Potentials of Industrial Solar Drying of Agricultural Produce

International Journal of Science and Technology Volume 3 No. 7, July, 2014

Potentials of Industrial Solar Drying of Agricultural Produce 1

Adeaga, Oyetunde Adeoye,2Dare, Ademola Adebukola 3Raji, Fatai Olasunkanmi 1Department

of Mechanical Engineering,The Polytechnic, IbadanAdeseun Ogundoyin, Campus, Eruwa 2Department of Mechanical Engineering,University of Ibadan 3Department of Mechanical Engineering,The Polytechnic, Ibadan (Main Campus)

ABSTRACT The applications of solar energy in all spheres of endeavours are now becoming more complex and demanding in developing nations of Africa like Nigeria. As such necessary analysis for the potentials of this renewable and sustainable energy source is essential. This paper focused on the potentials of solar drying for industrial purposes in three strategic locations in Nigeria (i.e. Ibadan, Kano and Port-harcourt).An editable data based software was developed using material balance equation and moisture content expression. Data of average sunshine and relative humidity were used to simulate 50,000kg (50 tonnes) of agricultural produce per month. The software (which was coded in Visual Basic Language )considers, the location of the site on the globe and a tilted flat plate solar collector using air as the collector fluid in a forced convection heat transfer system. The choice of fan depends on the mass flow rate of air required for the drying. With the economic analysis duration of 20 years for the three locations, a solar collector area of 85.46m 2 supplied about 67% of the annual energy needed for Ibadan, a collector area of 80.71m2 supplied about 88% of the annual energy needed for Kano while for Port Harcourt with collector area of 75.96m2 supplied about 55.8% of the annual solar energy needed. The make- up energy needed is expected to be supplied by auxiliary source. Keywords: Humidity, Produce, Convection, Software, Collector- Area, Auxiliary Source

1. INTRODUCTION Sun, the largest source of energy in the solar system has the potential and ability to supply all energy requirement of the earth. Solar energy is the most abundant energy source in the solar system. Despite the abundance of this energy, little use is being made of it in most part of the world. This could be attributed to the initial high cost of solar energy technologies. Although on a life cycle costing basis, it is generally competitive with other energy technologies where a level playing field is provided and environmental cost are considered. Solar system applications are found in different facet of life. These include space heating, water heating, industrial/domestic cooking, drying of agricultural products, solar cooling and photovoltaic generation of electricity. The energy from the sun reaching the earth’s atmosphere amounts to about 1.395k W/m2. This amount is only 1/1010 of the actual energy released by the sun. Out of this energy 23% are used as source of hydrological cycles and photosynthesis in plants, 47% are absorbed by the atmosphere, land and ocean and are converted to long wave radiation (terrestrial radiation) and 30% are reflected and scattered back into space [1] The use of solar dryers represents an alternative to the traditional open sun drying in developing countries. It satisfies several conditions such as fast processing, better quality of product, low energy demand and non-contaminating energy source. The main disadvantages of solar dryers are the limited time of solar radiation and the short season of harvesting of many agricultural products. It has been concluded that to meet

the increasing demands for food preservation in developing countries, simple, cheap but efficient solar dryers be developed where forced convection and supplementary heat are applied. [2] The proposed solar drying installation in this work is a coupling of solar collector, auxiliary energy source, and solar dryer of forced-convection type. The processes of mass and heat transfer in these units are simulated. The drying kinetics in a fixed-bed assumes a non-isothermal non-trace plug flow system with some basic variables. [7] One main reason for considering solar is due to its environmental friendliness, as it doesn’t give out any form of environmental pollution, like smoke which characterizes the conventional fossil fuel heater. It also runs smoothly (i.e. silently). This is because it has no mechanical moving part. And this also means that wear and tear in solar systems is relatively small, if not totally eliminated. [7]

2. MECHANICAL DRYING SYSTEMS In any commercial drying, a principal objective is to supply the required heat in the most efficient manner and optimum profit. Heat transfer may occur by convection, conduction or radiation or by any combination of these modes. Various types of industrial dryers differ fundamentally in the method used for transferring heat to the material. In general heat must flow first to the outer surface of the solid and later into the internal part. [10]

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International Journal of Science and Technology (IJST) – Volume 3 No. 7, July, 2014 2.1. Components of Solar Drying Systems

360 (n  81) 364 Where, n=day of the year 1  n  365 Where, B =

The principal components of a solar drying system are the following i.Solar Air Collectors ii.Drying unit iii.Air handling unit 2.2. Solar Collector They are used for heating the ambient air. There exist several designs of these solar air heaters. A typical design procedure is described. A solar collector is a special kind of heat exchanger that transforms solar radiant energy into heat. [6] The type of collector to be used in a particular application depends on the temperature at which energy is to be delivered, as well as the cost envisaged. The flat plate collector can be designed for applications requiring energy to be delivered at a moderate temperature up to 50oC above the ambient temperature. The sun can be said to have the effect of a continuous fusion reactor with its constituent gases as the ‘containing vessel’ which is held in place by gravitational forces. Several fusion reactions occur at the interior of the sun and the most important is a process in which hydrogen combines to form helium. When hydrogen (i.e. four protons) combines to form helium (i.e. one helium nucleus) the mass of helium nucleus is less than that of the four protons. The mass which is lost in the reaction is converted to solar radiation [2]

360n   Gsr  Sc 1  0.033 cos 365  

3.1

The extraterrestrial radiation also depends on geographic latitude, as well as the time of the day in the year and may also be determined from the following relationship [1]

Gs  Sc f x cos 0

3.2

In equation (3.1) Sc is of the value 1367W/m2 and n is the number of day of the year while in equation (3.2), S is of the value 1.353W/m2 and 0, is the zenith angle relative to the surface normal. Solar Time Solar time is based on apparent angular motion of the sun across the sky with solar noon being the time the sun crosses the observer’s meridian. Solar time is specified in sun angle relationship and it does not correspond to the local clock time. The expression below can be used to convert the standard time to solar time [2]. Where, Lst is the standard meridian for the local time zone Loc. is the longitude of the location in question in degrees west. E= 9.87 sin2B – 7.53 cos B – 1.5sin B

3.3

Direction of beam Radiation The geometric relationships between a plane of any particular orientation relative to the earth (whether fixed or moving) and the incoming beam solar radiation is described in terms of several angle and the relationship between them is as given below. [2]

Cos   sin  sin  cos  cos  cos cos cos  cos  cos sin  cos cos  cos sin  sin  sin  3.4 Where,

 , Latitude: The angular location north or south of equator, north positive,

 90   90

 , Solar declination: The angular position of the sun at solar noon with respect to the plane of equator, north positive,  23.45   23.45

 ,Slope: The angle between the plane surface in question and the horizontal.

 ,Surface azimuth angle: The deviation of projection on a horizontal plane of the normal to the surface from the local meridian with zero due south, east negative, west positive 180    180

 , Hour angle: The angular displacement of the sun east of west of the local meridian due to rotation of the earth on its axis at 15o per hour, morning negative, afternoon positive.

 , Angle of incidence: Angle between beam radiation on a surface and the normal to that surface. The solar declination,  , is given in the following expression [2]  

  23.45 sin 360

284  n 365

 

3.6

n = day of the year n = can be obtained from table Ratio of Beam Radiation on tilted surface to that on horizontal surface Monthly average of daily radiations incident on a horizontal surface are available for many locations. However, radiations on tilted surfaces are generally not available, but the following expression can be used to calculate the monthly average radiation. [3] IJST © 2013– IJST Publications UK. All rights reserved.

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International Journal of Science and Technology (IJST) – Volume 3 No. 7, July, 2014

HT  RH

Cos (   ) cos coss1

3.7







3.12

cos1 ( tan  tan  ),    min  1  cos ( tan (   ) tan   1 s

R , can be estimated from the expression below, [3]

 Hd  Hd 1  cos   / 2 R  1  Rb  H H     1  cos   / 2 3.8

The smaller parameter in magnitude inside the square bracket should be used for computation. The tilt factor is the ratio of the beam radiation flux falling on a tilted surface to that falling on a horizontal surface.

Where, H d is the monthly average daily diffuse radiation.

Rb , is the ratio of the monthly average beam radiation on the

Consider a tilted surface facing south i.e. angle)=0 [8]

tilted surface to that on a horizontal surface for each month.  ,is the ground reflectance, depending on snow cover,

 (surface azimuth

sin  sin (   )  cos cos cos (   ) cos rb   cos sin  sin   cos cos cos 4.1

0.2    0.7. 0.2 for no snow cover.

Hd in equation 3.8 can be calculated from the H

The ratio,



  180 s1 sin   sin  Rb  cos cos cos s   180 sin  sin 

Where, H is the monthly daily average radiation on a horizontal surface, R is the ratio of the monthly average daily radiation on a tilted surface to that on a horizontal surface for each month.

expression below [4] Where,

Hd =  0.3798  0.1838 K T 3.9 H = Monthly average daily total radiation KT  3.10  = Extraterrestial daily insolation =

= = z =

For the northern hemisphere [2]

Cos (   ) cos cos  1 s

Rb

 180 sin   sin   cos cos cos    180sin  sin  1 s

angle of declination angle between an incident beam of flux and the normal to be plane latitude the slope the hour angle surface azimuth angle angle of incident on the horizontal

3.11

s

Where s is the sunset hour angle for the tilted surface for the mean day of the month which is given by 1

cos1 ( tan  tan  ),    min  1  cos ( tan (   ) tan   1 s

Where ‘min’ means the smaller of the two items in the bracket And for southern hemisphere [2]

3. ENERGY OUTPUT OF A COLLECTOR The solar radiation, S absorbed by a collector of area Ac, is equal to the difference between incident solar radiation and the optical losses. Thus;

S  I b Rb ( ) b  1 cos    I  I  1b ( ) b g b d 2 1 cos   ( ) g 4.2 2 Where,

1 cos   / 2

= view factor from the collector to

the sky IJST © 2013– IJST Publications UK. All rights reserved.

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International Journal of Science and Technology (IJST) – Volume 3 No. 7, July, 2014

1 cos   / 2 = view factor from the collector to the ground. The thermal energy lost from the collector to the surrounding by conduction, convection and infrared ration can be represented by UL, times the difference between the mean absorber plate temperature. Tpm and the ambient temperature, T a. 3.1. Radiation Transmission through covers and Absorption by collector For a collector with N covers it has been shown that transmittance of radiation is given by [2]

Where  a = Transmittance of glazing when absorption loss is only considered Where  r= Transmittance of glazing when reflection loss in only considered If the diffuse radiation from the sky and ground are both isotropic, the transmittance of the glazing system can be found by integrating the beam transmittance over the appropriate incidence angles. The integration has been done and the following relationship for diffuse and reflected radiation angle produced. [2] For diffuse ground radiation the expression is

1  (1  rI ) (1  rII )   tN     2 1  2 N  1)rI  1  2 N  1)rII 

 c  90  0.5788  0.002693 2 4.3

3.1.1.

sin (2  1 ) sin 2 (2  1 )

4.4

tan 2 (   ) rII  2 2 1 tan (2  1 )

Transmittance absorbance product (  )

   1.01

4.5

respectively. In equation, 4.3 the subscript. r reminds that only reflective losses have only been considered. From Snell’s law, the refractive index, no of the collector cover can be expressed

1 and  2 as

Monthly Average Transmittance-Absorbance Product

 

This could be found in a manner analogous to equation 4.2 [3]

   

 / 

  H  R  1  d  b x H  R  

n

n1 sin  2  n2 sin 1

4.6



4.6

 sin  2   1  sin 1    n0 



4.7

 a will be Where,

given as [2]

For multiple glazing,

4.8

 a is evaluated

with L equal the total

glazing thickness. The subscript a, is a remainder when the absorption loss is only considered. The transmittance of the glazing is given by [2]

  ar

b n

      1  x x 1 cos s  / 2 x R  

 Hd 1 x 1  cos s  / 2 x H R 

d n t

n

If absorption loss is only considered, transmittance,

a  a  exp(KL / cos2 )

4.12

Where  , is the transmittance of the glazing system  , absorbtance of the collector plate.

Where, 1 and 2 are angle of incidence and refraction

no 

4.11

This is the product of the cover transmittance and the plate absorbtance. It is expressed mathematically as follows, [2]

2

in relationship to

For diffuse sky radiation

 c  59.68  0.1388  0.001497 2

Where, rI represents the perpendicular components of unpolarized radiation and rII is the parallel component. For smooth surface, Fresnel has shown that [2]

rI 

4.10

4.9

  ,   and   b

d

r

4.13 are the monthly average

values of the transmittance – absorptance product corresponding to beam, diffuse, and ground reflected radiation respectively. 3.1.2.

Flat plate collector energy balance equation

In steady state, the useful energy output of a collector is then the difference between the absorbed solar radiation and the thermal loss with collector heat removal factor [2] IJST © 2013– IJST Publications UK. All rights reserved.

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International Journal of Science and Technology (IJST) – Volume 3 No. 7, July, 2014





Qu  Ac FR S  U L Tp.m  Ta 

4.14



Where, Qu = Useful energy Ac = Area of Collector S = absorbed solar radiation FR= Collector heat removal factor UL= Coefficient of thermal heat loss Tpm = Mean plate temperature Ta= ambient temperature



1 0.089 h

w



4.15





mCp AcU L F1

4.17

U L  Ut  Ub  U c

4.18

1 UL

4.19 1

e=

0.43 1100 / Tpm 

 = collector tilt (degrees) g = emittance of glass (0.88)

p = emittance of plate Ta = ambient temperature (K) Tp.m= mean plate temperature (K) hw = wind heat transfer coefficient (w/m2C)

Tp.m  T f ,i 

1 1  h2 hr

For, 2 p. m



 Ta2 Tp.m  Ta 1 1  1 1 2

Tp.m [2]

Qu / Ac 1  FR  U L FR

4.22

Where, Tf,I = inlet air temperature The process to obtain Tp.m is basically iteration.

Where,

T hr 

2 for 0 0  b  70 o for 70 0    90 0. use   70 0

To obtain

 For the chosen configuration; [2]

h1 

 0.1166 hw p 



The collector mass flow rate is given as [2]

1

p

C  520 1 0.000051

mCp F F  R1  1  exp  ACU L F1 / mCp 4.16 1 F AcU L F

F1 

2 N  f  1  0.133 p  N

1 0.07866 N 

For collector flow factor,

Mc 

 0.00591Nhw 1 

N = Number of glass covers





p

4.21

mCp 1  exp  ACU L F1 / mCp AcU L

11



Where,

Where, collector that removal factor, FR is given as [2]

FR 

2  T pm  Ta  T pm  Ta2 



K [2] L

4.23

Where,

4.20 K = thermal conductivity of the insulator L = Length of the insulator Uc , is negligible for the chosen configuration More often than not, the choice of suitable solar air collector is one of the The significance of Ut, Ub, Uc which consequently give rise to UL is obvious in equation 4.12.

F1 = Collector efficiency factor U = total loss coefficient (W/m2C) UL=top/cover loss coefficient (W/m2C) Ub=back/base loss coefficient (W/m2C) Uc = edge loss coefficient (W/m2C)

       N 1 For, Ut     c hw   c   Tpm  Ta    T pm      N  f   

Ub 

1

If UL is largely considerable, the useful energy output of a collector, Qu reduced, hence a slower drying rate, reduced collector efficiency, waste of absorbed solar radiation and hence higher material cost.

Regardless of the type of fan, the fan is selected primarily on the basis of the quantity of air flow (mass flow rate) and the pressure against which the fan must work (static pressure). Other factors involved in the selection of the fan are ‘spare requirement, Installation cost, controls, flexibility in use and IJST © 2013– IJST Publications UK. All rights reserved.

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International Journal of Science and Technology (IJST) – Volume 3 No. 7, July, 2014 noise level. The fan can be powered by a solar P,V. (of appropriate rating) or solar panels, etc [6]

4. DESIGN CONSIDERATIONS In designing a Solar Cabinet dryer for agricultural purpose the following points are to be considered i.MR: Amount of moisture to be removed from a given quantity of crop to bring the moisture content to a required level in specified time.

M m  m  MR  1 o 1 100  m1 

4.28

Where M1 = initial mass of the drying sample m1 and mo = final and initial moisture content for storage on percent (%) wet basis respectively. i.DR: Total drying time, which is the daily sunshine hour for which drying will take place. Thus, average drying rate, DR is given as;

DR 

MR t

4.1.1.

Minimum spouting velocity, Ums

For any bed height, there exists a minimum flow rate below which the bed will not spout. It is called the minimum spouting velocity, Ums. A reasonably reliable empirical expression for estimating Ums especially for beds or diameter smaller than 0.5m is [10]

dp Ums  Dc 4.1.2.

 d 0  3  2 gh  p          Dc    1

1

2

4.30

Maximum spout height

The maximum height hms below which the spout remains just inside the bed is given by [10] 0.75

D  h  0.105DC  c   dp  4.1.3.

 Dc  0.4 1.2   2  p / 100  Do  s

Maximum Pressure drop

4.31

Pm

The air blower used in any spouted bed drying system must be 4.29

[8]

able to develop the maximum pressure drop, - Pm to be encountered during start up and is given by [10]

‘t’ is the total drying time required to remove, MR (kg) of water from the wet produce [8] i.Heat storage: This is necessary in case drying is to continue during off sunshine hours particularly in the night. Typical storage materials are rock pebbles [6] The auxiliary energy source: In case the total energy needed for drying cannot be met by solar energy only then the remaining fraction can be supplied by an auxiliary energy source, such as (i) oil fired method (ii) gas fired method (iii) electricity (iv) combustion e.g. coal etc or (v) Rock pebbles [6] 4.1. Design Procedures of a bed dryer (spouted) The complete design detail of a spouted bed dryer is not the major concern in this work and hence will not be treated to fullest. However, the basis equation for modeling a spouted bed dryer have been presented. A spouted bed dryer mainly consists of an air blowing systems, air heating system, solid feeding and discharging system, and the drying chamber. The possible design parameters of such a dryer are: a. Pressure drop b. Heating requirements for drying c. Solid feeding rate d. Dryer dimensions

Pm 6.8  hb g tan 

 d0  d     0.8  34.4  g  h  DC 

4.32

4.2. Materials/grain moisture content The thermal modeling of grain drying in a spouted bed is governed by [10]

dm D d  2 dm  r dt r 2 dr  dt 

4.33

Where the solution is given by

m  mcq  exp . 1  1.59 z1.3 mn  mcq



with,



z  6 / d p Dt1/ 2

4.34

4.35

Where, dp is the particle size (-3mm) [10] and t is the drying time in seconds. The equilibrium moisture content must also be determined. The diffusivity D is given by

D 1.01 x108 exp  14,160 / T 

4.36

The solid temperature, T is given by [10]

T  Tin  Tamb  / 2  273

IJST © 2013– IJST Publications UK. All rights reserved.

4.37 405

International Journal of Science and Technology (IJST) – Volume 3 No. 7, July, 2014 191kg per hour i.e. 0.191 tonnes per hour which is about 1.64 tonnes per day.

Where Tin is the dryer inlet temperature.

The specific drying rate is defined as the rate of moisture evaporation per unit mass of the bed is given by



dm D0  n2 2 X 2   24 2 mm  mcq  exp dt dp 9



4.38

The average overall specific drying rate, obtained from the relation [2] Where,

m 

dm dt

4.39

t= 17 min for T0 > 590C = 30 min for T0 0C Assuming that m is linearly dependent on the initial moisture content mm, temperature To, mass Mp, a statistical correlation can be developed in the following form;

m  ao  a1 min  a2T0  a3mp , It has recently been shown that

m is

4.40

independent of Mp.

Experimentally, the constant a0, a1 and a2 were determined and the final correlation for paddy becomes,

m  40.25min  0.09T0  10.43 x 10 5

For Port Harcourt location with the same 50,000kg produce the average sunshine hours per month is about 118 hours. Therefore the drying rate will be 424.3k per hour i.e. 0.42 tonne per hour which is about 1.624 tonnes per day.A close observation of the drying rate of Ibadan, Kano and Port Harcourt of 50 tonnes of the produce revealed close and neighbouring values. Hence, a better way is to fix the drying rate in kg/hr. and calculate the amount that can be dried in each location. However, the large difference between any industrial solar dryer located at Ibadan, Kano and Port Harcourt will be the initial investment cost of equipment (to include solar collectors unit area cost) and also the solar savings for a given period of time. The total cost which include, the installation cost, the equipment cost and the operating costs and maintenance cost at Ibadan and Port Harcourt will surely be on the high side when compared to that in Kano. Hence a relative advantage at locations with high average sunshine hours per day to those with lesser or lower average sunshine hours per day. Also affecting is the air flow rate required for drying, as it was revealed during simulation, that higher air flow rates, keeping other things constant, means increase in the annual solar fraction but for larger fan/blower and consequently cost of purchase. The simulation iteration stops when (i) The number of solar modules obtained can fully supply the energy needed for drying (ii) when the additional energy needed is less than 1/100 of the original energy supplied by the first solar module.

4.41 6. RECOMMENDATIONS 5. DISCUSSION AND RESULTS ANALYSIS Most agricultural produce exhibit about 25%-30% initial moisture content (wet-basis) before they are solar dried [6] When decreasing initial moisture content, i.e. 30%, 20%,10%,5%,3%(wet basis)were used in the simulation, the fraction of energy supplied by solar increased gradually. The collector area in m2, required consequently reduced, and hence a reduction in the overall solar dryer cost. The lower the initial moisture content, of the produce, the higher the energy supplied by solar, and the higher the fraction of energy supplied by solar. Consequently ,the lower the initial cost of the equipment set-up. For Ibadan location, with 50,000kg/month (50 tonnes per month) of agricultural produce the average sunshine hours per month is about 159.8 hours. Therefore the drying rate will be 313kg per hour i.e. 0.313 tonnes per hour which is about 1.643 tonnes per day.

Although the software performs the necessary calculation which is related to design, there is always room for improvement. One of the ways to maximize the use of the software is to have more locations with the required data. Also the material for lagging in the collector should be selected so that they are locally available and also affordable. Additional materials for construction could also be added to the database so as to have a wide variety for construction and choice in material selection. But this also means that the properties of these newly added materials will have to be available before they can be used with the software. The kinetics of moisture within the agricultural produce had not been dealt with. It is hereby recommended that this be carried out and put to test via simulation.

For Kano location, with the same 50,000kg (50 tonnes) per month of agricultural produce, the average sunshine hours per month is about 261.7hours. Therefore the drying rate will be IJST © 2013– IJST Publications UK. All rights reserved.

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7. CONCLUSION With careful selection of material and data in the simulation software both manufacturer and users will be able to predict the performance and cost of solar drying equipment for greater efficiency, cost effectiveness and performance prediction.

REFERENCES [1] Incropera, F.P.,DeWitt D.P. ‘ Fundamentals of Heat and Mass Transfer’. (1980) John Willey & Sons Inc.pp 102-335 [2] Duffie, J.A., Beckman W.A. ‘Solar Engineering of Thermal process’(1980) John Willey & Sons Inc.pp 147-168 [3] Fagbenle R.O. ‘Estimation of Diffuse Solar Radiation in Ibadan, Nigeria’. International Journal of Solar Energy. (1993), Vol. 13 pp. 145-153 [4] Fagbenle R.O..‘ Estimation of Total Solar Radiation in Nigeria Using Meteorological Data’.

(1990).Nigeria Journal of Renewable Energy. Vol. 1 pp 1-8 [5] Fagbenle R.O. ‘On Monthly Average Daily Extraterrestrial Solar Radiation for Nigeria Latitudes’ (1991) Nigeria Journal of Renewable Energy. Vol 2, No. 1, pp. 1-8 [6] Herick Otherno:‘Design factors of small scale thermosyphon solar crop dryers’(1991) [7] Lasode Journal of Applied Science, Engineering and Technology Vol. 4: No. 2 pp. 32-43. [8] Beckam, W.A. et-al Solar Heating Design by f-chart method. Willey interscience(1977) Publication [9] M.S. Soha, Ram Chandra ‘Solar Drying system and their testing procedures Review Energy convers. Mgmt’(1994) vol. 35, No. 3 pp. 219-267 [10] Sadhu Singh ‘Mechanical Engineers’ (2003) handbook. Khanna Publishers.ISBN:81-7409-074-6 pp. 727-729

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NOMENCLATURES SC=Solar Constant Gso=Extraterrestrial Solar radiation

z =Zenit angle

m =Air Mass Lst=Standard meridian for the local time zone Loc=Longitude of the location in question in degrees west n=Day of the year =Latitude  =Solar declination  =Collector tilt angle  =Surface azimuth angle  =hour angle

 =Beam angle

Hr=Monthly daily average radiation on a tilted surface H=Monthly daily average radiation on a horizontal surface R=Ratio of the monthly average beam radiation on the tilted surface Hd=Monthly average daily diffuse ratio Rb=Ratio of the monthly average beam radiation on the tilted surface  =Ground reflectance KT=Ratio of Monthly average daily total radiation to Extraterrestrial daily insolation  s=Sunset hour angle for horizontal surface  1s=Sunset hour angle for tilted surfaces Qu=Useful energy Ac=Collector Plate area S=Absorbed solar radiation U=Coefficient of thermal heat losses Tpm=Mean plate Temperature Ta=Ambient Temperature r1=Perpendicular Components of unpolarized radiation r11=parallel component of unpolarised radiation  =Angle of refraction  2=Angle of reflection ng=Refractive index of glass

 a =Transmittance

of glazing when absorption loss is only

considered  r =Transmittance of glazing when reflection loss is only considered K=material extinction coefficient (  )=Transmittance-absorbance product  =Absorbance of collector plate (  )=Monthly average transmittance-absorbance product UL=Total loss coefficient Ut=Top loss coefficient Ub=Back loss coefficient Ue=Edge loss coefficient

g

=Glazing emittance

 p=Plate emittance h  =Wind heat transfer coefficient X=Back insulation thickness k=insulator thermal conductivity QU=Total useful solar energy delivered during the month E=Total auxiliary energy needed during the month U =Energy change in the storage unit FR=Collector heat exchanger efficiency factor t =Total number of seconds in the month Tmf=Reference temperature empirically determined to be 100oC n=Number of days in the month FR=Collector heat removal factor Cr=Fluid specific heat capacity  =Effectiveness of heat exchanger m=Fluid mass flow rate Ts =Critical/safe drying temperature Fu=Collector flow factor Ums=Minimum spouting velocity Dr=Drying Rate hms=Maximum spout height Pm =Maximum pressure drop

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SAMPLE SIMULATION RESULTS FOR IBADAN, NIGERIA

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SAMPLE SIMULATION RESULTS FOR KANO NIGERIA

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SAMPLE SIMULATIONS FOR PORT HARCOURT, NIGERIA

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