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In this article, we present the study of a double-pass air insulated by crushed millet stem mixed with gum arabic. The study is carried out based on mathematical models obtained by writing energy conservation laws in the various components of the system, which made it possible to determine the evolution of the air temperature as a function of the length of the absorber and to make a comparison with the experimental results. After comparing the results obtained with those found in the literature, the influence of some physical and geometrical parameters on the performance of the solar thermal collector is presented.

Plan solar air collectors convert solar energy into thermal energy extracted from the air into flow in the solar collector [

To produce solar thermal energy, several types of flat solar collectors are designed for different performances [

The solar radiation captured has an impact on the efficiency of the solar collector [

The solar collector glazing shall have characteristics enabling it to optimize the energy transmitted to the absorber by the greenhouse effect [

The orientation of a collector has an influence on the solar radiation received by its surface [

The location of obstacles in the various channels of the solar collector influences its efficiency [^{2} [

The porosity of the fluid influences the temperature increase according to the mass flow rate [

To do this, a mathematical model based on the solar collector thermal balance method is studied. The results of the numerical simulations were used to evaluate the temperature profiles of each solar collector layer (glass, absorber, fluid and insulating plate). In order to validate the theoretical results, numerical results obtained with Comsol code are used to compare the evolution of the thermo-physical parameters of the fluid in the solar collector. The comparative analysis of the theoretical and experimental results of the double-pass solar thermal collector has enabled the model to be validated.

The solar thermal collector studied is shown schematically in ^{2} and a thickness of 0.005 m [_{f1} = 0.045 m on the outward flow and e_{f2} = 0.070 m on the return flow) connecting the inlet to the outl et al. lows air to be guided by forced convection through a fan placed at the outlet from which a drawn flow is drawn as shown in

Measurement campaigns were carried out at the Polytechnic High School of Dakar in natural sunshine during the months of April and May, obtained by a pyranometer on the solar collector facing south and inclined at 15˚.

The air at the solar collector inlet is at room temperature with fixed air flow rates measured with the anemometer. Daytime system performance is subject to outdoor conditions (solar radiation temperature). The measurements are made with a data acquisition (Agilent 34970A) equipped with two multiplexers, comprising 19 thermocouples for the first 34901A and 17 connections for the second 34908A. The Agilent data acquisition is placed underneath the solar collector with the computer. A potentiometer is used to adjust the fan speed which is proportional to the flow rate.

The model is based on the following assumptions:

• The external and internal convective heat transfer coefficients are constant over the length of the solar collector.

• The thermal conduction is neglected

• The pressure losses are neglected in the side walls and at the bottom of the solar collector.

• All surfaces of the different components are equal

Under the above-mentioned hypothesis, the heat balance equation of each component of the solar collector are.

Glass

( ρ C p e ) v ∂ T v ∂ t + h w ⋅ ( T v − T a ) − h c , v − f ⋅ ( T f 1 − T v ) + σ ⋅ ε v ⋅ ( T v 4 − T c 4 ) − α v ⋅ G − σ 1 − ε a b ε a b + 1 F v − a b + 1 − ε v ε v ( T a b 4 − T v 4 ) = 0 (1)

Fluid (f1)

( ρ C p e ) f 1 ( ∂ T f 1 ∂ t + V f ⋅ ∂ T f 1 ∂ x ) + h c , v − f ⋅ ( T v − T f 1 ) − h c , a b − f ⋅ ( T f 1 − T a b ) = 0 (2)

Absorber

( ρ ⋅ C p ⋅ e ) a b ∂ T a b ∂ t + h c , v f 1 − a b ⋅ ( T a b − T f 1 ) + σ ⋅ F a b − v ( T a b 4 − T v 4 ) − α a b ⋅ τ v ⋅ G ( t ) − h c , f − a b ⋅ ( T f 2 − T a b ) − σ ⋅ F a b − p ( T p 4 − T a b 4 ) = 0 (3)

Fluid (f2)

As the heat transfer fluid underneath the absorber exchanges with the plate (p) and the absorber (ab) by convection, then we have

( ρ C p e ) f 2 { ∂ T f 2 ∂ t + V ′ f ⋅ ∂ T f 2 ∂ x } + h c , a b − f ⋅ ( T f 2 − T a b ) − h c , p − f ⋅ ( T p − T f 2 ) = 0 (4)

Insulation plate

( ρ C p e ) p ∂ T p ∂ t + h c , p − f ⋅ ( T p − T f 2 ) + σ ⋅ F p − a b [ T p 4 − T a b 4 ] − h a r r i ⋅ ( T a − T p ) = 0 (5)

The modeling of the solar collector is based on a nodal discretization showing 5 knots.

The system of equations presented in section 4 is based on a good knowledge of the heat transfer coefficients to take into account the heat exchanges, by conduction, convection and radiation, between the different components of the solar collector.

Heat transfer between celestial vault and glass

h h r , v − c = σ ε v ( T c + T v ) ( T c 2 + T v 2 ) (6)

T c = ( T a − 6 ) (7)

Others use:

T c = 0.0552 ( T a ) 1.5 (8)

In our calculations, we will adapt this last expression for the calculation of T_{c}.

The heat transfer between the ambient environment and the glass is given by Mac Adams’ formula:

h w = 5.7 + 3.8 ⋅ V w (9)

Radiation heat transfer:

h r , v − a b = σ 1 − ε a b ε a b + 1 F a b − v + 1 − ε v ε v ( T a b + T v ) ( T a b 2 + T v 2 ) (10)

Heat transfer between fluid 1 and glass:

h c , v f 1 = 0.332 λ D R e 0.5 P r 0.33 (11)

where: R e = ρ V D μ , P r = μ ρ α for fluid 1 (12)

Heat transfer between fluid 1 and absorber:

The heat transfer coefficient between glass and fluid (f1) is assumed to be equal to heat transfer coefficient between the absorber and fluid (f1). Both plates are covered by the same fluid with the same fluid velocity and the glass and absorber have the same length.

The convective and radiative heat transfer coefficients of fluid f1 were used for return fluid f2.

The properties of the individual solar collector components are given in

- | Specific heat (kJ/kg∙K) | Thermal conductivity (W∙m^{−1}∙K^{−1}) | Density (kg∙m^{−3}) | Absorption coefficient |
---|---|---|---|---|

Glass | 840 | 0.0263 | 1375 | 0.05 |

Absorber | 398 | 384 | 8900 | 0.95 |

Insulating | 794.76 | 0.12 | 435 | - |

The system is modeled by Comsol multiphysics 3.5 code taking into account the couplings of conductive, convective and radiative heat transfers between the fluid flow and the solid components of the solar collector.

The influence of the grid number on the temperature is presented in _{max} = 800 W/m^{2}, a = 0.9, air ρ = 1.2 kg/m^{3}, C_{p} = 1.006 J/(kg∙K) and μ = 10^{−5} Pa∙s and physical properties presented in

N | Tmax | Tmin |
---|---|---|

295 | 568,342 | 271,659 |

1180 | 577,419 | 271,769 |

4720 | 579,712 | 271,769 |

18880 | 579,807 | 273,15 |

75520 | 579,74 | 273,15 |

Thus for Comsol the elements were defined with a number of degrees of freedom of 123,928, a number of mesh points equal to 9613, a number of meshelements corresponding to 18880 essentially composed of triangular meshes, with 848 delimiting elements for 12 vertices. The minimum quality of the elements is 0.652 for an element area ratio of 0.275.

The variation in mesh size has a slight influence on temperatures for numbers of elements ranging from 295 to 4720, although not optimal. It becomes regular from a number of elements equal to 18,880, which was chosen for its comparison with the thermal performance of the solar collector under working conditions (

The system of Equations (2) to (6) is discretized by finite differences method and then solved using Gauss-Seidel’s iterative method.

• Air temperature evolution in the solar collector

For a fixed flow rate of 0.023 kg/s, inlet air temperature of 298 K and solar heat flux ranging from 600 to 900 W/m^{2}, _{f1} and lower channel T_{f2} at 9 h, 11 h and 14 h. The maximum of air temperature flowing through the solar air collector, went respectively to 308 K, 325 K and 329 K (59 C maximum temperature). There is a temperature difference of 31C between the inlet temperature and the outlet temperature at 2 pm due to the temperature gradient of interest in the flow.

The air enters the second channel with the outlet temperature of T_{f1}. Thus the lower air temperature through the solar collector at the return flow went respectively up to 320 K (47 C), 338 K (65 C) and 341 K (68 C) output temperature. A temperature difference of 17 C is less important than in the first channel and remains relatively constant when the thermal equilibrium is reached (from 70 cm onwards).

• Influence of mass flow rate

For a solar heat flux of 900 W/m^{2} at 14 h,

length of time, more or less long, that the fluid stays in the solar collector, which causes more exchange between walls and air.

• Comparison of numerical results

For a flow rate of 0.023 kg/s and solar heat flux of 900 W/m^{2}, the analysis of the obtained results shows a small difference of 7C between the two models (

(Comsol) is more complete because it is based on the conservation equations of mass, momentum and energy, and associated boundary conditions. This enabled us to validate the global model.

^{2} and 900 W/m^{2} at 9 h and 14 h respectively, we note that the pace of the experimental curves is relatively equal to that of the theoretical curves. At 9 o’clock, the experimental and numerical curves have the same output temperature 320 K (47 C) and 14 o’clock respectively 335 K (62 C) and 341 K (63 C) with a deviation of 6 C. This difference can be explained by the thermal pressure losses of the solar collector in the experiment.

The collector efficiency is defined as the ratio of the effective power ϕ u extracted from the collector to the incident solar flux G. The effective power is evaluated using enthalpy balance.

η = ϕ u G S (13)

with ϕ u = С p q m ( T o − T i ) (14)

T_{i} is the inlet temperature of the fluid f1 and T_{o} is the outlet temperature of fluid f2.

^{2}.

We note, that at this flow rate and maximum irradiation, that the optimal efficiency is 80% for a double-pass single-glazed air solar collector with crushed millet rod as insulator.

In this work, we have proposed a numerical and experimental study of a double air-pass solar collector with the objective of producing hot air to supply and improve drying techniques.

For this, we realized a double pass air solar collector and developed a global model and a numerical code to simulate and follow its thermal behavior. The solar collector is insulated thermally by a local material composed of easily accessible crushed millet stem.

The influences of masse flow rate on the air transient temperature response are presented along the solar collector at different instants and solar heat fluxes.

A good agreement between calculated and measured temperatures is observed in the pm of the day while in the am. The results show a significant difference due to the lateral thermal losses and also of the thermal inertia of the insulation material of the solar collector that are not taken into account in our global model.

Further investigations are in progress with the COMSOL code, which offers the possibility of taking into account the three-dimensional effects and the nature of the materials used in the experimental setup.

Ndiaye, M.M.D., Diallo, B., Abboudi, S. and Azilinon, D. (2018) Theoretical and Experimental Study of a Double Air-Pass Solar Thermal Collector with an Insulating Rod of Millet. Energy and Power Engineering, 10, 106-119. https://doi.org/10.4236/epe.2018.103008

C_{p}: specific heat (kJ/kg∙K).

D: hydraulic diameter

S: surface

e: thickness of the fluid channel (m)

F: shape factor

G: solar heat flux

h_{c}: convective heat transfer coefficient (W/m^{2}∙K)

h_{r}: radiative heat transfer coefficient (W/m^{2}∙K)

Nu: Nusselt number

Pr: Prandtl number

q_{m}: mass flow rate of the fluid (kg/s)

Re: Reynolds number.

T: temperature (K).

V: fluid velocity (m/s).

a: absorption coefficient/diffusivity

τ: transmission coefficient

ρ: density (kg/m^{3}).

σ: Stephan Boltzmann constant (σ = 5.673 × 10^{−8} W∙m^{−2}∙K^{−4})

e: emissivity coefficient

λ: thermal conductivity

h: thermal efficiency.

ϕ u : effective power

a: ambient

ab: absorber

v: glass

p: plate

f1: fluid 1

f2: fluid 2

win: wind

c: celestial vault

i-j: between medium i (=a, v, ab, p, f1, f2) and medium j (=a, v, ab, p, f1, f2)

i: input

o: output