of the thermal storage are reduced when using Erythritol as a phase change material. This result can be explained by the fact that this material possesses the best characteristics such as latent heat and melting temperature higher than those of the other materials studied to supply the storage of latent heat. Indeed, for different latent heat storage materials, the smallest storage volume is obtained for the phase change material whose latent heat and the density are higher. The number of tubes obtained for each Scenario has been calculated in order to ensure a laminar flow in the storage unit. This parameter is essential in

15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

MANUSCRIPT order to give the storage unit the possibility toACCEPTED operate during a discharge period of 12 hours while respecting the output requirements such as the fluid flow rate and the supply temperature. For all the Scenarios studied, it is observed that the size of the storage unit (Tank diameter and Tank volume) increases as the temperature range of function rises. However, the value of the inner and outer radius of the tube decreases from Scenario 1 to 4, in turn the number of tube increases. In the first conclusion, the design results obtained by our methodology have shown us that it is possible to design a thermal storage system whose size varies from 0 to 14 m3 for possible use in a drying project. it remains to analyze the performance of latent heat storage designed and also evaluate its energy and economic criteria. Table 8 shows the variation of thermal parameters for various times along the heat exchanger in case of RT64 (Scenario 1). The discharge period started at time = 0h and the HFT enters the tube at Ti =25 ° C causing the melting of some PCM, consequently, the temperature of HFT rises along the heat exchanger and becomes maximal at its exit. The maximum and minimum outlet temperatures of HFT recorded during the discharge process are 53.99 and 46.85 °C respectively. It can be observed the effectiveness of thermal storage unit increases along the heat exchanger and decreases during the discharge process since the solidification front radius of the PCM increases with time. The maximum value of effectiveness was 0.72. The front radius at the beginning of the recovery heat process coincided with the outer radius of the tube (Ro = 0.0786 m) because it was calculated from its centre (boundary conditions). The NTU increases along the heat exchanger but, not depend on the time parameter. The NTU reaches a value equal to 2.73 m at the outlet of the thermal storage (x = 3 m).

Table 8 Thermal parameters along the heat exchanger and against the discharge period. Time x(m) Tf( °C) ε

0h

4h

8h

12 h

20 21 22 23 24 25 26 27 28 29 30 31

0

25

1

rm(m)

NTU

0

0.0789207

0

38.9864

0.34966

0.0789207

0.910484

2

48.0823

0.577058

0.0789207

1.82097

3

53.9977

0.724944

0.0789207

2.73145

0

25

0

0.0915647

0

1

36.2202

0.280505

0.0887084

0.910484

2

45.364

0.509100

0.0862985

1.82097

3

52.6444

0.691110

0.0843343

2.73145

0

25

0

0.100722

0

1

34.535

0.238375

0.0968317

0.910484

2

42.787

0.444675

0.0933173

1.82097

3

48.8034

0.595085

0.0902222

2.73145

0

25

0

0.108203

0

1

33.4558

0.211395

0.0824797

0.910484

2

41.1731

0.404327

0.0944414

1.82097

3

46.8596

0.546490

0.0957846

2.73145

All phase change materials studied in this work were considered at liquid state at the beginning of the discharge process (at time t = 0 h, the temperature of the PCM was assumed to be equal to its melting point). The HFT enters the tube at Ti = 25 °C and picked up heat from the latent heat storage material. The heat transfer rate from PCM to the HTF provokes freezing of the PCM on the outside of the tube simultaneously causing a rise in the fluid temperature. Fig. 7 shows the front radius of the PCMs at the inlet of the heat exchanger as a function of the discharge period. At the beginning of discharge process, the minimum front radius coincided with the outer radius of the heat exchanger tube since it was measured from its centre. The solidification inlet front radius of PCM increased with time and has a maximum value at t =12 hours. The results of the Scenario 1 showed that the front solidifications of different phase change materials formed at the inlet of the heat exchanger at t = 12 hours were 0.108, 0.191 and 0.089 m respectively for RT64, RT82 and Erythritol. For Scenario 2, these values were 0.187 and 0.099 m respectively for RT82 and Erythritol. Scenarios 3 and 4 have the values of frontal solidification 0.104 and 0.099 respectively at t = 12 hours for the

16

Erythritol phase change material. It is notedACCEPTED that the inlet front MANUSCRIPT radius curves of Scenarios 2 and 4 are similar, but the size of the thermal storage tank is different for these two Scenarios (Table 7). In Fig. 8, the variation of the outlet temperature in the heat exchanger is given as a function of the discharge period for different studied Scenarios. It is observed that the outlet temperature of HFT at the storage unit decreases slowly with time between the maximum and minimum temperatures related to each Scenario considered, because of the increasing of the solidification front radius and the PCM cools as the discharge process evolves over time. The outlet temperature in case of Scenario 4 is higher compared to the other cases considered because it has the highest melting temperature, which offers the advantage of working over several temperature ranges according to the demand for energy of the storage tank. This solution is advantageous from a thermal point of view and economically more expensive for solar wood drying applications, including the costs that will be granted to the installation of the parabolic solar collector capable of producing a temperature of the order of 120 °C. In addition, safety instructions must be taken into consideration, since this is an operating range or fire protection tools or fluid leaks may be considered. The temperature ranges adopted in Scenarios 2 and 3 may be adequate for drying the wood, but the disadvantage is manifested in terms of the charging process of the storage unit, especially during the winter, the wettest season which the values of outdoor temperature and solar intensity can be dropped. These thermal quantities harvested during winter are generally insufficient to properly feed the storage unit and to satisfy the solar drying of wood. The fluid output temperature in Scenario 1 for RT82 and Erythritol is acceptable for a wood drying operations. However, the disadvantage lies in the sizing of a solar generator likely to meet the needs of these two materials because of their high melting points and also the effectiveness of heat exchanger when the difference between the operating temperature in the drying system and the temperature generated at the solar collector is growing (see Fig. 10 below). For the same Scenario 1, the fluid outlet temperature for RT64 which has the lowest melting temperature (Tme = 64 °C) is similar to those of RT82 and Erythritol. This melting temperature offers RT64 the particular advantage of working on low temperature for many drying applications. In particular, this temperature range is required for solar drying of wood [15]. The simulation results of the solar drying of wood coupled to the storage unit in operating mode according to Scenario 1 and RT64 as phase change material are shown in paragraphs 5.3.

28 Scenario 1 (RT64) Scenario 1 (RT82) Scenario 1 (Erythritol) Scenario 2 (RT82) Scenario 2 (Erythritol) Scenario 3 (Erythritol) Scenario 4 (Erythritol)

0.24 0.22

Inlet front radius (m)

0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06

100

0.04 0.02

27 32 33 34 35 36 37 38 39 40 41 42 43

0

2

4

6

Time (hr)

8

10

Scenario 1 (RT64) Scenario 1 ( RT82) Scenario 1 (Erythritol) Scenario 2 (RT82) Scenario 2 (Erythritol) Scenario 3 (Erythritol) Scenario 4 (Erythritol)

110

Outlet temperature (Degree Celsius)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

80 70 60 50 40 30

12

Fig. 7. Front solidification at the inlet of the heat exchanger against the discharge period.

90

0

2

4

6

Time (hr)

8

10

12

29 30 Fig. 8. HTF outlet temperature at the outlet of the heat 31 exchanger against the discharge period.

The variation of the heat transfer rate during the solidification process as a function of the discharge period is shown in Fig. 9. It is observed that the heat transfer rate during solidification decreases slowly with time. The maximum heat transfer rates were 6200, 9000, 13800 and 15800 W respectively for Scenario 1, 2, 3 et 4. At the end of discharge process, the heat transfer rates were 4000, 7000, 11700 and 13900 W respectively for Scenario 1, 2, 3 et 4. The curve of heat transfer rate was similar to the curve of the HTF outlet temperature since the heat transfer rate is a function of a temperature difference at the outlet and inlet of the tube heat exchanger. The thermal power is an important physical parameter to which particular attention must be paid especially when one wants to properly size the solar dryer or to ensure its good performance during the night or periods of low sunlight in general. In fact, when increasing the thermal power of the storage unit, this leads to accelerating the drying rate of wood in the dryer and reduce the drying time [17]. The simulation results of the solar drying of wood coupled to the storage unit for all the Scenarios studied in this work are shown in section 5.3.4.

17

ACCEPTED MANUSCRIPT

1 2

Scenario 1 (RT64) Scenario 1 (RT82) Scenario 1 (Erythritol) Scenario 2 (RT82) Scenario 2 (Erythritol) Scenario 3 (Erythritol) Scenario 4 (Erythritol)

18000 16000

Thermal power (W)

14000

6 Scenario 1 (RT64) Scenario 1 (RT82) Scenario 1 (Erythritol) Scenario 2 (RT82) Scenario 2 (Erythritol) Scenario 3 (Erythritol) Scenario 4 (Erythritol)

0.9 0.8 0.7

Effectiveness [-]

12000 10000 8000 6000

0.6 0.5 0.4 0.3

4000 0.2 2000

3 4 5 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

0

2

4

6

Time (hr)

8

10

12

Fig. 9. Heat transfer rate during the solidification process as a function of the discharge period. .

0.1

7

0

2

4

6

Time (hr)

8

10

12

Fig. 10. Variation of the effectiveness at the outlet of the heat exchanger as a function of the discharge period.

A heat exchanger is an apparatus for transmitting heat from a hot fluid to another cold without mixing them. The heat transfer performances in a heat exchanger are quantified in terms of effectiveness. Effectiveness is defined as the measure of the power of a heat exchanger compared to what it could transmit. From an economic point of view, an exchanger is often sized to have an effectiveness greater or equal to 0.5 [30]. Fig. 10 presents the variation of the effectiveness at the outlet of the heat exchanger as a function of the discharge period. Effectiveness values were estimated using equation (5). This figure shows that the effectiveness of the storage unit is extremely different in the same Scenario. For example, in the case of Scenario 1, it is observed that the RT64 has the best effectiveness than RT82 and Erythritol. At the beginning of the storage process, the values of the effectiveness were 0.72, 0.52 and 0.30 respectively for RT64, RT82 and Erythritol. As for Scenario 2, at the beginning of the storage process, the effectiveness values were respectively 0.72 and 0.43 for RT82 and Erythritol. Scenarios 3 and 4 (Erythritol only) have respectively the values of 0.64 and 0.74. In conclusion, the use of RT82 and Erythritol as a solution to effectively meet the thermal storage requirements of Scenario 1 is not economically feasible, as shown in Fig 10. Similarly, Erythritol is not a good solution for the operation of the storage unit with the temperature difference imposed by the Scenario 2. We can retain the following effective solutions: - RT64 can be used for the case of Scenario 1; - RT82 for the case of Scenario 2; - Erythritol can be used as a good solution for Scenarios 3 and 4. These results show to what extent the judicious choice of the change phase material used for the storage and the application temperature range for which this storage will be intended is preponderant. These results are in agreement with the conclusions of Basakayi [32].

5.2. Drying with and without thermal storage We considered a stack of Red pine wood with an initial moisture content of 0.5 kg water/kg dry solid. Each board has a dimension of 0.027 m× 0.2 m × 2.6 m. The dimensions of the stack were: 2 m× 2.5 m × 2.6 m = 13 m3 with a distance of 0.027 m between layers (battening) and a vacuum rate of ε = 0.5. The total calculated volume of the scaled Kiln was 27 m3. The drying time is completed when the final moisture continent of wood reaches the equilibrium moisture continent assumed to be equal to 0.10 kg water/ kg dry matter. It should be noted that the simulation results of the solar drying model with thermal storage system presented in paragraphs 5.2 and 5.3 (section 5.3.4 is an exception) of this document are related to Scenario 1 with the use of RT64 as phase change material.

18

ACCEPTED MANUSCRIPT

X (kg water / kg dry matter)

0.6

80

50

0.4

40 30

0.3

20 0.2

0.1

0.4

0.3

0.2

10

0

100

200

Time (hr)

300

0 400

Fig. 11. Variation of moisture content and drying air temperature against drying time.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

June September December March

70 60

0.5

0.5

X (kg water/kg dry matter)

0.7

Temperature (Degree Celsius)

Moisture content : without storage Drying air temperature : without storage Moisture content : with storage Drying air temperature : with storage

0.1

0

100

200

300

400

Time (hr)

500

600

700

Fig. 12. Variation of moisture content against drying time in June, September, December and March (Dm=0.225 kg/s, Th = 0.027 m).

The variation of drying air temperature and average moisture content of wood stack with and without thermal storage unit in June is shown in Fig. 11. About 874 kg of water was removed from a stack volume of 13 m3 with initial weight of 13 × 504 kg/m3 × 0.5= 3276 kg to produce about 2402 kg of wood boards at 0.10 kg water/kg dry matter in both drying modes. The maximum drying air temperature recorded at inlet of the dryer was about 68 °C with and without thermal storage. The minimum drying air temperature recorded at inlet of the dryer was about 45 and 23 °C with and without thermal storage respectively. Regarding to the drying rate, the equilibrium moisture content of 0.10 kg water/ kg dry matter is reached 12.5 and 17 days with and without thermal storage respectively. This result shows that the integration of thermal storage unit can be reduced the drying time as much as 26.5 % for June. The performance of the solar dryer kiln was evaluated in terms of daily reduction in moisture content and supplied energy in different months with the optimum parameters of the solar air heater and thermal storage. Fig. 12 gives the drying times for four representative months (June, September, December and March) during drying process with thermal storage. For all the months considered, the drying rate was faster in the earlier part of the drying process. For example, in June, the reduction in MC is 0.0025 kg water/kg dry matter per hour for the first fifty days and 0.001 kg water/kg dry matter per hour on the rest of the drying time. This is due probably to high driving force to free water movement within the boards at the beginning of drying process lead to faster drying rate. It has been reported that solar dryers could be able to dry large amounts of wood faster when they receive significant amounts of solar energy [18]. Table 9 shows some thermodynamic parameters such as energy supplied, drying time and thermal efficiency of the solar kiln in mode of drying with thermal storage (Case 1) and without thermal storage (Case 2). The energy supplied to the dryer in June was respectively 1374 and 1290 KWh with and without thermal storage. It is observed that the drying time is considerably shorter in June (hottest month) and longer in December (wettest month). The drying time is also shorter in September than March because of the drying conditions which are in general favorable during September in Tangier city (Table 2). The longer drying time recorded in December and March (coldest months) is a result of the crop air temperature produced by the solar air collector which is too low for the timber drying. The results show that the drying efficiency of the solar kiln has dropped slightly for drying process with thermal storage and is due to the more energy that has been supplied to the dryer system. The drying efficiency could also be reduced if the heat losses towards the outside of the drying system are taken into account in the drying model. However, in this study, it was considered that the walls of the dryer are adiabatic. The evaporation capacity produced using thermal storage is important than that without thermal storage (Table 9). The evaporation capacity of the drying system was greatly important in June than for all other studied months because the daylength (the period between sunrise and sunset) and global radiations reach higher values during summer. This result can be explained by the amount of solar radiation coming in, for Tangier city in summer or winter. For example, at the beginning of June it is up to about 1000 W/m2, but in December the maximum value may be about 500 W/m2. As it has been reported previously the heat was transferred into the boards when the ambient temperature and solar intensity are important. It was concluded that the integration of

19

1 2 3 4

ACCEPTED MANUSCRIPT the thermal storage in solar drying system increases the evaporation capacity, reduces the drying time and makes drying process continuous without interruption. It has been reported in the literature survey that the maximum solar intensity throughout the year in a given region is the most important parameter for site selection of solar kiln and receiving solar wood drying facilities [20, 21]. Table 9 Energy and thermal parameters of the studied drying system (Dm=0.225 kg/s, Th = 0.027 m). Thermal parameters

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

March + April

June

September

December + January

Case 1

Case 2

Case 1

Case 2

Case 1

Case 2

Case 1

Case 2

Water evaporated (kg)

874

874

874

874

874

874

874

874

Energy required (KWh)

688

688

682

682

686

686

692

692

Energy supplied (KWh)

2030

2213

1290

1374

1497

1572

2769

3012

Drying time (days)

49

34

17

12.5

29

20

62

44

Drying efficiency (%) Evaporation capacity (10-6×kg/m2.s)

34

31

53

47

45

44

25

23

1.12

1.4

2.52

3

1.73

2.12

0.52

0.88

The drying process of wood is usually an energy intensive process, since the evaporation of moisture requires large amounts of energy. Thus, using direct solar energy through the best possible design of solar dryers can greatly improve the overall sustainability and profitability of the wood processing industry. However, the development of solar drying technology, such as large-scale solar drying facilities, must be based on a thorough knowledge of the energy resource and expected performance of kiln designs [11]. In order to analyze the capability and usefulness of the studied solar kiln model and its simulation procedure for predicting the drying behaviors for different drying conditions, the simulation results under climatic and geographical conditions of Tangier city are compared with predicted results of two typical solar drying systems of wood that are Oxford and Boral kiln with reference to summer weather conditions in Brisbane (Australia). Table 10 summarizes the performances comparison results between these three solar dryer designs. The total calculated volume of the scaled Tangier Kiln (27 m3) was smaller than that of Boral kiln (101 m3) and of Oxford kiln (58 m3). However, the volume of dried wood for Tangier solar kiln (6,5 m3) was smaller than that of Oxford and Boral kiln (10m3). The drying air temperature for the scaled Tangier kiln varies between 23 °C and 68 °C, this difference of temperature is little greater than that recorded for Oxford and Boral (20 °C – 50 °C). It is interesting to note that the difference in the drying air velocity between the Tangier solar dryer and Boral kiln is zero. Moreover, the drying air velocity for Oxford Solar kiln was 0.5 m/s. The predicted drying periods in summer for the Tangier, Oxford and Boral kilns were respectively 17, 38 and 46 days. The results have shown that the Tangier design is likely to produce faster drying rates (lower drying times required) than those for the Oxford and Boral kiln. For this present study, it is important to remember that heat losses to the outside of the drying system are not taken into account in the drying model, but, for Oxford and Boral Kiln, the radiation and convection losses are considered and therefore, additional heat is required in order to remove the water from wood stack. The drying time is quickly different because the drying conditions such as drying air temperature, air velocity, volume of wood stack, vacuum rate and the boards thickness are slightly different. These results are interesting because the net present energy value (difference between input solar energy and thermal losses) of the Tangier solar dryer was predicted to be greater (198.46 KWh/m3 of dried wood) than that predicted for the Oxford (182.5 KWh/m3 of dried wood) and Boral kiln (113.33 KWh/m3 of dried wood), as shown in Table 10. These differences in terms of energy supplied cause the observed differences in drying times. However, the difference in the drying efficiency between the Tangier solar kilns (53 %) and Oxford (55 %) is not very large, especially in the drying time range of (0 – 38) days. The dropped drying efficiency recorded for the Boral solar kiln (40 %) is probably due to greater velocity appeared to cause a correspondingly larger heat‐transfer coefficient and consequently the greater amount of thermal losses towards outside of the dryer, which in turn lowered drying air temperature. This situation may indicate that much of the input energy for the Boral kiln leaves without effectively drying the wood stack, resulting in slower drying in this kiln. The estimated drying time and the net present energy value for the Tangier solar dryer could be further reduced if the equilibrium water content of the wood was 0.15 kg water/ kg dry matter instead of 0.1 kg water/ kg dry matter, a value adopted in this study for reasons of wood exploitation after drying. From the overall discussion, it is clear that, for a given set of geographical and operating conditions, the Tangier solar kiln is likely to be better as well as the Oxford and Boral kiln for the purpose of wood drying. However, it is still necessary to carry out a more focused and detailed study to the analysis of operating costs and life cycle energy by considering the annual energy requirements for the three solar kilns in order to compare their life cycle benefits for the purpose of drying.

20

ACCEPTED MANUSCRIPT

1

Table 10 Comparison of the thermal performance of three solar dryers in different climatic and geographical conditions. Present study Previous work Previous work Difference Difference Drying characteristics (Tangier) [11] (Oxford) [11] (Boral) (Tangier/Oxford ) (Tangier/Boral) Solar dryer volume (m3) 27 58 101 – 31 – 74 Volume of wood (m3)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

13 × 0.5 = 6.5

10

10

– 3.5

– 3.5

Drying air temperature (°C)

23 – 68

20 – 50

20 – 50

(+ 3) – (+ 18)

(+ 3) – (+ 18)

Air velocity (m/s) Initial moisture content (kg water / kg dry matter) Equilibrium moisture content (kg water/kg dry matter) Drying time (days)

1

0.5

1

+ 0.5

0

0.5

0.53

0.53

– 0.03

– 0.03

0.10

0.15

0.15

– 0.05

– 0.05

17

38

46

– 21

– 29

53

55

40

–2

+ 13

198.46

182.5

113.33

+ 15.95

+ 85.13

Drying efficiency (%) Net present energy value (KWh)/m3 of dried wood

5.3. Drying quality In order to assure a good quality during drying, it is recommended to respect the tables of drying for each species of wood. Drying table is enabling to obtain a good quality of wood over length of drying time. In fact, drying air conditions have an important influence on the mechanical behavior and structure of wood during drying. In addition, the drying rate increases and decreases periodically and may be affects the final quality of wood [10]. In order to obtain good physical and mechanical properties at the end of drying, it is important to dry wood in the optimal drying conditions. So, the purpose of the following paragraphs is also to analyze the effects of some drying conditions on the drying rate and the characteristics of wood under the climatic conditions of June in Tangier city (Morocco).

5.3.1. Influence of the boards thickness: The influence of the board thickness on drying rate is shown in Fig. 13. It appears that the drying rate is also affected by the board thickness and the drying time increases significantly with thickness. For a thickness of 0.02 m, only 7.5 days are needed to reach the required equilibrium moisture continent of wood. However, for a thickness of 0.04 m, the equilibrium moisture content was obtained after 23.5 days of drying. This result is a bit far with the observation proving that the drying time is proportional to the square of the board thickness [36]. It was deduced that increasing the board thickness needs to supplier more power energy for drying.

5.3.2. Influence of the mass flow of the air: The effect of mass flow rate of air on drying rate is shown in Fig. 14. These results show that there is an acceleration of the drying rate due to the decrease of the mass flow rate from 0.285 to 0.165 kg/s. This is because when increasing the mass flow rate in solar drying, the outlet temperature at the solar air collector can be dropped. In fact, the increase of the mass flow rate in the solar air collector leads to increase the drying air velocity and the convective heat transfer losses between the glass cover and the environment [16]. We have demonstrated that the drying time could be reduced when the mass flow rate is adjusted by optimization according to the specified drying conditions. The simulations carried out under the June drying conditions have shown that the mass flow rate is optimal for a value equal to 0.165 kg/s which results in a drying time of 7.5 days. It has been shown that the decrease of the mass flow rate increases the input solar energy and improves the thermal efficiency of the drying systems [25].

21

ACCEPTED MANUSCRIPT 0.5

0.5

Th = 0.02 m

Dm = 0.165 kg/s

0.4

0.3

0.2

0.1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

X (kg water/kg dry matter)

X (kg water/kg dry matter)

Th = 0.027 m Th = 0.04 m

0

100

200

300

Time (hr)

400

500

Fig. 13. Variation of moisture content against drying time. Influence of the thickness of the boards (Dm=0.225 kg/s).

0.4

0.3

0.2

0.1

600

Dm = 0.225 kg/s Dm = 0.285 kg/s

0

100

300

Time (hr)

400

500

600

Fig. 14. Variation of moisture content against drying time. Influence of the mass flow rate (Th = 0.027 m).

5.3.3. Influence of heat recovery process: In order to improve the thermal efficiency of drying, it is necessary to reduce the energy expenses by recycling a fraction of air into the drying system. In fact, the outlet air temperature rejected at the outside of drying unit is humid and often considerably higher than the air ambient temperature. Therefore, the inlet air temperature in the solar air collector and thermal storage can be heated by transferring heat to it from the rejected hot air into a heat recovered unit. During the recovery heat process, a part (fraction) of the recuperated hot air was recycled inside the drying chamber and the rest part was taken from the ambient air. In this work, we analyze the effect of recovered hot flow at a fraction of 50 % on drying time in June for three different strategies described as follow: -

Strategy A: Recycling between the solar air collector and the drying unit; Strategy B: Recycling by night between the thermal storage and the drying unit; Strategy C: The combination of the two Strategies A and B. Table 10 The effect of recovered hot flow on drying rate (Dm=0.225 kg/s, Th = 0.027 m). Thermal parameters Strategy A Strategy B

18 19 20 21 22 23 24 25 26 27

200

Strategy C

Energy supplied (KWh)

1018

1180

892

Energy saving (KWh)

356

194

482

Drying time (days)

9.5

10

9

Drying efficiency (%)

67

58

77

For all these strategies, it is obvious that the process of heat recovery during drying is more efficient than an operation of drying. In fact, the recycling process of hot air reduces the drying time and decreases the energy required for the drying (Table 10). From these results, the maximum recovered energy was registered for the third strategy (Strategy C) and the drying process has been achieved 9 days in month of June demonstrating that the time saving can be reach 47 % compared with drying process without thermal storage and heat recovery. Concerning the Strategy A and B, the drying process has been achieved respectively 9.5 and 10 days. This is due to the fact that more enthalpy was introduced into the solar air collector and thermal storage; more hot air was also diffused into the wood boards, which consequently increases the mass and heat transfer coefficient between air and the product [20]. This process extends the discharge time of the thermal storage tank and increases the amount of energy saved during the recovered

22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

process. The drying efficiency of all theseACCEPTED strategies has beenMANUSCRIPT improved by comparing it to an operation of drying without the process of heat recovery (section 5.2). The energy saving is defined as the difference between the supplied energy with and without recovered heat. The maximum values of drying efficiency and energy saving with recovered heat process are 77 % and 482 KWh respectively. The drying efficiency of the solar kiln increases as a result of regeneration heat since the energy portion of the humid air normally rejected to the surroundings environment is now used to preheat the air entering the thermal storage and solar air collector. This, in turn, decreases the amount of heat input requirements for the drying. From these results, we can deduce that the drying time can be reduced by recycling the hot flow between the drying unit and the solar air collector during the sunshine period, and between the thermal storage and the drying unit during the nocturne period.

5.3.4. Influence of latent heat thermal storage Scenario In this section, the effect of the latent heat thermal storage Scenario on the thermal performance of the solar drying system is presented. Four Scenarios were compared and the characteristics of the thermal storage tank used in the numerical simulations are those presented in Table 7 (Section 5.1). During the day (sunshine period), the temperature of the drying air produced by the solar air collector varies between 23 °C and 68 °C (see Fig. 11). During the night, the storage unit takes over as a means of substituting for the solar collector and the drying air temperatures produced by this storage unit vary according to the four Scenarios as shown in Fig. 8 (Section 5.1). Concerning the simulation results of the thermal storage unit, it should be noted that the discharge process begins every day at 07 pm and finish at 07 am (a discharge period of 12 hours). The performances of each Scenario related to the thermal storage unit in terms of drying time, efficiency, energy supplicated and evaporation capacity are given in Table 11. It is obvious the supplied energy to the dryer decreases by moving from Scenario 1 to 4 indicates that the input latent heat energy from the storage unit to the dryer during the night is high which increases the drying air temperature. In Table 11, it is clear that Scenario 4 records the shortest drying time followed by Scenario 3, then Scenario 2 comes in third, and Scenario 1 has the longest drying time. These results can be interpreted by the very high values of drying air temperatures harvested at the outlet of the storage unit and which become more and more important by going from Scenario 1 to 4. For example, by adopting Scenario 2 during the drying process, the drying time is reduced to 9.5 days instead of 12.5 days recorded for the case of Scenario 1 (a reduction of 24 %). There is also a reduction of 60 % and 76 % for Scenarios 3 and 4 respectively compared to the baseline Scenario. The drying efficiency and evaporation capacity are also more and more greater from Scenario 1 to 4 which demonstrate that these two parameters increase with drying air temperature. The thermal power released by the storage unit is particularly the direct cause of these reductions in terms of drying time and improvement of the drying efficiency and evaporation capacity of the solar kiln. If we consider the construction costs are not expensive for the realization of the thermal storage unit according to each Scenario, supplying the drying unit according to Scenario 3 or 4 would clearly satisfy the demand for wood production without wasting time and energy. However, as has been seen in the dimensioning of the storage unit according to the desired minimum and maximum temperatures at its output (Table 7), the geometric and physical parameters and the size relative to each Scenario are different and consequently the design costs and realization remains dependent on these characteristics obtained by adequate sizing. It is therefore crucial to specify the characteristics such as thermal power and efficiency in a project to realize a solar dryer equipped with a thermal storage tank if we want to accelerate the production rate of dried wood and to satisfy the notebook customer orders. In general, it can be concluded that the investigations carried out in latent heat storage topic are intended to optimize the performance of these thermal storage systems and to improve their effectiveness and operation. In addition, they are considered as perspectives for encouraging the integration of renewable energies into drying systems and techniques. The interest in integrating the thermal latent energy storage in drying applications is to contribute to the reduction of the often very heavy energy bill which companies complain in particular in a large sector as vast as that of the wood industry. For selection, it should be to take into consideration the environmental impacts of the solar dryer and thermal storage unit. The other important factor is the temperatures, since at much higher drying temperature the emissions to the air are likely to be under scrutiny by the regulatory authorities. However, in this project, these is no release of carbon dioxide (CO2) generated from the drying unit because the drying air temperatures remains under 150 °C. It has been shown that at high temperatures of air drying, the chemical components of wood decompose and degrade and are likely to generate emissions of greenhouse gases into the atmosphere [26].

Table 11 The effect of latent heat thermal storage Scenario on drying rate (Dm=0.225 kg/s, Th = 0.027 m). Thermal parameters Scenario 1 Scenario 2 Scenario 3 Energy supplied (KWh)

1374

1310

910

23

Scenario 4 802

Drying time (days) Drying efficiency (%) Evaporation capacity (10-6.kg/m2.s)

ACCEPTED9.5MANUSCRIPT

3

47

52

75

85

3

3.4

4.78

5.4

5.3.5 Moisture and temperature evolution at surface, centre and outlet of the wood stack To produce a good quality of wood product, it is recommended to obtain a uniform distribution of the moisture content at the end of drying as possible throughout the board thickness. For this, it is also important to know how the heat and moisture transfers are distributed locally in the wood. This information can be used to adjust the right properties and to control more effectively the final quality of the product [9, 10, 22]. Fig. 15 shows the temperature and moisture content evolution in wood for three different positions: the surface, centre and outlet of wood boards as a function of time. It is obvious that the surface temperature of wood boards follows the curves of drying air temperature. This seems obvious since the heat transferred from the hot air to the surface of wood takes place initially by convection. Therefore, the product surface is heated or cooled depending on whether this heat flows is hot or cold. The moisture transfer at the surface of wood boards is fast because the inlet air temperature at the wood stack is high which generate high evaporation capacity and consequently the water migration on the surface of the product is easy. From Fig. 15, it can be seen that the differences between the surface and the centre moisture content are the highest at the beginning of the drying process, as drying progresses, this difference becomes more and more smaller. It should be noted here that, while the surface moisture content reduced from 0.4 to 0.1 kg water/ kg dry matter (the equilibrium moisture content) after 160 hrs, the centre moisture content decreased from 0.4 kg water/ kg dry matter at the beginning of drying to around 0.17 kg water/kg dry matter during this time. It is observed that the maximum temperature attained in the centre of wood stack at the end drying was 53.4 °C in the middle. This is achieved because, in solar drying (cyclic drying), the temperature of the drying air varies according to the climatic conditions of the day and the night. Thus, it is difficult for the depth of wood pile to reach the temperature that has occurred on its surface. Surface moisture content Centre moisture content Outlet moisture content Surface temperature Centre temperature Outlet temperature

0.7

X (kg water / kg dry matter)

0.6

80 70 60

0.5

50

0.4

40 30

0.3

20 0.2

0.1

22 23 24 25 26 27 28 29 30 31 32

5

Temperature (Degree Celsius)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

12.5

10

0

100

Time (hr)

200

0 300

Fig. 15. Moisture content and temperature evolution of wood during drying (Dm=0.225 kg/s, Th = 0.027 m). Concerning the outlet of wood boards, the lower temperature was observed during drying especially at the beginning of the drying process, and the maximum temperature attained at the end drying was 46 °C. This lower temperature results in high moisture contents which are observed during the beginning of the drying process and the drying rate is slower with respect to the surface and the centre. This difference in moisture content and temperature profile between surface and the middle of wood stack can be probably explained by the influence of thermal inertia of the wood stack on heat transfer from one board to another. The length and width of wood stack are normally far greater than the thickness, and thus the moisture transport is slower through the boards from the center to the outlet of the wood stack. It has been shown that a non-uniform distribution of moisture content causes probably a less residual stress in the timber during the relaxation time [8, 11].

24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

ACCEPTED MANUSCRIPT 6. Conclusion This work shows that it is enable to describe the solar drying which incorporates heat latent storage by using a simplified mathematical model that simulates heat and moisture transfer in a wood stack during drying process. Results show that the drying time is affected by the mass flow rate, the board thickness, recycling heat process and the operation mode of the thermal storage unit. Results found that there were advantages in energy latent storage and recovered heat for several reasons. First, up to 26.5 % of drying time can be reduced in June for Tangier city. Second, using recycling process of air, the supplied energy to the system decreased and the drying time reduced up to about 47 % compared with the drying method without recovered heat. Third, by adopting a high level temperature for operation of the thermal storage unit (Scenario 4), the wood stack can be reaching the required equilibrium moisture content of use after three days of drying, a reduction of 76 %, compared to a storage process operating at a lower level temperature (Scenario 1). However, several operating criteria and economic factors must be taken into account to implement this solution. The main results of this work can be summarized as:  The sizing of the latent heat storage unit is depended on the melting point of the phase change material;  The effectiveness of the heat exchanger is significantly important when the level of minimal and maximal output temperature is close to melting point of the PCM;  The output fluid temperature, effectiveness and thermal power of the latent thermal storage decrease with discharge time;  The drying time is reduced as the boards thickness and mass flow rate decrease;  The integration of latent storage system into the solar dryer reduces the drying time and makes drying continuous;  The recovered heat process improves the drying efficiency, decreases the drying time and the amount of heat input requirements for the drying;  The effect of the thermal storage Scenario on drying rate is effective while the level of minimal and maximal output temperature at the storage tank is raised;  The moisture content removes faster at the surface than the centre and the outlet of the boards. For future research works in this topic, the following recommendations are made:  Numerical modeling of a heat exchanger coupled to a solar cylindrical parabolic solar collector;  Modeling with the TRANSYS software of the operation of the drying unit with reference to different climatic zones in Morocco;  Realization of the coupling between the cylindrical parabolic solar collector, the drying unit and the latent storage unit. References:

[1] [2] [3] [4]

[5] [6] [7] [8] [9] [10]

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ACCEPTED MANUSCRIPT Highlights: 1. The tank volume of the storage unit varies between 0 and 14 m3 for a discharge period of 12 hours. 2. The integration of the thermal storage unit in the solar kiln reduces the drying time as much as 26.5 % 3. The process of heat recovery reduces the drying time as much as 47 % 4. The maximum energy saving in the drying system was 482 KWh 5. The maximum drying efficiency of the solar dryer was 85 % 6. The maximum evaporation capacity of the dryer without recovery process was 5.4×10-6 kg/m2.s