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βππ =π π£π +π π£π ββπ =π(πΏ(π π£π +π π£π )) (3.18) πΏ hπ2 π€π2 π hπ2 π€π2 A DN is formed by dividing the first term over the second one to find the dominant term on the RHS: π π£π hπ2 = π€π2 = π€Μ , π€Μ = πππ πππ’π πΉπππππ ππ π¦βππππππ‘πππ (3.19) π π£π2 hπ2 π π πππ πππ’π πΉπππππ ππ π§βππππππ‘πππ π€π wΜc is in order of 1 for the most cases studied, therefore, both terms are considered for further analysis. The governing equation is reiterated as: πππ =ππ2π£π +ππ2π£π ππ₯ ππ¦2 ππ§2 3.4.2- Analysis of the fluid dynamics in the porous medium The governing equation for the fluid dynamics in the porous medium is: πππ = π π£ +0.55π|π£ |π£ +ππ2π£π +ππ2π£π +ππ2π£π ππ₯πΎπβπΎππππ₯2 ππ¦2 ππ¦2 By implementing a scaling analysis, Equation 3.22 is produced: (3.20) (3.21) (3.22) DNs are formed by dividing each term over the others to find the dominant terms on the RHS: βππ = π π£ + 0.55 ππ£ 2 + π π£π + π π£π + π π£π πΏ πΎπ βπΎ π hπ2 π‘π2 ππ2 π π£π hπ2 πΎ π·π1 = ππ£ = h2 = π΅ππππππππ ππ π¦βππππππ‘πππ π·ππππ¦β²π πππ€ π΅ππππππππ ππ π₯βππππππ‘πππ π·ππππ¦β²π πππ€ πΎππ π π£π π‘π2 πΎ π·π2=ππ£ =π‘2= πΎππ (3.23) ππ£π π·π3 = ππ2 = πΎ = π΅ππππππππ ππ π§βππππππ‘πππ { π2β² πΎπ£π ππ π·ππππ¦ π πππ€ 30PDF Image | Analysis of Fluid Flow in Redox Flow Batteries
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