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Residential CO2 Heat Pump System for Combined

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Residential CO2 Heat Pump System for Combined ( residential-co2-heat-pump-system-combined )

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6 – Modelling With reference to Eqs. (6.4) through (6.8), the following equations were derived to estimate the outlet temperature of CO2 and water from each sub-section when the inlet CO2 temperature and the inlet water tempe- rature were known (Stoecker, 1989): where: ⎝H⎠ ⎡⎛ 1 ⎞ ⎛ 1 ⎞ ⎤ T H,out = T H,in )⋅ ⎜ ⎟ − ∆T CP H − (T − T H,in C,in ⎛⎞ ⎜ 1−eXH ⎟ (6.14) (6.15) (6.16) (6.17) In Eq. (6.14), ∆TH represents the temperature drop of the supercritical CO2 gas due to pressure loss in the sub-section, i.e: T =T −(T −T )⋅⎜ 1−eXC ⎟ C,out C,in C,in H,in ⎜CP ⎟ XH=U⋅Ai⋅⎢⎜& ⎟ −⎜& ⎟⎥ ⎢⎣⎝m⋅cp ⎠H ⎝m⋅cp ⎠C⎥⎦ ⎜ H−eXH⎟ CP ⎝C⎠ ⎛⎜ ⎞⎟ ⎜ C−eXC⎟ CP ⎡⎛ 1 ⎞ ⎛ 1 ⎞ ⎤ XC=U⋅Ai⋅⎢⎜& ⎟ −⎜& ⎟⎥ ⎢⎝m⋅c ⎠ ⎝m⋅c ⎠ ⎥ ⎣pCpH⎦ ⎝ ⎠v 6.1.3.3 Heat Transfer Correlations ⎛∂T⎞ ∆TH =⎜∂p⎟ ⋅∆p (6.18) The convective heat transfer coefficients h in terms of the Nusselt number (Nu) for single-phase turbulent tube flow can generally be expressed as a function of the Reynolds number (Re) and the Prandtl number (Pr), i.e.: Nu = f(Re,Pr) (6.19) 176

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