# Solar Thermal Heat Utilization

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```					Solar Thermal Heat Utilization

Definitions
• Absorption: A body’s capacity to absorb radiation is called absorption capacity or absorption α. • Absorptivity: ratio of the radiation absorbed to incident radiation

• Emission ε : represents the power radiated by a body. (Emissivity) The relationship between α and ε is defined by Kirchhoff's Law
At thermal equilibrium, the emissivity of a body (or surface) equals its absorptivity.
Hence

A good absorber is a good emitter

Definitions
• Reflection coefficient ρ : ratio of the light reflected to the incident radiation • Transmission coefficient τ : ratio of the light transmitted to the incident radiation.
For a given material the sum

α +ρ +τ = 1 (100%)

Perfect absorber : α= 100%, no reflection, no transmission

An ideal absorber
For solar energy applications, we want most the radiation to be absorbed but very small emission i.e.

α

1

and

ε

0

An ideal absorber absorbs all the short wave solar radiation and does not reflect in this range (ρ =0 in this range )

For long wavelength region (IR region) : it reflects all ( no absorption) and hence has very low emittance ( Kirchhoff’s law)

Selective absorbers
• Ordinary absorber surface ( e.g. ) black paint have high absorption but equally high IR (thermal) emittance • Selective surfaces have high absorptivity in the visible and NIR range but high reflection coefficient ( and hence low emittance) in the IR range

absorption

ideal
Real selective absorber
reflection

Solar Collectors

Main parts of a liquid-type collector
1. Absorber 2. Transparent cover 3. Frame 4. Heat insulation

Different types of collectors

Flat plate collectors
In a steady state condition The rate of energy absorbed by per unit area of the absorber plate = rate of useful energy transferred to the fluid + the rate of thermal energy lost per unit area

   qab  qL  qu

Where

 qab (W / m )  ( 0 0 )G (t ),
2

TP= Absorber plate temp Ta = Air temperature

 qL  U L (Tp  Ta )
We can then write

UL = Heat transfer coefficient
α0 = Absorptivity of the absorber τ0 = Transmittivity of the glass cover

 qu  (0 0 )G(t )  U L (Tp  Ta )
The value of α0 τ0 depends on the angle of incidence. The above equation is true only for a flat absorber

We write

 qu  F  (0 0 )I (t ) U L (Tf T a)





Where F’ is the collector efficiency factor and is defined as : the ratio of actual useful heat collection rate to the useful heat collection rate when the collector absorbing plate temperature (T p) is at the local fluid temperate (T f). F´ is between 0.90 and 0.95
If Ac is the collector area , then the useful energy from one collector

 Qu  F Ac (0 0 )G(t )  U L (Tf  Ta )
For N collectors in parallel , above equation becomes





 Qu N  F NAc [(0 0 )G(t )  U L (Tf  Ta )]
These equations are applied only to natural circulation ( thermosyphon) flow of fluids through pipes.
If the collectors are connected in series

 Qu N  FRN NAc (0 0 )G(t ) U L (Tf T a)





Where FRN is the collector heat removal factor given by
1  (1  k N ) N  FRN  FR   Nk N   where kN   mC f Ac FRU L  and  FR   mc f AcU L   A U F   1  exp  c L    mC   f     

m˙ ( kg/s) and Cf are the mass flow rate and the specific heat of the fluid. The outlet fluid temperature is given by
T foN  NAcU L F     NAcU L F     0 0 I (t )      Ta 1  exp   T fi exp     U    mC f   mC f    L       

(Tfi= input fluid temp.)

collector  area 

Energy  demand ( solar  energy  per  m 2 )  (collector  efficiency )

Collector optimum tilt = Latitude ± 150

Solar Water Heaters
A domestic solar water heater has following components
1. The solar collector

2. An insulated storage tank 3. Pipes and fittings
Water can be circulated using 2 methods

1. Passive system : No external pump- water is circulated using thermosyphon –warm water rises up (fig 1) .Mainly in hot climates 2. Active system: A pump forces the hot water up into the tank.

Thermosyphon mode

The energy balance equation is

dTw F NAc  0 0G(t )  U L (Tw  Ta )  M wCw  (UA)t (Tw  Ta ) dt
Tw= Tfi We assume there is no withdrawal of hot water.

We can write the above equation as

dTw  aTw  f (t ) dt
where
a and f (t )  F NAc  0 0G (t )  UA t  F NAcU L  M wC w (UA ) t  F NAcU L M wC w

Equation (A

Taking t 0= 0, a = constant , average value of f(t) between t=0 and t also Tw(t=0) =Tw0

The solution of eq. (A) is

f av (t ) Tw  (1  e  at )  Tw0 e  at a and f av (t )   T  1  w a  t   ln  f av (t )  a T   w0 a  
The overall thermal efficiency is given by

Water temp at time t



M wCw Tw( at t )  Tw0 ACN  G (t )dt
0 t





Thermosyphon flow
Á closed vertical loop filled with fluid
b

At section aá
‘
b b

b a

 gdz 
a ( left )

 gdz  0
a ( right )

Left column of fluid is exerting a greater pressure at aa’than the right column, The fluid moves Where the integral is over the closed loop, dz is the vertical increment

The driving pressure is
Cold Hot

dense
a

Less dense

pth   0 gdz

We can write the above equation as

pth  gH th
Here Hth (called the Thermosyphon Head ) =

 ( / 

0

 1)dz

Hth is the energy gain per unit weight of the fluid.
The energy gain is lost by fluid in overcoming the pipe friction represented by the Friction head Hf

We define the expansion coefficient β as

  1 /  d / dt
And then , the Thermosyphon Head

H th  IT    (T  T0 )dz
Where T0 is a reference temperature. Flow is in the direction for which IT is positive.
Lu 2 2( 16 ) uD Dg

Where u= flow speed, D=diameter of pipe, L=length of pipe, v= kinematic viscosity

Efficiency of a collector
The amount of heat energy collected i.e. the energy gain is given by

Qu  Qa  QL  G  U L (Tp  Ta )
Tp = plate temperature , Ta = ambient temperature

Then, the collector efficiency is given by

U L (Tp  Ta ) Qu     G G

We substitute Tp by the average water temperature T f , then

Where F’ is called the absorber efficiency

U L (T f  Ta     F    G  

Experimental determination of η
The efficiency is given by
η = heat transferred by water per second / irradiance in the plane of the collector Or

mc (Tout  Tin )  Gc Ac

Where
m= mass flow rate (kg/s) = ρAv/2 C= specific heat of water (V is the centre line velocity)

Gc = irradiance in the plane of the collector Ac = projected area of the collector A= cross-sectional area of the tube where the line velocity is measured.

Selective Coatings : Transparent Conductors
Transparent conductors also known as Heat Mirrors are optical coatings that transmit the visible part of the solar radiation ( 0.4 < λ< 0.7 μm) and reflect the near infra red part ( 0.7 <λ< 3 μm). The other property of these materials is their high electrical conductivity. There are mainly two types of transparent conducting (TC) coatings i) Metal films: Thin metal films can transmit about 50% of the visible light and reflect near infra red radiation. In practice, a metal film such as Ag is sandwiched between two dielectric films (e.g. ZnS, Bi2O3, TiO2 etc.). This combination can yield a visible transmittance of about 80%.

ii) Highly doped wide band gap semiconductors Wide band gap semiconductors viz. SnO 2, ZnO transmit visible light due to their high band gap. The optical and electrical properties of these semiconductors can be controlled by suitable doping. The optical properties i.e. transmission ,reflection and absorption of electromagnetic radiation are strongly affected by the concentration of free charge carriers in the semiconductors. With suitable doping a wide band gap semiconductor can be made conducting and behave as heat mirrors. These coatings can be used to produce energy efficient windows. The solar spectrum consists of IR part which leads to heating. In warmer climates, this unwanted radiation enters the buildings through windows and air-conditioning is required to bring the temperatures to a comfortable level. Now, if we coat the outer side of the windows with a heat mirror coating ,we can cut the heat entering the building without cutting on the visible light. In colder climates ,heat mirrors can be applied to the inner side of the windows thus trapping the heat inside.

Applied to the inner side of the glass cover of a solar collector, they trap the IR radiation thus, reducing the losses,

Heat Mirrors

Visible region High transmission

IR region High reflection

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 views: 174 posted: 11/10/2009 language: English pages: 21