Global Journal of Researches in Engineering, J: General Engineering, Volume 22 Issue 1

e) Evaluation of Thermal Efficiency of the Collectors ( η th ) The thermal efficiency of the collector (dish) ( η th ) can be defined as the ratio of the useful energy delivered Q u to the energy incident on the concentrator aperture Q S [29]. (10) Assuming that the concentrator has an aperture area A ap and receives solar radiation at the rate Q S from the sun, the net solar heat transfer Qs is proportional to A ap and the direct normal insulation per unit of collector area I b is given[ 30&31]; (11) Under steady state condition, the useful heat delivered by a solar collector system is equal to the energy absorbed by the heat transfer fluid Q a , which is determined by the radiant solar energy falling on the absorber minus the direct or indirect heat losses Q i from the absorber to the surrounding .i.e. (12) f) Determination of Optical Efficiency of the Collector ( Η o) The optical efficiency depends on the optical properties of the materials involved, the geometry of the collector and the various imperfections arising from the construction of the collector. The equation to be used in deducing the optical efficiency given by [32&33] is: (13) where λ is the un-shaded factor, ρ is the dish reflectance, τα is the transmittance-absorptance product, γ is the intercept factor of the absorber i.e. obstacle e.g, dust, birds e.t.c. θ is the angle of incidence. The total heat lost by the absorber can be through the three basic heat transfers i.e. conductive heat loss (Q lk ), convection heat loss (Q lc ) and radiation heat loss (Q lr ) therefore; g) Evaluation of Instantaneous Efficiency of the Collector Instantaneous thermal efficiency of a solar concentrator may be calculated from the energy balance on the absorber. If the useful thermal energy delivered by a concentrator is given by [34&35] (14) then, the instantaneous thermal efficiency may be written as: (15) where A ap is the aperture area, q u is useful thermal energy delivered, I b is the beam radiation, T abs is the absorber temperature, T a is the ambient temperature, C is the concentrator ratio respectively η 0 , is optical efficiency and U L is then overall heat loss coefficient. At higher operating temperatures, the radiation loss term dominates the convection losses and the energy balance equations become [36] (16) where T is the temperature of heat transfer fluid entering/leaving the collector, while the U L takes into account the accompanying convection and conduction losses, therefore, the instantaneous thermal efficiency η is given as [37&38]: (17) Since the absorber surface temperature is difficult to determine, it is convenient to express the efficiency in terms of the inlet fluid temperature by means of heat removal factor FR defined by Ibrahim, (2012), as: (18) where T L is the overall temperature of the system. The optical efficiency, heat loss coefficient and heat removal factor are dependent on the design parameters while the solar flux, inlet fluid temperature and the ambient temperature define the operating conditions. Therefore, the instantaneous thermal efficiency is dependent on two types of quantities, namely the concentrator design parameters and the parameters characterizing the operating conditions as shown in the equation. h) Evaluation of Efficiency of the Receiver (Absorber) Cooking occurs faster or at higher temperature, therefore, the heat lost is simply described by [39&40] as; (19) where, is the difference between the initial and final temperature T ∆ R is the thermal resistance of the receiver, V is the volume of the receiver, thus; (20) Note that, the thicker the walls of the receiver, the greater the value of the R, since (21) Therefore, the solar energy reflected upon the receiver per unit area can be calculated [41]; Energy = IVT (22) Where I is the Solar Insolation and V is the volume of the receiver and T is the time taken. Therefore, the efficiency of the receiver can be deduced from specific heat capacity i.e. Analysis of Thermal and Optical Efficiency of Parabolic Concentrating System for Thermal Application lobal Journal of Researches in Engineering ( ) Volume XxXII Issue I Version I J G 55 Year 2022 © 2022 Global Journals