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Chapter 6: Case studies Heat transfer type Heat transfer law 1-2 Convection Gnielinski correlation for turbulent heat transfer in pipes (Incropera & DeWitt, 2001) q =2πk T2−T3 2-3 Conduction 23 23 ln(D3/D2) q23 is the assumed-to-be-constant steel conductivity 3-4 4-5 5-6 5-6 5-7 Hollands correlation for natural convection in an annular Convection space between horizontal cylinders (Hollands et al., 1975). Radiation q =σπD (T43−T4) 34,rad 3 1+1−ε4 D3 ε3 ε4 D4 Conduction q =2πk T4−T5 45 45 ln(D5/D4) Free convection Churchill and Chu correlation for laminar convection from a horizontal cylinder (Incropera & DeWitt, 2001). Zhukauskas’ correlation for external forced convection Forced convection flow normal to an isothermal cylinder (Incropera & DeWitt, 2001) Radiation q57,rad=σπD5(T54−T47) T 7 is taken 8 degrees below the ambient temperature. Table 24: Absorber heat transfer model The amounts of radiation absorbed by the collector and by the glass envelope are respectively given by (Forristall, 2003): q sun , 3 =q sun⋅ηopt⋅τ env⋅αcoating (77) qsun,5=qsun⋅ηopt⋅αenv (78) where qsun=S⋅Wcol[W/m] is the linear beam insolation and: ηopt =ρmirror⋅ηtracking⋅ηshadowing⋅ηgeometry⋅ηunaccounted (79) is the optical efficiency, lumping different sources of losses such as mirror reflectivity ( ρmirror ), tracking losses ( ηtracking ), shadowing ( ηshadowing ), geometrical effects ( ηgeometry ) and other unaccounted losses ( ηunaccounted ). The values of the different efficiencies are the ones recommended by Forristall (2003), except for ηtracking and ηgeometry , where a significantly lower efficiency is selected. This conservative hypothesis is made to account for the relatively lower optical intercept factor (~0.9) resulting from the low-cost design of the collector, which could reduce the performance of the system. 6PDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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