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28 ноября, 2020
For the radiative thermal resistance between the two slabs of the duct the following relation has been considered:
Г = (Ve1 +1/ є2 — 1)/4oT3
with о StefanBoltzmann constant, T = (T1 + T2)/2, є1 and є2 emissivity of the duct’s inner faces, respectively of the slabs A and B.
A detailed description of the used calculation procedure is reported in [8].
In the calculations the following reference dimensions have been considered: L=15 m; h=10 m; d=0.04 m. Assuming Pr=0.72, D~2d=0.08 m, the Eq. (1) is fully satisfied for all values of the Reynolds number (Re<2500) being peculiar to laminar flow.
For a standard situation the following reference climatic conditions have been assumed: Ti=24 °C, T0=28 °C in summer and Ti=20 °C, T0=0 °C in winter; all the graphs reported hereinafter should be meant to refer, unless it is indicated otherwise, to such values.
An iterative calculation procedure has been used to evaluate the quantities defined by the Eq. (2), to take into account the dependence of Г on the temperatures T1 and T2, and also to consider the variability of the air density and viscosity with the temperature T. All calculations have been developed in Maple programming software. For the friction factors Xin and Xou the following values have been considered as reference values: Xin=2 and Xou=4.
As reference values for the thermal resistances re, ri, and Rcd, (see Tab. I) the ones recommended by the technical rule EN ISO 6946 [11] have been chosen. For the considered values of d, Rcd=0.18 m2KW1 has been assumed.
In the studied cases, the outer slab is supposed to have been realized so that the air infiltrations through the joints and the permeability to air of the used material could be disregarded.
Figure 2 represents the studied reactors in this work. They consist of 1 m long and 2 mm thickness steel tubes resisting to the maximum pressure reached by the fluid. The total surface covered is 1 m2 which is composed by a number of cylindrical tubes with an external diameter De, figure 2a. This number is inferior when finned tubes are used considering a De/2 width fins, figure 2b. The rectangular reactor has a width of 1 m and a height of H, figure 2c. All these reactors are isolated from the lateral wall and the back. The tubes are filled by an amount of activated carbon reacting by adsorption with ammonia constituting a porous medium. This medium can be heated or cooled through the metallic wall along a daily cycle.
Figure 2a. Reactor without fins
Figure 2. Solar reactor
The thermal and mass transfer calculation in the reactor been made by taking account the next hypotheses; characteristics of the porous medium:
— the porous medium pressure is uniform and to be constant when the reactor is opened.
— the distribution of temperature is bidimensional in the rectangular reactor and radial in the case of cylindrical tubes.
— the three phases of the porous medium, in elementary elements of volumes, solid phases made up of coal particle of activated carbon, liquid phases (ammonia adsorbed) and gas phases (ammonia gas) are in thermal, mechanics and chemical local equilibrium.
— the thermal transfer by convection is neglected
— the exchange between the metal wall and the porous medium and the thermal transfer by conduction are characterized respectively by a coefficient of exchange hi and an apparent thermal conductivity Xe [16].
— the physical properties of metal and the activated carbon are constant.
— the condenser and the evaporator are considered to be idea.
ma = PL Vo Exp[D (T Log ( fs / f ) )n] (1)
where; ma is the total mass of the adsorbed fluid at the pressure P and the temperature T; The product pL Vo is the maximum volume of the pores accessible to the adsorbate. D and n represents the parameters of Dubinin, which depend on the adsorbent / adsorbate couple and which are given experimentally for the activated carbon and ammonia pair [17].
For determining the appropriate temperature levels for the acid rain tests, stagnation temperature for an unglazed absorber was calculated iteratively on a hourly basis (Konttinen et al, 2004). Surface samples were immersion subjected to O2aerated or zero — aerated (with N2) simulated acid rain (Table 1) with pH 3.5 or pH 4.5 and simulated neutral rain with pH 5.5 in temperatures of 60, 80 or 99 °C. Saturating gas was fed at room temperature into the solution. The solution was heated within ±1 K of the required temperature in a flask, which was in a paraffine oil bath (Fig. 1). The oil was typically 6 10°C (at 60/80°C) or 4045°C (at 99°C) warmer than the solution. Details of the setup are described in (Konttinen et al, 2004). Samples tagged as “nonaerated” in Figures 35 were tested with EIS at similar temperatures and pH. Changes in optical properties of nonaerated EIStested samples AB in Figs. 35 are included in this paper for comparison to aerated and zeroaerated test results.
Polarisation measurements and EIS measurements were carried out in a conventional three electrode cell using platinum sheet as a counter electrode (CE) and saturated calomel electrode (SCE) as a reference electrode (RE) (Fig. 2). The methods and measurement system are described in ASTM standard G5 (ASTM, 1987) and in (Lorenz and Mansfeld, 1981), respectively. The RE was connected to the cell with Luggin capillary.
Corresponding author. Tel.: +35894513212; fax: +35894513195; Email:
The salt bridge filled with 0.1 mol/l Na2SO4. was used between the RE and the Luggin capillary to avoid possible chloride contamination of the test solution. In some polarisation tests 500 mg/l Na2SO4 sulphate was added to increase conductivity (Table 1, bsolutions). The polarisation measurements were conducted in an Avesta cell (Fig. 2a) where a sample was pressed against a round hole on the cell bottom and the system was sealed with a rubber oring gasket. The sample area was 0.8 or 1.3 cm2. Longterm immersion EIS tests were conducted in a cell (Fig. 2b) where the samples (working electrode WE) were attached with stainless steel screws to a sample holders made of copper rods. The copper rods and the back sides of samples were insulated with PTFE tape and nolan lacquer. The sample area was 5 cm2.
Before polarisation measurements the corrosion potential was followed for 1h until a stable corrosion potential was achieved. Potential was first changed — 150 mV to cathodic direction and cyclically back to the corrosion potential with a scan rate of 10 mV/min. After cathodic polarisation the potential was changed +150 mV to anodic direction or to potential 200 mV vs. SCE. The EIS measurements were done at the corrosion potential with the amplitude of 10 mV. The EIS system consists of a NF 2000 potentiostat and NF 5050 frequency response analyser and the polarisation measurements system consists of a ACM Instruments Autotafel potentiostat.
Test duration needed to degrade the a and є of the absorber samples according to performance criteria (PC) was determined in each test:
PC = — Дa + 0.25Д^< 0.05
Although not defined for unglazed collectors, Eq. 1 was used as it is typically used to estimate failure limit for solar absorbers inside glazed collectors (Brunold et al., 2000). PC value of 0.05 is generally equivalent to 5 percentage unit decrease of the solar heat gain by the flatplate solar collector water heating system.
Hemispherical reflectance of the samples was measured before and after each test at room temperature. Solar absorptance, a, was determined between 0.39 — 1.1 pm with a LICOR LI1800 type spectroradiometer and a BaSO4 coated integrating sphere. Thermal emittance, e, was determined between 2.5 — 20 pm with a MIDAC Prospect FTIR — spectrometer with a semihemispherical integrating device. Spectral reflectance, p^, was analysed for estimating the hydration levels of alumina.
Table 1. Chemical composition of the simulated acid rain. pH 3.5 (a) adapted from (Magaino, 1997). pH 4.5 and 5.5 (a) gained by adjusting the amount of NOj and SO4~ . pH 3.5 (b) and 5.5 (b) gained by adding 500 mg/l Na2SO4 for better conductivity for EIS. Concentration/mg dm 3

Fig. 1. Photograph of the acid rain totalimmersion setup including 250 ml threenecked flask, 100 ml simulated acid rain, 23 x 50 mm sample and gas distribution tube (excluding heating system consisting of paraffine oil bath, heater and temperature controller).
Fig. 2. Schematic pictures of the measurement cells in polarisation tests (a) and longterm immersion tests (b).
M. Hiller 1, S. Holst 1, T. Welfonder 1, A. Weber 2, M. Koschenz 2 TRANSSOLAR Energietechnik GmbH
1 CuriestraKe 2, D — 70563 Stuttgart, tel.: +49 711 / 67976 — 0, fax: +49 711 / 6797611 welfonder@transsolar. com, http://www. transsolar. com
2 EMPA, Abteilung Energiesysteme/Haustechnik, CH8600 Dubendorf
In the planning process and evaluation of innovative energy concepts simulation of buildings and systems gets more and more important. With the internationally well known software program TRNSYS [1] those simulations can be accomplished with a very high complexity.
The paper describes the Program TRNFLOW [2] which is a new addon for TRNSYS for the simulation of natural ventilation. Also the main new features of the TRNSYS Version 16 released in Mai 2004 will be described.
Coupled Airflow Simulation — Current Situation
In order to achieve sustainable buildings new energy systems have been generated using natural effects to renew the air and lead away the heat. Examples are passive night cooling, double facades, solar chimneys, inside courtyards and so on. In these systems the mutual impacts of thermal and air flow behavior are very distinctive. Thus for numerical building simulation programs an integral approach is inevitable.
Already in 1993 in the frame of the IEA project Annex 23 the EMPA has developed a coupling of the multizone air flow model COMIS [3] with the thermal building and system simulation program TRNSYS and this was presented at the TRNSYS Userday 1994. The selfcontained program COMIS was modified to TRNSYS Type 157 which can be linked to the thermal building model Type 56 within the TRNSYSDeck via in — and outputs. The input information of the air flow model are read in by Type 157 from the standard COMIS Input File (CIF). The TRNSYS solver iterates the results of the two models until they match. Meanwhile the coupling has been successfully applied by several projects and simulation tasks. However thereby it was pointed out that the coupling is not very userfriendly and also requires a laborious handling. As the mutual classification of the data is made by hand the inputs tend to be incorrect. This errorproneness is also increased by the redundancies of the two input files. Furthermore it was proven that the TRNSYS solver is not always the perfect solution for such a system. The solver possibly has to be supported by additional convergence promoting Types what makes the handling again more difficult. Yet the need of an integral approach concerning thermal building dynamics and natural air exchange was clearly necessary. Therefor with TRNFLOW an improved version including a deepened integration of the two models (thermal and airflow) has been developed.
Multizone Air Flow Model in TRNFLOW and COMIS
Multizone air flow models idealize the building as a network of nodes and airflow links. A node represents a room volume which a set of state variables can be assigned to. Cracks, window joints and openings, shafts as well as ventilation components like inlets and outlets, ducts and fans represent the links. Boundary conditions and thereby also input factors are: State variables of the air in the zones Local wind pressures
The pressure pZ is a free parameter in the node which is evaluated according to the continuity equation (mass flow balance in the node = 0 ). This results in nZ equations where nZ represents the number of zones.
The relation between mass flow rate m and pressure difference dp and the zone pressure pZ is not linear. Therefor an iterative process is used to solve the system of equations. The mass flow rates per link and all dependent factors such as air exchange rates, air age etc. are calculated of the resulting zone pressures pZi. The calculation is static without an explicit consideration of the timestep. In principle calculating a condition based on a new time is independent of the previous timestep.
The total hemispherical reflectivity R(A) and transmission T(A) for singlelayer on glass samples show a quasizero absorption of the films, confirming the previous results from laser reflectometry and spectroscopic ellipsometry methods. The theoretical curves of Figs. 2 and 3 are calculated using the experimental optical constants determined by spectroscopic ellipsometry on singlelayer samples. In our model, we suppose homogenous layers and sharp interfaces.
Figure 2 represents the total hemispherical reflectivity of Ti02/Si02 multilayers formed by three and five alternating layers of Ti02/Si02. The thicknesses of the layers are indicated in table 2. We observe a reflectivity peak in the visible range. The peak position determines the color of the multilayer film. The dotted lines indicate the theoretical reflectivity. We observe a good agreement between the experimental and the theoretical values. The reflectivity peak position, its maximum value and its FWHM depend on the layer thicknesses and on the number of layers. In general, at one wavelength the reflectivity peak maximum increases with increasing layer number.
Figure 3 shows the total hemispherical reflectivity of Al203/Si02 multilayers formed by an increasing number of alternating layers having the same thicknesses. The dotted lines indicate the theoretical reflectivity increasing with the layer number. This evolution shows the same tendency as previously presented results obtained by using the simplified model of constant refractive indexes [17].
The thicknesses of the individual layers of Fig. 3 are indicated in table 3. The peak position is relatively constant and its maximum value increases by increasing the number of alternating layers. The disagreement between the experimental and calculated values for
the ninelayers samples can be explained by the long deposition time and an eventual change of the deposition conditions.
Wavelength [nm]
Within the framework of the IEA Task 27 "Performance of Solar Facades" we have tested a series of different combinations of solar protection and glazings. These systems include internal, integrated and external shading devices. The characteristic data are given in the following section.
External blind systems
• three devices with identical complex lamellae
• white, white perforated and brown lamellae (see Figure 1) external blinds
• 90 mm width, a distance of the lamellae of 80 mm
• combination with a lowe glazing (pos. 2, 16mm Argon), g=48%, U=1.3 W/(m2K)
Internal systems
• white lamella type blinds using slats 25mm white, distance 22mm
• textile roller blind silver (outside) and white (inside)
• combination with a lowe glazing (pos. 2, 16mm Argon), g=48%, U=1.3 W/(m2K)
• combination with a lowe glazing (pos. 2, 16mm Argon), g=35%, U=1.1 W/(m2K)
Integrated systems
• white lamella type blinds using slats 15mm white, distance 13mm
• textile roller blind grey (both sides)
• integrated in lowe glazing (pos. 2, 27mm air), g=47%, U=1.5 W/(m2K)
• integrated in lowe glazing (pos. 2, 27mm air), g=32%, U=1.4 W/(m2K)
The heat transfer governing equations for steady state laminar natural convection in cavities are the mass, momentum and energy conservation equations in x, y and z axis for an incompressible fluid [Versteeg, 1995]. These equations can be expressed in conservative form:
Conservation of mass:
where T0 is the reference temperature, and is calculated by the mean temperature distribution of the exterior glass surface and its result is averaged with the temperature of the isothermal wall, so:
Hx, Hy y Hz are the lengths of the edge surfaces of the cubic cavity, Hgx is the thickness of the glass and Tci it is the temperature of the wall 2.
The boundary conditions for the momentum equation are:
u(0,y, z)= v(0,y, z)= w(0,y, z)= 0 u(Hx, y,z)= v(Hx, y,z)= w(Hx, y,z)= 0
u(x,0,z)= v(x,0,z)= w(x,0,z)= 0 (6)
u(x, Hy, z)= v(x, Hy, z)= w(x, Hy, z)= 0 u(x, y,0)= v(x, y,0)= w(x, y,0)= 0
u(x, y,Hz)= v(x, y,Hz)= w(x, y,Hz)= 0
The boundary conditions for the energy equation are:
Wall 1
— k“ (X’0’Z ) = ЧГ3 (X’0’ Z ) (7)
dy
Wall 2
T(0,y, z)= Tci (8)
Wall 3
— ka T(x, Hy, Z ) = ЧГ3 ( Hy, z)
dy
Wall 4
d — dT
— ka (Ях ’У’z)=~kg (Hx, y,z)h qr4(Hx, y, z)h Sa, f
Wall 5
— ka (x’ y ’ Hz ) = qr5 (x y ’ Hz )
dz
Wall 6
дт
— k a —(x’ y,0) = qr6(x ’ y,0)
dz
where qr1(x,0,z), qr2(x, y,0), qr3(x, Hy, z), qr4(Hx, y,z), qr5(x, y,Hz) and qr6(x, y,0) are the energy flux from the radiative exchange between the wall surfaces, Saf is the absorbed energy by the solar control coating and Tg(x, y,z) is the glass temperature for Hx<x< Hx+Hx2, where
d—
Hx is the thickness glass. The temperature gradients (Hx, y,z) in the glazing were
dx
evaluated by using the heat conduction model.
Andreas Gombert, Benedikt Blasi, Wolfgang HoRfeld, Volker Kubler, Michael Niggemann, Peter Nitz, Gunther Walze, FraunhoferInstitut fur Solare Energiesysteme ISE, Heiden — hofstr. 2, 79110 Freiburg, Germany
Jorg Mick, Institut fur Mikrosystemtechnik, AlbertLudwigsUniversitat, GeorgesKohler — Allee, 79110 Freiburg, Germany
An overview of known methods to modify the optical properties of solar energy materials by using microstructured surfaces is given. Applications for micro structures in solar energy components are wavelengthselective absorbers, heat mirrors, light traps for PV cells, wavelengthselective concentrators for solar radiation, daylighting components, antireflective zeroorder gratings, and radiation emitters with selective optical properties based on grating resonances. This paper addresses the design and the whole experimental process chain from the microstructure origination on large areas to the replication. The need for costeffective production technologies and durable structured materials is emphasised.
Introduction
A wide variety of solar energy systems from PV cells to buildings exists. All the very different systems have in common that they demand sophisticated optical solutions for an efficient transport, collection and conversion of the solar radiation. Modifying the optical properties of surfaces or planar devices by coatings and microstructures is often used in order to optimise the radiation power management of solar energy systems. Publications in which diffractive structures were proposed to finetune the optical properties date back to the 1970’s [1 — 4].
In fact, advances in diffractive optics like the first approaches to solve the problem of dou — blyperiodic gratings were driven by scientists having solar applications in mind, e. g. Mc Phedran and Maystre [2]. Since the fundamental work of the mentioned authors, diffractive structures in solar energy systems were published for a variety of components in solar energy systems, e. g. [5 — 15]. In Table 1, the quoted publications are classified according to the components for which the diffractive structures were proposed. Additionally, the required optical properties and the proposed structures are listed.
The advantage of considering periodic microstructures is the possibility to model their optical properties rigorously, i. e. by solving the Maxwell equations [16]. Thus, the optical properties of periodically microstructured surfaces can be simulated with rather high accuracy. This is not the case for aperiodic structures.
The challenge of using microstructures is the requirement on very precise manufacturing technologies. Such technologies exist in the field of microelectronics or microsystems technology but are in general not suitable to structure large areas homogeneously. Thus, many of the published approaches are difficult to realise especially due to the mismatch of dimensions between the microstructures and the areas which have to be microstructured in solar applications.
From the technical point of view, homogeneous origination of precise microstructures on large areas is the most difficult step in the process chain. Because of its ability to share the high origination cost with a large number of products, microreplication is very promising from the commercial point of view. Microreplication is a suitable process for some of the applications listed in Table 1 but not for all of them.
At Fraunhofer ISE, we have picked up the idea of using periodic microstructures in solar energy applications at the beginning of the 1990s. Since then we have been working on the design and the manufacturing techniques for the following optical components: antireflective surfaces, light traps for PV cells, sun protection systems, and wavelength — selective radiation emitters. By using interference lithography we were able to originate microstructures on areas of up to 4800 cm2.
In Fig. 3 the trend of S varying with d is shown, for the two cases of copper wall (CW) and brick wall (BW). For d<0.045 m the flow is laminar with Reynolds numbers inferior to 2500; for d>0.060 m the flow is turbulent with Reynolds numbers superior to 3500: the laminar — turbulent transition zone is pointed out in dashed outline. In the case of turbulent flow the roughness value of the ventilation duct has been assumed to be equal to 0.005 m.
The brick outer slab turns out to be more convenient, from an energy point of view, than the copper one.
The following figures all refer to a ventilation duct being 0.04 m in thickness.
In Fig. 4 the trend of S varying with G for the two examined walls, CW and BW, is reported. Two values have been considered for the indoor air temperature: T=24°C and T=26°C. The percentage energy saving S distinctly increases as G and the indoor air temperature Ti rise. In Fig. 5 the trend of S varying with G is shown for the wall BW. The following values have been considered for the friction factors on the inlet and outlet sections: Xin=0.5 and Xou=1; Xin=1 and Xou=2; Xin=2 and Xou=4; Xin=4 and Xou=8. The graphs clearly show the convenience to reduce, as much as possible, the head losses occurring on the inlet and outlet sections.
Figure 3 — Variation of S with d (m) for the two walls CW (solid line) and BW (dashed line). The laminarturbulent transition zone is pointed out in dashed outline.
Figure 4 — Variation of S with G for two values of the indoor air temperature: Tj=24°C (solid line) and Ti=26°C (dashed line).
The trend of the mean heat flux Q coming into the room through the ASW varying with G is reported in Fig. 6, for the two examined walls, CW and BW. The two cases of T=24 and T=26 °C have been considered. The trend of the mean heat flux Q0 (obviously the same for the two walls) coming into the room when the ventilated duct is closed (dotted line) is also reported for comparison. The difference (Q0Q) and, therefore, the reduction in summer thermal loads, achievable by using a ventilated wall, increases as G and Ti rise.
In Fig. 7 the trend of Q varying with the solair temperature Te, for the wall BW, is reported for three values of the air temperature in the shade: T0=24°C, 26°C and 28°C. The trend of Q0 (dotted line) is reported for comparison. Obviously, it results that Q=Q0 for Te=T0 (without solar radiation). The ventilation convenience increases as Te rises as well as it increases, for a given value of Te, as T0 decreases.
The Fig. 8 refers to winter and the two examined walls. In this figure the trend of Q varying with G for two outdoor air temperatures in the shade is shown: T0=0°C and 7°C. The trend of Q0 (dotted line) is reported for comparison. Notice that, in this case, the wall showing less heat losses is the copper one; it happens as a consequence of the fact that the thermal resistance RB of the wall CW, with copper outer slab, is higher than the resistance RB of the wall BW, with brick outer slab (see Tab. 1). The graphs clearly show that, in winter, the ventilation always determines a rise in heat losses.
Conclusions
The ASW can meet, if well designed, the aesthetic and formal requirements of contemporary architecture, and also contribute to reduce energy consumption in buildings. The examined graphs clearly show that the use of ASW can determine a remarkable reduction in summer thermal loads; the duct is, obviously, required to be, as much as possible, free from any obstacle and the head losses to be reduced on the inlet and outlet sections for the abovestated reduction in summer thermal loads to occur. Hence the necessity of an accurate design of the inlet and outlet openings.
The energy saving achievable using the ASW distinctly increases as insulation increases; for a given value of the insulation and of the outdoor air temperature in the shade, the
reduction in the summer thermal load increases sensibly as the temperature provided for the indoor environment increases. In the examined situations the brickfaced wall (BW) has turned out to be more convenient than the copperfaced one (CW), from an energy point of view. In any case, it seems to be not convenient to consider air duct thicknesses inferior to 45 cm.
In winter, remarkable rises in heat losses can occur, leaving the duct open, especially connected with remarkable values of G. This leads to advise closing the duct in winter. But, considering that in winter the values of G are usually moderate, it would be advisable reducing the ventilation, e. g. with selfregulating dampers at the duct inlet and outlet sections, in order to drain the humidity due to possible infiltrations or condensation phenomena.
Acknoledgements
This research was supported by Italian Ministry of Education, University and Scientific Research (MIUR) and by University of Pisa within the National Relevant Interest Project (PRIN 20032005): "Energy and environmental diagnosis on existing buildings: research methodologies, determination of qualification parameters and technicoeconomic assessments”.
1.
The solar radiation daily variation corresponding to the typical clear days characterized by a sunshine fraction a > 0,9 and a nebulosity index Kd < 0,2 [18], The variation of temperature, pressure and the total are obtained by establishing a mass and a thermal balance of the volume elements of the porous medium discretised on equal thickness and to evaluate the equations of heat and mass transfer in each slices separately.
In each slice, the transfer of heat is obtained by applying the first principle of thermodynamic for an open system by taking into account the fractions corresponding to the adsorbed fluid, the gas and the solid:
d(^U) + ^ qs hs — ^ qe he = Ф + E (2)
Su = Vc [(1 — s)psUs + (є — a)pgUg + a paUa] (3)
The combined of equations (3) and (4), enable us to obtain the general equation of heat and mass transfer in a layer, equation (5), these equations are written in the case of :
— cylindrical elements:
rn 4 4 , idT P d[(sa)pg]
TOC o "15" h z [(1 S)pscs + (є — a)pgcg +apaca] —
dt pg St
d(apa) P d(apa) d2T 1 d)T
AHads (T, P) =2e ( +
dt pa dt dr2 r dr
These equations in the porous medium are completed by the initial and boundary conditions:
— Initial condition:
— T(r,0) = Ta ( r = 0,…, R ) (7)
— T(i, j,0) = Ta ( i = 1,., n ) and ( j = 1,., m ) (8)
Ta is the ambient temperature before the sunrise All the reactor is a constant temperature.
— Boundary conditions:
The boundary conditions to the center of the porous medium is a condition of symmetry;
(ffr) _ 0 , (ffr) _ (ffT) _ 0 (9)
(~&r ) r=°_0 (Ж) x=i, у — ~оу) x, y=i — 0 w
The thermal balance of the metallic wall is given by the following equations;
— Cylindrical tube without fins
pac VacCac — TvUacPsDe —UlDe(Tac—Ta) — hinDi(Tac — T) (10)
— Cylindrical tube with fins
Caofitc Vc— = Tv Oca Ps (De + 2 ШУ — U (Dev + 2 Qi)(TacTa ) — k 7t D, (Tac~T)
TOC o "15" h z dt 2
In this equation we take account the efficiency of the fins into consideration [19]
Q =tanh (m £) (19) and m = VUl/2acs (11)
m t
I is the wide of the fin
— Rectangular tube
Qj m
pac Vac Cac— = Tvaac Psu — Ul Sr (Tac ~ Ta) ~ 4 ^ hi AY (Tac ~ Tnj) —
» ‘ (12)
2 hi AY (Tac — Tnl) — 4 £ hi AX (Tac — Tim) — 2 hi AX (Tac — T 1m)
i
The obtained equations from a system of non linear differential equations that are solved by the implicit finite difference method [20].
The efficiency of the machine is characterized by the thermal coefficient of performance; COP and a solar performance coefficient COPs, deduced from the characteristic points of the obtained cycle using the following relations;
Tmax
Qc ^ mi Cpi dT + Qdes
Index i relates to ammonia, the activated carbon and the metal tube.
Qdes is the quantity of energy necessary to the desorption of the quantity Am [20];
5. Results:
The numerical simulation of the modelled reactor, under ambient temperature and solar radiation recorded in Tetouan, enable to describe aspects of heat and mass transfer inside the porous medium. The results gives the characteristic parameters of the functionning machine.
The numerical results obtained under real conditions of ambient temperature and solar irradiation relative to typical clear days of each season, allow the evaluation of the considered reactors performances from the cycle characterising points. The adsorption temperature is equal to the ambient one, the evaporation temperature is zero and the condensation temperature corresponds to the ambient temperature related with the beginning of ammonia desorption inside the condenser.
Figure 3 shows the variation of the thermal performance coefficient COP versus the normal and finned tubes diameter for the studied typical days. We observe that for each case there is a maximum value corresponding to a given tube diameter representing the optimum values.
Hence, under the applied functioning conditions the optimum COP value (diameter) are variable and depends strongly on solar radiation and on the ambient temperature. The same remarks are observed for the variation of the daily cycled mass versus the diameter figure 4a, considering a collector of a 1 m2 of surface composed a number of equal tubes. The total cycled mass corresponds to the sum of the desorbed quantities by each cylindrical tube. We note that the optimum values are higher for the rectangular reactors compared to the cylindrical ones figure 4b corresponding to the amount of the activated carbon used and thus to the offered volume to the reacting mixture.
The high values of the COP in April and October can be explained considering the fact that ammonia adsorption takes place before the sun rise in a uniform temperature porous medium, equal to the ambient temperature but less than that in July. So, the adsorption is very important, the choice of typical clear days characterised with high solar radiation allows to heat to the maximum values the reactors and thus the COP is a function of the considering temperature and that the maximum heating of the absorbent permits an important heat adsorption.
The variation of the maximum temperature at the center of the porous medium is a decreasing function of its width, it is had has the thermal conductivity of the porous medium and the thermal capacity of the whole of the reactor figure 5. We notice that the finned tubes improves the thermal exchanges between the metallic walls and the porous medium, consequently the maximum temperature attained is greater allowing an important desorption for the finned reactor with regard the same diameter normal tube, figure 5a. Figure 6 shows the evolution of temperature at the center of the porous medium versus the time for the three optimum widths reactors. For the cylindrical tube, we compare the temperature variation inside the tubes with a similarly diameter for the finned and normal reactor. The studied cycle begin the morning where all the reactor is at the ambient temperature and finish at midnight marking the start of a new cycle relatively to the temperature recorded at LT.
The rectangular reactor heating duration is higher, owing to the important volume of the fixed bed containing the mixture, than the cylindrical cases.
Figure 7 shows the pressure evolution inside the reactors versus time, causes by the temperature variation. The temperature elevation during the heating phase of the closed reactors causes an increases in the gas pressure until it becomes just larger than the condensation pressure which corresponds to the saturation pressure at the temperature condensation, then the desorption of ammonia into the condenser starts at a constant pressure and the heating of the fixed bed continues until the temperature reaching the maximum value. The reactors are closed and both temperature and pressure decrease.
At the pressure value of 4,2 bar the reactors are opened and the adsorption phenomena of ammonia vapour start with a cooling product quantity.
These evolution of temperature and pressure is represented in a Clapeyron diagrams, corresponding to the variation of Log P versus the temperature figure 8, and shows the daily thermodynamic cycle characterised by two isosters and two isobars representing four phases relatively to the heating or the cooling of the reactors.
In figure 9, we show the daily evolution of ammonia total mass, both adsorbed and gaseous, inside two cylindrical tubes having the same diameter in the two optimal cases. At the beginning the temperature is the same inside both of the tubes implying that their respective ammonia masses are also the same. During the heating of the closed reactor, condensation pressure inside the finned reactor is reached before the tube without fins, causing the opening of valve V1 and hence ammonia desorption. This desorption is important considering the temperature elevation and the values of 2,42 kg and 1,55 kg are collected for the unit area respectively for the normal and finned reactor.
Inside a 1m2 surface captor, 1 m long and 1 m wide, equals to the multiplication of the number of tubes by their external diameter. The total desorbed mass represents the sum of all the desorbed amounts in each tube. The non desorbed mass is the total fluid mass inside the reactor which the variation during a cycle is showed in figure 10.
We gives in table I the values of the computed amounts and those of the parameters under which the reactors functioning for the typical clear days of July, of which can be compared the three reactors. The obtained optimal geometry of each reactor presents an evaluation of the parameters that characterises the functioning conditions, the efficiency of the machine and the computed both provided and useful energy.
6. Conclusion
In this work, the aims is to present a model and an optimisation of solar adsorption cooling machine using ammonia / activated carbon couples, that allows a design according to the real functioning condition. The prediction of the performance of the solar refrigerator require the knowledge of various parameters, which characterise the daily thermodynamic cycle. The optimisation is based on heat and mass transfer in the porous medium consider the collected mass, the thermal and solar performance coefficient, allow to give an idea of the transitory evolution of temperature, pressure and ammonia concentration inside the reactors. The efficiency of each reactors are enhanced and the preferential adsorber depends on the desired role to generate (the useful cooling quantity).
A presentation of temperature and adsorption ammonia quantity inside the reactor that develop solar radiation is carried out in this paper. Thus, the simulation has been performed using some assumption will be applied to an experimental test.
Table II. Comparison of the operating parameters and results of each reactors

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Figure 4. Total daily condensed mass versus the tube dimensionless — January April July 0 October
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