Figure STYLEREF 3 s 2

Figure STYLEREF 3 s 2.7 Indirect Solar DryingSolar Radiation Intensity
The knowledge of supply availability is necessary whenever solar energy is required to be utilised for engineering purposes. The frequency of occurrence and solar radiation intensity knowledge is vital and helpful when designing the solar collector for drying maize.

Solar constant
The solar constant is the amount of thermal radiation which is received from the sun per unit time per unit area on a surface perpendicular to the sun’s rays and it is measured at a mean distance from the earth’s surface. Several research works came with different values of the solar constant. The value of the solar constant is approximately 1367 watts per square metre.

Solar radiation at the earth’s surface
Solar radiation depletes as it passes through the earth’s atmosphere due to scattering and absorption of molecules caused by not only air molecules, but also caused by dust, water vapour ozone. The selective properties various atmospheric elements cause a difference in the transmission of solar radiation at different portions of the solar spectrum. Ashrae in 2007 gave a spectrum distribution of direct solar radiation which is shown in Table XXXX below;
Spectral region Wavelength range Percent of
Spectral region (microns) Percent of
Spectral region (microns) total energy
ultraviolet 0.29 to 0.40 9.0
visible 0.40 to 0.70 38.0
infrared 0.70 to 3.50 53.0
Dust and air molecules scatter shortwave radiation which makes it reaches the surface of the earth in form of separated radiation while ozone absorbs most of it in the upper atmosphere. The incident solar radiation that reach the surface of the earth is the sum of direct incident solar radiation and diffuse solar radiation. It is noted that the value varies widely depending on the amount of dust and moisture in the atmosphere. The general relationship is given by
It = ID + Idwhere
It=total incident solar radiation at the earth’s surface, Wm2ID=direct incident solar radiation, Wm2Id=diffuse solar radiation, Wm2The solar radiation intensity was studied to affected by season, latitude, altitude, degree of cloudiness and orientation of receiving surface for different localities in the world (Becker and Boyd (1957). A similar study was also done by Buelow (1967) wherein he developed equations predicting the quantity of solar energy’ falling on a surface on earth when latitude, time of year, slope and orientation of surface are known. His results were tabulated for a latitude range of 0 to 60 degrees north and for six surface orientations and configurations. Threlkeld and Jordan studied that the direct normal radiation at the earth’s surface on a clear day IDN , is represented by:
IDN=Aexp (BsinB)Wm2where
A = apparent solar radiation at air mass =0, Wm2B = atmospheric extinction coefficient, dimensionless
? = solar altitude angle, degrees
The values of A and B vary during the year and are given in Appendix A. Solar altitude angle, ? , may be obtained from the relationship
sin? = cos L cos ? cos ?+ sin L sin?where
L = latitude angle of location, degrees
? = declination angle at the date in question, degrees
? = absolute value of solar hour angle measured from solar noon, degrees
The World Atlas gives the latitude angle of a locality, L. The solar declination, ? , is derived from an approximate equation given by
? = 23.45 sin (360284+n635)where n is the day of the year. The hour angle, w, is obtained from the relationship
? = 15 X (number of hours from solar noon)Now the direct incident solar radiation, ID , that falls on the earth’s surface is given as
ID = IDN× cos? Wm2where ? is the angle of solar incidence on the surface, in degrees, and is obtained by the equationcos ? = cos ? cos ? sin ? + sin ? cos ?where
? = surface tilt angle from the horizontal, degrees
? = surface-solar azimuth, degrees
Surface-solar azimuth, ?, is equal to the solar azimuth, ? for all south-facing surfaces and is obtained from
sin ?=cos?sin?cos?Diffuse solar radiation
The range of diffuse radiation component, ID , is from 15 percent on clear days to 100 percent on completely overcast days. There is a challenge in predicting the intensity of diffuse solar radiation due to wide variations in day-to-day atmospheric conditions. A generalized relationship of the diffuse solar radiation falling on the surface is given by ID=CIDNFSS Wm2 where
C = diffuse radiation factor, dimensionless
FSS= angle factor, dimensionless
Appendix C gives a value for the constant C whilst the angle factor, FSS, from the relationship
FSS=1+cos?2Solar Heat Collectors
General description
A solar heat collector comprises of a surface that absorbs solar energy which is then transmitted to a working fluid in form of heat energy. The surface absorber is usually painted black to efficiently absorb much solar energy. Collected energy is transported to whatever that needs to be heated by circulating air between the collecting surface and absorber plate. Solar heat collectors are classified according to the insulation type, solar radiation concentration degree, and the nature of orientation. One or more transparent cover plates are used to reduce the heat losses from the collector in any direction usually the upward losses. The materials used for making the cover plate are glass, plexiglass and clear plastic because they can transmit short-wavelength solar radiation but can allow little long-wave radiation to pass through. Insulation materials like glass wool, materials wool and wood are used to reduce heat losses from the back of the collector.
Some solar collectors are designed with or without the concentration of solar radiation. The absorptance of the collecting surface can be increased by use of selective surfaces. This consist of the use of selective paint coatings with proper configurations such as corrugations and V-shaped grooves on the collecting surface. Focusing type collectors are also used to increase solar radiation intensity. They utilize optical systems that concentrate a given amount of solar radiation on a smaller collector area. These types of collectors’ best suit where there is need of high-temperature and specialized applications like the generation of steam. The solar collectors are oriented such that they are stationary and horizontal, stationary but tilted toward the sun on an east-west axis, mounted on an east-west axis to follow the sun’s seasonal motion, mounted on the north-south axis to follow the diurnal motion of the sun, mounted on both equatorial and transverse axes to fully-track the sun and maintain the collector normal to the sun’s rays at all times. Solar collectors are also classified as passive or active solar collection systems, and as free standing or attached as an integral part of a building roof or wall structure.

Flat-plate solar collectors
The flat-plate solar collector as the simplest and basic type and is usually used to collect thermal energy at low to medium temperatures. Solar heating is usually employed for temperatures below 65° C and flat-plate type collectors best suit this application. Figure XXXX below shows the conventional flat-plate collectors for air heating. Bare-plate collectors consist of air being drawn between the absorber plate and an insulated black plate to reduce heat loss. Covered plate collectors consist of air being drawn from one or both sides of the absorber plate.
Schematic diagrams of conventional flat-plate solar collectors for air heating
The flat-plate solar collector performance resulted in researchers developing empirical equations describing performance of various types of solar collecting devices. The main objectives of the researches being the evaluation of useful energy gain and collection efficiency. The collector performance can be determined the amount of solar energy incident on the collector surface is known as well as the fraction of incident energy absorbed by the collector absorber plate together with the amount of useful energy transferred to a working fluid. The energy balance on a collector under stable conditions can be determined asqU=qa+q1where
qU= rate of useful energy collection per unit area of collector surface, Wm2qa=rate of absorption of solar energy by the collector plate per unit area, Wm2q1=rate of energy losses from the collector to the surroundings by radiation, convection and conduction, Wm2.

Energy absorbed in the collector qa depends on the insolation rate, the absorptivity of the collecting surface to solar radiation and the transmissivity of the collector cover plate. The third factor doesn’t apply to flat plate collectors since they don’t have a cover. Not all incident solar radiation comes directly from the sun as some comes from diffuse sky radiation which accounts for about 10 % to 40% of the total incident radiation. The rate of absorption of energy on a covered flat plate collector is given by
qa=H-HDRD?e?D+ HdRd?e?d(1-D) (1-S)H = total insolation rate on a horizontal surface, Wm2HD = diffuse sky radiation falling on a horizontal surface Wm2RD,Rd = orientation factors to convert horizontal incidence to incidence on tilted collector, for direct and diffuse components, respectively
?e?D,?e?d= effective transmittance-absorptance products of the cover-absorber plate combination, for direct and diffuse components, respectively
S = shading factor to allow for shading of absorber plate by cover supports
D = dirt factor to allow for reduction in transmittance due to dirt deposits on the cover
If the effects of shading and dirt factors are neglected, the equation reduces to
qa=HRD??D+ HRd??dwhere subscripts D and d refer to the direct and diffuse components, respectively. The relationship that gives the orientation factor, Rd , is as follows
Rd=cos?sin?where angles ? and ? are obtained from equations (3) and (7), respectively. The diffuse orientation factor, Rd , is the same as the angle factor, FSS, obtained in equation (10) for bare plate collectors, equation (13) is further reduced to
qa=HRD?D+HRd?d wherein the absence of a cover plate eliminates the transmittance factor, ?. The values for direct and diffuse components of solar radiation that fall on a tilted surface are calculated from equations (6) and (9), respectively, wherein
ID=HRDId=HRdand from equation (1)
It = ID + Id=HRD+ HRdThermal losses from the collector q1When the collector plate temperature is greater than its surroundings, thermal losses occur from solar heat collectors. Thermal losses in flat-plate collectors comprises of heat losses from the top of the collector, heat loss from the bottom of the collector through the rear insulation and heat losses from sideways through the edge insulation. There are basically three modes of thermals losses in the collector which comprise of conduction, convection and radiation. The heat transfer mechanism in flat-plate solar collectors can be defined by a thermal resistance network as shown in Figure XXX below wherein Ta is the ambient air temperature, U1 , the overall collector heat loss coefficient and Tpm the mean collector plate temperature.

Equivalent thermal resistance network for a flat-plate solar collector
The collector heat loss coefficient, U1 , consist of all the losses in the collector and is equivalent to
U1=Ut+ Ub+Uedge(Ap Ac ) where
Ut=top or upward heat loss coefficient, Wm2.°CUb= bottom or back heat loss coefficient, Wm2.°CUedge=edge heat loss coefficient, Wm2.°CAp= perimeter area of collector, m
Ac= area of collector absorber plate, m
The thermal loss from flat-plate collectors can thus be expressed by
q1=U1(Tpm+Ta)where
Tpm= mean collector plate temperature, °C
Ta=ambient air temperature, °C
U1=overall collector heat loss coefficient, Wm2.°Cq1=heat loss from the collector, Wm2The overall heat loss coefficient is slightly modified under certain condition so as to account for geometries of particular collector designs. The useful energy collection per unit area of collector surface may be rewritten as
qU=HRD??D+ HRd??d-U1(Tpm+Ta)The useful heat gain can be expressed in terms of known collector dimensions, fluid flow characteristics and local fluid temperature and the heat-removal factor, FR , is used instead. A convenient expression for the useful heat gain of slightly different form is given by
qU=FRqa- U1(Tfi-Ta)Where
FR = heat-removal factor, dimensionless
Tfi= transport fluid temperature at the collector inlet, °C
There is a restriction in the above expression as it assumes that the fluid temperature at collector inlet, Tfi, is greater than the ambient air temperature, Ta. An expression that gives FR which function of the transport fluid flow-rate and is
FR=(Gcp U1 )1-exp(-F’U1 Gcp)where
G = mass flow rate of transport fluid per unit of collector area, kgh.m2cp = specific heat of transport fluid, kJkg.°CU1= heat-loss coefficient of collector, kJh.m2.°CF’ = collector efficiency factor determined wholly by the collector design, dimensionless
Any type of collector can apply the above expression. The value of FR depends on the solar intensity and the operating temperature of the collector. The basic equation that the rate of useful heat gain is
QU=macpTfo-Tfiwhere
QU= net rate of useful energy gain, kJhma = mass flow-rate of transport fluid, kghcp = specific heat of transport fluid, kJkg.°CTfo= transport fluid temperature at collector outlet, °C
Tfi= transport fluid temperature at collector inlet, °C
The collector efficiency gives an account of collector performance and it is defined as the useful heat gain over any time period to the incident solar radiation over the same time period. The equation XX below gives an expression for finding the collector efficiency.

?coll=qu?tIcoll?t×100where
?coll=collector efficiency, percent
Icoll= total insolation rate incident on a unit area of collector surface, Wm2qu=rate of useful heat collection per unit area of collector surface, Wm2?t=differential time element