# How to find Heat Exchanger NTU?

 The heat exchanger (HXC) raw performance data is usually provided by the vendor that manufactures HXC. The raw data consists of total heat rejection (q) for varying air mass flow rates and for a given coolant and air inlet temperatures and coolant mass-flow rate. These raw data are determined at uniform air conditions. One example of such raw data is provided below. An example of Heat Exchanger Raw Data: 1 -hx type 1-radiator, 2-condenser 3 - No. of coolant input points 6 - No of air input points 121.1 - Hot fluid inlet temperature (deg C) 46.0 - Cold fluid inlet temperature (deg C) 0.864 - Width of the heat exchanger 0.438 - Height of the heat exchanger 1006.43 - cp of air 3669.5 - cp of coolant 2.75 - collant flow rate for the case Coolant Air Heat (Kg/s) (Kg/s) (watt) 2.5354 0.5670 26186.5 2.5354 0.9450 40890.5 2.5354 1.512 56176.5 2.5354 2.268 70569.2 2.5354 3.024 81529.4 2.5354 3.78 90792.8 3.1693 0.5670 26369.4 3.1693 0.9450 41354.7 3.1693 1.512 57127.8 3.1693 2.268 72142.9 3.1693 3.024 83676.5 3.1693 3.78 93500.8 3.8031 0.5670 26494.2 3.8031 0.9450 41676.5 3.8031 1.512 57792.4 3.8031 2.268 73249.0 3.8031 3.024 85195.8 3.8031 3.78 95428.0 In the above example, there would be 3 curves for each coolant mass flow rates. Each curve has 6 air mass flow rates. Lets say a steady-state underhood simulation is run at 2.7 kg/s coolant flow rate, using the above table, how to calculate NTU versus air flow rate at coolant flow rate of 2.7 kg/s? STEP 1: If the data comes in English units (lbs/min, BTU), make another table with SI units (kg/s, Watts) STEP 2: Data for coolant flow rate of 2.7 kg/s is not provided in the raw data, but it is available for 2.5354 and 3.1693 kg/s. We need to interpolate (linear is good enough) the data for air flow rates and total heat rejection at 2.7 kg/s coolant flow rate between 2.5354 and 3.1693 kg/s. Generate another table for air flow rates and heat rejection at 2.7 kg/s coolant flow rate. STEP 3: Create another column for effectiveness, e = q/qmax = q /[Cmin * ( Tcoolant_in - Tair_in)], where Cmin = (mdot*Cp)_min is the smallest value either air or coolant. For example, for coolant, (mdot*Cp)_coolant = (2.7 kg/s * 3669.5 J/kg-K) = 9907.65 Watts/K. This value should be compared with (mdot*Cp)_air at each air flow rate, and the smallest value should be taken for effectiveness, e, calculation. STEP 4: Using effectiveness, calculate NTU using NTU-Effectiveness relations for that particular heat exchanger configuration. Config A: both fluids unmixed E =1-EXP((1/Cr)*(NTU)^0.22*(EXP(-Cr*(NTU)^0.78)-1)) Config B: Cmax (mixed), Cmin(unmixed) E =(1/Cr) * (1-EXP(-Cr * (1-EXP(-NTU)))) Config C: Cmin(mixed), Cmax(unmixed) E =1-EXP(-Cr ^ (-1) * (1-EXP(-Cr * (NTU)))) where Cr = Cmin/Cmax. For car radiators, heat exchanger configuration A is common. In this relation, NTU has to be solved implicitly, that is, given a value of e, NTU has to be determined. This has to be performed iteratively. There is another relation, which is a good approximate for all heat exchangers, but at small NTU values (NTU=0 - 4). That relation is: E =1-exp(-NTU) This relation can be solved for NTU directly, NTU = -LN(e-1). Now you have NTU as a function of air mass flow rate for coolant flow rate of 2.7 kg/s. NOTE: What is the difference in magnitude for NTU-E relation between different configurations? Cr NTU Config A Config B Config C E =1-exp(-NTU) 0.5 0.1 0.091502779 0.092934087 0.092934986 0.095162582 0.5 0.5 0.351947785 0.357182903 0.357506407 0.39346934 0.5 1 0.544763712 0.541968992 0.544763712 0.632120559 0.5 1.5 0.662251831 0.643765295 0.651900491 0.77686984 0.5 2 0.738758463 0.702012715 0.717546436 0.864664717 0.5 2.5 0.791120823 0.736115797 0.75996977 0.917915001 0.5 3 0.828405162 0.756362299 0.788544283 0.950212932 0.5 3.5 0.855830937 0.768484072 0.808420443 0.969802617 0.5 4 0.87656375 0.775778661 0.822596669 0.981684361 0.5 4.5 0.892606915 0.780181986 0.832906468 0.988891003 0.5 5 0.905274235 0.782845017 0.840518923 0.993262053 0.5 5.5 0.915454004 0.784457394 0.846206468 0.995913229 0.5 6 0.923762919 0.785434309 0.850495063 0.997521248 0.5 6.5 0.930639172 0.786026456 0.853752017 0.998496561 0.5 7 0.936400577 0.78638547 0.856239309 0.999088118 0.5 7.5 0.941281897 0.786603172 0.858147077 0.999446916 0.5 8 0.945459417 0.786735195 0.859615294 0.999664537 0.5 8.5 0.949067488 0.786815264 0.860748208 0.999796532 0.5 9 0.952209881 0.786863826 0.861624186 0.99987659 0.5 10 0.957405208 0.786911144 0.862828609 0.9999546