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Energies 2021, 14, 8238 11 of 25 Figure 6. Discretization heat exchanger. For each discretized volume, it was possible to identify three nodes: a node referring to the refrigerant flow (Cr), a node referring to the state of the heat exchanger’s walls (Cw), and a node referring to the state of the air or water, respectively, (Ca). The refrigerant and water flow were considered one-dimensional and the fluid properties varied only on the direction of the flow. In each discretized volume, the refrigerant pressure and density in the associated volume were computed according to Equations (16) and (17), which are given by the mass and energy balance equations applied to the j-th element: (j) ∂ ρ ( j ) d p ( j ) ∂ ρ ( j ) d h ( j ) . . (j)rrrr (j)(j−1) V +=m−m (16) r∂phdt∂hpdtr r (j)(j) (i) (j) V(j) h(j)∂ρr −1 dpr + h(j)∂ρr +ρ(j) dhr =m.(j−1)h(j−1)−m.(j)h(j)−Q.(j) (17) rr∂pdtr∂hrdt r rconvi hp From the above equations, the trend of the mean thermodynamic properties of the refrigerant flowing inside the j-th tube element (T(j), p(j), h(j)) were obtained. The internal convective heat flux between the refrigerant and the wall of the heat exchanger in each element is given by Equation (18): Q. (j) =α(j)A(j)T(j)−T(j) (18) convi i i w r where αi is the internal convective heat transfer coefficient, computed from empirical correlations available in the literature, which will be explained later in this section. The thermal-capacity component accounting for the thermal structure of the heat exchanger quantifies the mean wall temperature T(j) through Equation (19), obtained by the energy w conservation equation with the assumption of monodimensional heat flow, as conduction heat flow through wall elements was neglected: rrr (j) dT(j) . (j) . (j) C W =Q −Q (19) W dτ convi conve The external flow component assessed the mean thermodynamic properties of the air or water flowing outside of the j-th tube element (T(j), p(j), h(j)). In the case of water, the aaa flow was assumed to be one dimensional as with the refrigerant flow, while in the case of air, zero-dimensional flow and negligible conduction in air flow direction was assumed. The convective heat flow of the external flow was computed through Equation (20). Q. (j) =α(j)A(j)T(j)−T(j) (20) conve e e a WPDF Image | Dynamic Modelling and Validation of an Air-to-Water Reversible R744
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