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S-CO2 Brayton Cycle Coupled with ORC as Bottoming Cycle

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S-CO2 Brayton Cycle Coupled with ORC as Bottoming Cycle ( s-co2-brayton-cycle-coupled-with-orc-as-bottoming-cycle )

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Energies 2020, 13, 2259 10 of 24 (RH) in the Brayton cycle, which are fabricated by such technologies as chemical etching and diffusion Energies 2020. 13. x FOR PEER REVIEW 10 of 26 bonding, where flow channels are imprinted chemically on the metal plates and produce one block by diffusion adhering, as shown in Figure 4. Figure 4. Printed circuit heat exchangers geometrical design. The heat exchangeFrigisucreal4c.uPlaritnetdedbycirdciuviitdhienagt eitxicnhtaongsmersalglesoumbe-etrxichaladnegseigrsn.(Equation (18)) in which the properties of the fluid, temperature, and pressure are known, and an iterative process is followed The heat exchanger is calculated by dividing it into small sub-exchangers (Equation (18)) in until both the heat exchanged and the maximum pressure drop are satisfied. The correlations used for which the properties of the fluid, temperature, and pressure are known, and an iterative process is each of the i divisions were obtained from the literature [31] followed until both the heat exchanged and the maximum pressure drop are satisfied. The   correlations used for eachof the i divisio4n.s08w9ere obtained froifm the lRiter5000 } 𝑁N =−4.089 􏰰f􏰱 𝑈UI i i (18) (18) (19) (19) 5000  ·(Re −1000)·Pr  ∙ ( 𝑅 𝑒 8 − 2 3i 0 0 ) i 𝑖𝑖 4 . 0 8 9 + if Th{e heat transfer𝑖coefficient8is then calculated using Equation (19) where 𝑓 is the Darcy factor and 𝑃 is theHPr=andNtUl n·(ukm/Dber.) 𝑟 i I hid The heat transfer coefficient is then calculated using Equation (19) < 5 0 0 0 􏰱􏱮 if R >5000 2f ei 5000−2300 􏰰 i f 2 3 0 0 < 𝑅 𝑒 𝑁= 𝑓  𝑈𝐼 (𝑖)∙(𝑅 −1000)∙𝑃 1+12.7·Pr3−1·i i 8 8 𝑒𝑖 𝑟𝑖 where f is the Darcy fa2ctor and P is the Prandtl number. 𝑓r 1+12.7∙(𝑃 3 −1)∙√ 𝑖 𝑟 where k is the conductivity of the exchanger material [W/m·K]. 𝐻𝑖=𝑁𝑈 ∙(𝑘/𝐷h𝑖𝑑) 𝐼 Finally, the overall coefficient U of each element is calculated using Equation (20), and the length of each of the sub-exchangers with Equation (21). where 𝑘 is the conductivity of the exchanger material [W/m∙K]. Finally, the overall coefficient U of each element is calculated using Equation (20), and the length ofeachofthesub-exchangerswithEquatUion=(21). 1 (20) i 𝑈𝑖=Hht1Hct k 1+1+t 1 + 1 +𝑡 (20) 𝐻h 𝐻𝑐Qi 𝑘 𝑡𝑡 Li= 􏱃 􏱄 (21) 𝑄𝑖 𝐿𝑖 = Pi·Qi· Thm − Tcm (21) 𝑃∙𝑄∙(𝑇 −𝑇 ) ∆𝑃 = 𝑓 ∙ ( 𝑖𝑖 𝐿𝑖 𝐷h𝑖𝑑𝑖 𝑐𝑖2 ) ∙ ( ) (22) 2 The heat exchanger mass can be calculated using Equation (23) 𝑖 𝑖 h𝑚 𝑐𝑚 where t is the thickness of the plate, and Pi is the wet parameter. where 𝑡 is the thickness of the plate, and 𝑃 is the wet parameter. When calculating the hea°t exchanger, you check that it meets the introduced pressure drop using Equation (22). 𝑖

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