Analysis of Fluid Flow in Redox Flow Batteries

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Analysis of Fluid Flow in Redox Flow Batteries ( analysis-fluid-flow-redox-flow-batteries )

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∆𝑃 = 𝑓(𝑤 ,𝐾,𝜇,𝑣 ,𝐿,𝜌,h ,𝑤 ,h ),𝑚𝑎𝑠𝑠,𝑡𝑖𝑚𝑒 𝑎𝑛𝑑 𝑙𝑒𝑛𝑔𝑡h 𝑎𝑟𝑒 𝑢𝑛𝑖𝑡𝑠 𝑚𝑟𝑐𝑐𝑐𝑝 → 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 = 9 − 3 = 6 Where wr, wc, vc, L, and hc are the width of ribs, width of channels, velocity in channels, length of channels, and height of channels, respectively. Finding dimensionless numbers requires a set of recurring variables. Each variable must provide a dimensionless number when integrated with this set of recurring variables. To ensure this condition, the criteria for choosing recurring variables are: 1- Each of the independent units must appear in at least one of the variables. 2- Forming a dimensionless group out of variables within the recurring set must not be possible. ρ, vc, and hc are the chosen set of recurring variables. Each variable forms a dimensionless number by manipulating the recurring variables. MATLAB RREF function is a tool that assists forming dimensionless numbers out of the set of recurring variables and the target variable. It implements Gauss-Jordan elimination method on its input matrix to return a reduced row echelon form (RREF) of the matrix. Each row in the input matrix represents an assigned independent unit, and each column represents a variable and its dimensions. The RREF function transforms this matrix into an output matrix, which each variable are compared to the recurring variables instead of the independent units. The recurring variables must occupy the first columns. ρ vc hc ΔPm μ K L wc hp Mass 1 0 0 1 1 0 0 0 0 Length-3 1 1 -1 -1 2 1 1 1 Time 0 -1 0 -2 -1 0 0 0 0 24

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