# Macro Heat Exchanger Model Theory

 Some salient features of Macro Heat Exchanger Model Theory.Macro Heat Exchanger Model Theory---------------------------------A. ***************Givens:1. Heat Exchanger Performance Curve: NTU_full (mdot_air_full)2. NTU-E CurveEven if full exchanger is multi-pass, a macro is always single-pass. So NTU-E ofsingle-pass can be applied on a heat exchanger that has multiple passes.NTU - Number of Transfer UnitsE - EffectivenessB.***************Determining NTU_macroThe NTU_full (mdot_air_full) curve is for the full heat exchanger and does notdirectly apply to the macro. However, using simple ratios, we can relateNTU_macro to the NTU_full curve.NTU_macro = NTU_full * A_macro/A_full * Cmin_full/Cmin_macrowhere A is the surface area at which heat transfer takes place, which would bethe fins, tubes, etc. For homogeneous core, the ratio of the areas has to equalthe ratio of the volumes: A_macro/A_full = V_macro/V_full.Also, NTU_full has to be evaluated at local flow rate (mdot_macro *Af_total/Af_full), where Af is the frontal inlet let area.NTU_macro = NTU_full * V_macro/V_full * Cmin_full/Cmin_macroNTU_macro = V_macro/V_full * Cmin_full/Cmin_macro * NTU_fullC. ***************Given NTU_macro, calculate effectiveness of the macro using NTU-effectivenessrelations.E_macro = f (NTU_macro, R_macro), where R_macro =Cmin_macro/Cmax_macroD. ***************Calculate heat rejection of the macro.Q_macro = Cmin_macro * E_macro * ( Tcoolant-in_macro - Tair-in_macro)E. ***************Calculate heat rejection/added for each cell within a macro.Q_cell = Q_macro * Vcell/Vmacrowhere Vcell, and Vmacro are volumes of cell and macro, respectively.Notes:-To properly account for variable density, mdot, not velocity, is used.-The above assumes fixed coolant flow rate.-Only one performance curve is used for a single coolant flow-rate is used.-If it is a multi-pass heat exchanger, use multi-pass NTU-E relation toconvert raw heat exchanger data into NTU_full (mdot_air_full) for Step A.-The macro always uses single-pass NTU-E relation, where both fluid are unmixed.The curve is:E = 1-exp[(1/Cr)(NTU)^.22{exp[-Cr(NTU)^.78] - 1}],

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