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3 – Theoretical Background and System Analysis ∂2T + ∂2T + ∂2T = 1 ⋅ ∂T (3.28) (3.29) and ∂x2 ∂y2 ∂z2 α ∂t α = ρ ⋅kc where α is the thermal diffusivity of water. p Figure 3.28 shows the estimated heat flux across a thermocline as a func- tion of the thickness of the thermocline zone (HTC) and the initial tempera- ture difference (∆T) between the hot and cold water reservoirs. Constant thermal conductivity for the water was assumed. 3000 2500 2000 1500 1000 500 0 0 50 100 150 200 250 Thermocline Thickness [mm] Variable initial temperature difference ∆T ∆T=70 K ∆T=40 K Figure 3.28 The heat flux across the thermocline as a function of the thermocline thickness HTC and the initial temperature difference ∆T. Since the heat flux between the reservoirs is inversely proportional to the thickness of the thermocline zone, the growth rate of the zone (∂HTC/∂t) will drop off gradually during the tapping and charging periods. When the average temperature Tm and the volume of the thermocline zone VTC are known, the exergy loss in the DHW tank and the reduction in COP for the CO2 heat pump can be estimated according to Eq. (3.23) and (3.26), respectively. 61 Heat Flux [W/m2]PDF Image | Residential CO2 Heat Pump System for Combined
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