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&TB ⎜ i ⎟ A (6.33) Q =⎛π⋅D2⎞⋅U⋅[T−T(i)] Since it proved to be impossible to combine the equations for transient heat conduction and mass transfer in the selected programming tool (ref. Section 6.2.2.4, Programming Tools and Input Parameters), an indirect method was used when computing the outlet water temperature from the DHW tank during operation in the charging (heating) mode. By selecting the number of nodes in the tank model in accordance with Eq. (6.34), the mass of water that entered each sub-volume or node during each time step equalled the total mass of the sub-volume. (6.34) where m& is the water flow rate through the tank, t is the time step, V is the total water volume in the tank and ρ is the average density of the water. The required number of nodes were calculated for the lowest gas cooler heating capacity (e.g. 0.5 kW), since this corresponded to the lowest water flow rate in the hot water circuit. The latter was calculated as follows: & where the subscripts in and out refer to the inlet and outlet of the gas cooler, Q& GC is the heating capacity of the gas cooler and cp is the average specific heat capacity of the water. ⎛V⋅ρ⎞ n=⎜m⋅t⎟ ⎝&⎠ m= QGC (6.35) & (Tout −Tin)⋅cp 6 – Modelling where n is the total number of nodes, i is the node number, dx is the node distance, Di and Do are the inner and outside diameters of the DHW tank, respectively, TA is the ambient temperature, and U is the overall heat transfer coefficient of the tank wall (ref. Do). For node i=1 and i=n, the heat transfer rate through the top and the bottom of the tank was added to the right-hand side of Eq. (6.32). ⎝4⎠ 6.2.2.3 Incorporating Mass Transfer in the Tank Model 195PDF Image | Residential CO2 Heat Pump System for Combined
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