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Energies 2022, 15, 6347 4 of 15 channel with a pitch length was added at the inlet and outlet, respectively. The mass flow rate and average temperature were set for the inlets of cold and hot fluids. The channel surfaces at the front and back were set to be adiabatic. The hot fluid was compressed air with different pressures, and the cold fluid was water. All the inlet parameters of the working fluid were from Park’s study [5]. The property parameters of the two fluids were all related to the temperature and were derived from REFPROP 9.1. (Gaithersburg, MD, USA) [25]. 2.2. Numerical Method This work was conducted with the commercial software of ANSYS FLUENT 14.5 (Pittsburgh, PA, USA). It was assumed that the flow in present heat exchanger in calculation is 3D, laminar, incompressible, and steady. The governing equations contain the continuity conservation, momentum conservation and energy conservation, which are expressed as follows [6]: ∂ (ρui) = 0. (1) ∂xi ∂ρuiuj=−∂p+∂ μ∂ui+∂uj −2μ∂ukδij. (2) 3 ∂xk (3) ∂xi ∂xi ∂xj ∂ ∂xi ∂xj ∂xi ∂ ∂T (ρHui) = ∂xi λ . ∂xi The governing equations were solved using the finite volume method. The pressure and velocity coupling was addressed using the SIMPLEC algorithm. The criterion of convergence is that the residuals of each variable were smaller than 10−6. The calculation equations regarding the flow and heat transfer parameters are as follows [6]: Re = ρuDh , (4) μ h= qw , (5) (Tw − Tb) Nu = hDh , (6) λ j= Nu , (7) R e P r 13 where the thermal properties of the working fluid could be determined with the average temperature of the working fluid in each pitch, and u is the average velocity calculated through averaging the thermal property parameters. The inlet and outlet temperatures are the mass-weighted average temperature. The heat flow qw and temperature of the surface Tw are derived from the surface area and weight [26]. Dh is the hydraulic diameter of the channel. The local Fanning friction factor is defined as follows: f = ∆pfDh , (8) 2ρu2 Lp 22 ∆pf = ∆p−∆pa = ∆p− ρoutuout −ρinuin , (9) where ∆p, ∆pf, ∆pa indicate the overall pressure drop in each pitch, frication pressure drops, and acceleration pressure drop, respectively. ρin, ρout are the density of the inlet and outlet working fluids, respectively. uin, uout are the inlet and outlet velocity, respectively. Lp is the flow channel length.PDF Image | Thermal–Hydraulic Performance of a Printed Circuit Heat Exchanger
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