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38 Components design where A stands for the heat transfer area and ∆TLM for the logarithmic mean temperature difference. The overall heat transfer coefficient U is calculated with the contributions of the cold side, the hot side and the methal wall between them, U= 1 , (3-7) 1 +δ−0.5DCH + 1 αC λRG αH where αC and αH correspond to the heat transfer coefficient for the cold and hot sides re- spectively, δ stands for the plate thickness and λRG for the thermal conductivity of the heat exchanger material. The heat transfer coefficient of the working fluid inside the channels is a function of the Nusselt number, αCH = NuλCH , DHD where DHD corresponds to the hydraulic diameter of the semicircular channels, DHD = DCH , 1 + π2 (3-8) (3-9) and DCH is the channel diameter. The thermal conductivity of the fluid can be obtained as a function of the pressure and temperature of the working fluid with the computational fluid library, λCH =λ(P,T). (3-10) There are several expressions available to calculate the Nusselt number for supercritical fluids. They have been developed for both straight channels and wavy channels, as shown in the next paragraphs. Straight channels The Gnielinski correlation is one of the most widely used relations and it is recommended by Hesslegraves [52], (3-11) FFI = [0.79ln (Re) − 1.64]−2 . (3-12) The Gnielinski correlation is valid for Reynolds numbers between 2300 and 5·106 and Prandtl numbers between 0.5 and 2000. Hesselgraves recommends a Nusselt number of 4.089 for laminar flows. Dostal [16] proposes an interpolation to calculate the Nusselt in the transition region between Re = 2300 and Re = 5000, N u = 4.089 + NuRe=5000 − 4.089 (Re − 2300). (3-13) 2300 The Gnielinski equation (3-11) has been tested in different heat exchangers and conditions. Kruizenga et al. [40] study the heat transfer coefficient in a straight channel PCHE with FFI (Re−1000)Pr 8 Nu= 2 , 1.0 + 12.7 Pr3 −1 FFI 8 where Pr corresponds to the Prandtl number and FFI to the Filonenko friction coefficient, J.S. Bahamonde Noriega Master of Science ThesisPDF Image | Design method for s-CO2 gas turbine power plants
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