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Equations [B.1] and [B.2] require fluid inlet and initial solid temperature boundary conditions. Type 994 also makes the “infinite-NTU” assumption. That is, the fluid-solid heat transfer coefficient is sufficiently large that at any time t and location x, the fluid and solid are in thermal equilibrium. This was shown to be an appropriate assumption for thermal storage systems by McMahan [2006]. When the storage tank is idle the fluid-solid constituents are treated as a continuum and are governed by equation [B.3], with corresponding energy flows shown in figure B.2: [B.3] [B.4] dT ffs scdteffc∂x2loss,wwamb (ρ εC +ρ (1−ε)C )A where; Keff =εKf +(1−ε)Ks =k A −h A (T−T ) ∂2T 163 Figure B.2 1-D fluid-solid continuum differential energy balance for long-term idle loss simulation The boundary conditions for equation [5.2.14][B.3] are: −kAdT =h A(T −T) x=0 [B.5] [B.6] eff c dx −kAdT =h A(T −T) loss,top top x=o amb eff c dx loss,bot bot x=L amb x=L Nomenclature As = Total solid-fluid heat transfer surface area [m2] Ac = cross-sectional area in the direction of flow [m2] Anode = heat transfer surface area in a numerical control volume [m ] Abot = bottom loss heat transfer surface area [m2] Atop = top loss heat transfer surface area [m2] Aw = wall loss heat transfer surface area [m2] Cf = fluid specific heat [J/kg-K] 2PDF Image | Organic Rankine Cycle Solar-Thermal Powerplants
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