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Cross Flow Heat Exchanger
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Cross-Flow Heat Exchanger
ParametersAir Temperature 20 C Ta
Heat transfer coefficient 40000 UPipe diameter 0.1 m D
Liquid density 1000 rho
Specific heat capacity 4200 Cp
Liquid flowrate 1 FInlet liquid temperature 100 C T0Time step 0.01 s dtSpace step 0.02 m dx
Distance x0 0.02 0.04 0.06 0.08
Time t 0 100.00 100.00 100.00 100.00 100.000.01 100.00 99.70 99.70 99.70 99.700.02 100.00 99.41 99.39 99.39 99.390.03 100.00 99.15 99.09 99.09 99.090.04 100.00 98.90 98.79 98.79 98.790.05 100.00 98.67 98.50 98.49 98.490.06 100.00 98.45 98.21 98.19 98.190.07 100.00 98.25 97.93 97.89 97.890.08 100.00 98.07 97.65 97.60 97.590.09 100.00 97.89 97.38 97.31 97.30
0.1 100.00 97.73 97.12 97.02 97.010.11 100.00 97.58 96.87 96.73 96.710.12 100.00 97.44 96.62 96.45 96.420.13 100.00 97.30 96.38 96.17 96.130.14 100.00 97.18 96.15 95.89 95.840.15 100.00 97.07 95.92 95.62 95.560.16 100.00 96.96 95.71 95.35 95.270.17 100.00 96.86 95.50 95.08 94.990.18 100.00 96.77 95.30 94.82 94.710.19 100.00 96.68 95.10 94.57 94.43
0.2 100.00 96.60 94.92 94.32 94.160.21 100.00 96.52 94.74 94.07 93.890.22 100.00 96.45 94.57 93.83 93.620.23 100.00 96.39 94.40 93.60 93.350.24 100.00 96.33 94.25 93.37 93.090.25 100.00 96.27 94.10 93.15 92.830.26 100.00 96.22 93.95 92.93 92.570.27 100.00 96.17 93.82 92.72 92.320.28 100.00 96.12 93.68 92.51 92.07
http://excelcalculations.blogspot.com
W m-2 K-1
kg m-3
J kg-1 K-1
kg s-1
0.29 100.00 96.08 93.56 92.31 91.820.3 100.00 96.04 93.44 92.11 91.58
0.31 100.00 96.00 93.32 91.92 91.340.32 100.00 95.97 93.22 91.74 91.100.33 100.00 95.93 93.11 91.56 90.870.34 100.00 95.90 93.01 91.38 90.650.35 100.00 95.87 92.92 91.22 90.420.36 100.00 95.85 92.83 91.05 90.210.37 100.00 95.82 92.74 90.90 89.990.38 100.00 95.80 92.66 90.74 89.780.39 100.00 95.78 92.59 90.60 89.58
0.4 100.00 95.76 92.51 90.45 89.380.41 100.00 95.74 92.44 90.32 89.180.42 100.00 95.72 92.38 90.18 88.990.43 100.00 95.71 92.31 90.06 88.800.44 100.00 95.69 92.25 89.93 88.620.45 100.00 95.68 92.20 89.81 88.440.46 100.00 95.66 92.14 89.70 88.270.47 100.00 95.65 92.09 89.59 88.100.48 100.00 95.64 92.05 89.48 87.940.49 100.00 95.63 92.00 89.38 87.78
0.5 100.00 95.62 91.96 89.29 87.620.51 100.00 95.61 91.92 89.19 87.470.52 100.00 95.60 91.88 89.10 87.320.53 100.00 95.59 91.84 89.01 87.180.54 100.00 95.59 91.81 88.93 87.040.55 100.00 95.58 91.77 88.85 86.900.56 100.00 95.57 91.74 88.78 86.770.57 100.00 95.57 91.71 88.70 86.650.58 100.00 95.56 91.69 88.63 86.520.59 100.00 95.56 91.66 88.57 86.40
0.6 100.00 95.55 91.63 88.50 86.290.61 100.00 95.55 91.61 88.44 86.180.62 100.00 95.54 91.59 88.38 86.070.63 100.00 95.54 91.57 88.32 85.960.64 100.00 95.53 91.55 88.27 85.860.65 100.00 95.53 91.53 88.22 85.770.66 100.00 95.53 91.51 88.17 85.670.67 100.00 95.53 91.49 88.12 85.580.68 100.00 95.52 91.48 88.08 85.490.69 100.00 95.52 91.46 88.04 85.41
0.7 100.00 95.52 91.45 87.99 85.330.71 100.00 95.51 91.44 87.96 85.250.72 100.00 95.51 91.42 87.92 85.170.73 100.00 95.51 91.41 87.88 85.100.74 100.00 95.51 91.40 87.85 85.030.75 100.00 95.51 91.39 87.82 84.960.76 100.00 95.51 91.38 87.79 84.89
0.77 100.00 95.50 91.37 87.76 84.830.78 100.00 95.50 91.36 87.73 84.770.79 100.00 95.50 91.35 87.70 84.71
0.8 100.00 95.50 91.35 87.68 84.650.81 100.00 95.50 91.34 87.65 84.600.82 100.00 95.50 91.33 87.63 84.550.83 100.00 95.50 91.33 87.61 84.500.84 100.00 95.50 91.32 87.59 84.450.85 100.00 95.50 91.31 87.57 84.410.86 100.00 95.49 91.31 87.55 84.360.87 100.00 95.49 91.30 87.53 84.320.88 100.00 95.49 91.30 87.51 84.280.89 100.00 95.49 91.29 87.50 84.24
0.9 100.00 95.49 91.29 87.48 84.200.91 100.00 95.49 91.29 87.47 84.170.92 100.00 95.49 91.28 87.45 84.130.93 100.00 95.49 91.28 87.44 84.100.94 100.00 95.49 91.27 87.43 84.070.95 100.00 95.49 91.27 87.41 84.040.96 100.00 95.49 91.27 87.40 84.010.97 100.00 95.49 91.27 87.39 83.980.98 100.00 95.49 91.26 87.38 83.950.99 100.00 95.49 91.26 87.37 83.93
1 100.00 95.49 91.26 87.36 83.90
0.1 0.12 0.14 0.16 0.18 0.2 0.22
100.00 100.00 100.00 100.00 100.00 100.00 100.0099.70 99.70 99.70 99.70 99.70 99.70 99.7099.39 99.39 99.39 99.39 99.39 99.39 99.3999.09 99.09 99.09 99.09 99.09 99.09 99.0998.79 98.79 98.79 98.79 98.79 98.79 98.7998.49 98.49 98.49 99.92 99.92 99.92 99.9298.19 98.19 98.19 99.53 99.62 99.62 99.6297.89 97.89 97.89 99.14 99.31 99.32 99.3297.59 97.59 97.59 98.76 99.00 99.01 99.0197.30 97.30 97.30 98.38 98.68 98.71 98.7197.00 97.00 97.00 98.02 98.36 98.41 98.4196.71 96.71 96.71 97.66 98.04 98.11 98.1196.42 96.42 96.42 97.30 97.72 97.81 97.8296.13 96.13 96.13 96.95 97.40 97.50 97.5295.84 95.84 95.84 96.60 97.07 97.20 97.2295.55 95.55 95.55 96.26 96.75 96.90 96.9395.26 95.26 95.26 95.93 96.43 96.60 96.6394.98 94.97 94.97 95.60 96.10 96.29 96.3494.69 94.69 94.69 95.27 95.78 95.99 96.0494.41 94.40 94.40 94.94 95.46 95.69 95.7594.13 94.12 94.12 94.62 95.14 95.39 95.4693.85 93.84 93.84 94.31 94.82 95.08 95.1793.57 93.56 93.56 93.99 94.50 94.78 94.8893.29 93.28 93.28 93.68 94.19 94.48 94.5893.02 93.00 93.00 93.38 93.87 94.18 94.2992.74 92.72 92.72 93.07 93.56 93.87 94.0092.47 92.45 92.44 92.77 93.25 93.57 93.7192.20 92.17 92.17 92.48 92.94 93.27 93.4291.93 91.90 91.89 92.18 92.63 92.97 93.13
Air at 20 oC
Liquid at 100 oC
91.67 91.63 91.62 91.89 92.33 92.67 92.8491.40 91.36 91.35 91.60 92.02 92.37 92.5691.14 91.09 91.08 91.31 91.72 92.07 92.2790.88 90.82 90.81 91.02 91.42 91.78 91.9890.63 90.56 90.54 90.74 91.12 91.48 91.6990.37 90.29 90.27 90.45 90.83 91.19 91.4190.12 90.03 90.00 90.17 90.53 90.89 91.1289.88 89.77 89.74 89.90 90.24 90.60 90.8489.63 89.51 89.47 89.62 89.95 90.31 90.5589.39 89.25 89.21 89.35 89.67 90.02 90.2789.15 89.00 88.95 89.07 89.38 89.73 89.9888.91 88.74 88.69 88.80 89.10 89.44 89.7088.68 88.49 88.43 88.53 88.81 89.15 89.4288.45 88.24 88.18 88.27 88.53 88.87 89.1488.22 88.00 87.92 88.00 88.26 88.59 88.8688.00 87.75 87.67 87.74 87.98 88.30 88.5887.78 87.51 87.41 87.47 87.70 88.02 88.3087.57 87.27 87.16 87.21 87.43 87.74 88.0287.35 87.03 86.91 86.95 87.16 87.47 87.7487.14 86.80 86.67 86.70 86.89 87.19 87.4786.94 86.57 86.42 86.44 86.62 86.91 87.1986.74 86.34 86.18 86.19 86.36 86.64 86.9286.54 86.11 85.94 85.93 86.10 86.37 86.6586.35 85.88 85.70 85.68 85.83 86.10 86.3786.15 85.66 85.46 85.43 85.57 85.83 86.1085.97 85.44 85.22 85.18 85.31 85.56 85.8485.78 85.23 84.99 84.94 85.06 85.30 85.5785.61 85.01 84.75 84.69 84.80 85.03 85.3085.43 84.80 84.52 84.45 84.55 84.77 85.0385.26 84.60 84.30 84.21 84.30 84.51 84.7785.09 84.39 84.07 83.97 84.05 84.25 84.5184.93 84.19 83.85 83.73 83.80 83.99 84.2484.77 83.99 83.63 83.50 83.55 83.74 83.9884.61 83.80 83.41 83.26 83.30 83.48 83.7284.46 83.61 83.19 83.03 83.06 83.23 83.4784.31 83.42 82.98 82.80 82.82 82.98 83.2184.16 83.23 82.76 82.57 82.58 82.73 82.9584.02 83.05 82.56 82.35 82.34 82.48 82.7083.88 82.87 82.35 82.12 82.10 82.23 82.4583.74 82.70 82.14 81.90 81.87 81.99 82.1983.61 82.53 81.94 81.68 81.63 81.74 81.9483.48 82.36 81.74 81.46 81.40 81.50 81.7083.36 82.19 81.55 81.25 81.17 81.26 81.4583.24 82.03 81.35 81.03 80.94 81.02 81.2083.12 81.87 81.16 80.82 80.72 80.78 80.9683.01 81.71 80.98 80.61 80.49 80.55 80.7182.89 81.56 80.79 80.40 80.27 80.31 80.4782.79 81.41 80.61 80.20 80.05 80.08 80.23
82.68 81.26 80.43 79.99 79.83 79.85 79.9982.58 81.12 80.25 79.79 79.61 79.62 79.7682.48 80.98 80.08 79.59 79.40 79.39 79.5282.38 80.84 79.91 79.40 79.18 79.17 79.2882.29 80.71 79.74 79.20 78.97 78.94 79.0582.20 80.58 79.57 79.01 78.76 78.72 78.8282.11 80.45 79.41 78.82 78.55 78.50 78.5982.03 80.33 79.25 78.64 78.35 78.28 78.3681.95 80.21 79.09 78.45 78.14 78.06 78.1381.87 80.09 78.94 78.27 77.94 77.85 77.9181.79 79.97 78.79 78.09 77.74 77.63 77.6881.72 79.86 78.64 77.91 77.54 77.42 77.4681.64 79.75 78.49 77.74 77.35 77.21 77.2481.57 79.64 78.35 77.57 77.16 77.00 77.0281.51 79.54 78.21 77.40 76.96 76.79 76.8081.44 79.44 78.07 77.23 76.77 76.59 76.5881.38 79.34 77.94 77.07 76.59 76.38 76.3781.32 79.24 77.81 76.90 76.40 76.18 76.1581.26 79.15 77.68 76.75 76.22 75.98 75.9481.20 79.06 77.55 76.59 76.04 75.78 75.7381.15 78.97 77.43 76.43 75.86 75.59 75.5281.10 78.88 77.31 76.28 75.68 75.39 75.3181.05 78.80 77.19 76.13 75.51 75.20 75.1181.00 78.72 77.07 75.99 75.34 75.01 74.90
0.24 0.26 0.28 0.3 0.32 0.34 0.36
100.00 100.00 100.00 100.00 100.00 100.00 100.0099.70 99.70 99.70 99.70 99.70 99.70 99.7099.39 99.39 99.39 99.39 99.39 99.39 99.3999.09 99.09 99.09 99.09 99.09 99.09 99.0998.79 98.79 98.79 98.79 98.79 98.79 98.7999.92 99.92 99.92 99.92 99.92 99.92 99.9299.62 99.62 99.62 99.62 99.62 99.62 99.6299.32 99.32 99.32 99.32 99.32 99.32 99.3299.01 99.01 99.01 99.01 99.01 99.01 99.0198.71 98.71 98.71 98.71 98.71 98.71 98.7198.41 98.41 98.41 98.41 98.41 98.41 98.4198.11 98.11 98.11 98.11 98.11 98.11 98.1197.82 97.82 97.82 97.82 97.82 97.82 97.8297.52 97.52 97.52 97.52 97.52 97.52 97.5297.22 97.22 97.22 97.22 97.22 97.22 97.2296.93 96.93 96.93 96.93 96.93 96.93 96.9396.64 96.64 96.64 96.64 96.64 96.64 96.6496.34 96.35 96.35 96.35 96.35 96.35 96.3596.05 96.05 96.05 96.05 96.05 96.05 96.0595.76 95.76 95.77 95.77 95.77 95.77 95.7795.47 95.48 95.48 95.48 95.48 95.48 95.4895.19 95.19 95.19 95.19 95.19 95.19 95.1994.90 94.90 94.90 94.90 94.90 94.90 94.9094.61 94.62 94.62 94.62 94.62 94.62 94.6294.33 94.33 94.33 94.33 94.33 94.33 94.3394.04 94.05 94.05 94.05 94.05 94.05 94.0593.76 93.77 93.77 93.77 93.77 93.77 93.7793.47 93.48 93.49 93.49 93.49 93.49 93.4993.19 93.20 93.21 93.21 93.21 93.21 93.21
92.91 92.92 92.93 92.93 92.93 92.93 92.9392.62 92.64 92.65 92.65 92.65 92.65 92.6592.34 92.37 92.37 92.37 92.37 92.37 92.3792.06 92.09 92.10 92.10 92.10 92.10 92.1091.78 91.81 91.82 91.82 91.82 91.82 91.8291.50 91.54 91.55 91.55 91.55 91.55 91.5591.23 91.26 91.27 91.28 91.28 91.28 91.2890.95 90.99 91.00 91.00 91.01 91.01 91.0190.67 90.72 90.73 90.73 90.73 90.73 90.7390.39 90.44 90.46 90.46 90.47 90.47 90.4790.12 90.17 90.19 90.20 90.20 90.20 90.2089.84 89.90 89.92 89.93 89.93 89.93 89.9389.57 89.63 89.65 89.66 89.66 89.66 89.6689.29 89.36 89.39 89.40 89.40 89.40 89.4089.02 89.09 89.12 89.13 89.13 89.13 89.1388.74 88.83 88.86 88.87 88.87 88.87 88.8788.47 88.56 88.59 88.60 88.61 88.61 88.6188.20 88.29 88.33 88.34 88.34 88.35 88.3587.93 88.03 88.07 88.08 88.08 88.09 88.0987.66 87.76 87.80 87.82 87.82 87.83 87.8387.39 87.50 87.54 87.56 87.57 87.57 87.5787.12 87.23 87.28 87.30 87.31 87.31 87.3186.85 86.97 87.02 87.04 87.05 87.05 87.0586.58 86.71 86.76 86.79 86.80 86.80 86.8086.32 86.44 86.51 86.53 86.54 86.54 86.5486.05 86.18 86.25 86.28 86.29 86.29 86.2985.78 85.92 85.99 86.02 86.03 86.04 86.0485.52 85.66 85.74 85.77 85.78 85.79 85.7985.26 85.40 85.48 85.52 85.53 85.53 85.5484.99 85.14 85.23 85.26 85.28 85.28 85.2984.73 84.89 84.97 85.01 85.03 85.04 85.0484.47 84.63 84.72 84.76 84.78 84.79 84.7984.21 84.37 84.47 84.51 84.53 84.54 84.5483.95 84.12 84.22 84.27 84.29 84.29 84.3083.69 83.86 83.97 84.02 84.04 84.05 84.0583.44 83.61 83.72 83.77 83.79 83.80 83.8183.18 83.36 83.47 83.52 83.55 83.56 83.5682.93 83.10 83.22 83.28 83.31 83.32 83.3282.67 82.85 82.97 83.03 83.06 83.08 83.0882.42 82.60 82.72 82.79 82.82 82.83 82.8482.17 82.35 82.47 82.55 82.58 82.59 82.6081.92 82.10 82.23 82.30 82.34 82.35 82.3681.67 81.85 81.98 82.06 82.10 82.12 82.1281.42 81.61 81.74 81.82 81.86 81.88 81.8981.17 81.36 81.50 81.58 81.62 81.64 81.6580.92 81.11 81.25 81.34 81.38 81.41 81.4180.68 80.87 81.01 81.10 81.15 81.17 81.1880.43 80.62 80.77 80.86 80.91 80.94 80.95
80.19 80.38 80.53 80.62 80.68 80.70 80.7179.95 80.14 80.29 80.39 80.44 80.47 80.4879.71 79.90 80.05 80.15 80.21 80.24 80.2579.47 79.66 79.81 79.91 79.97 80.01 80.0279.23 79.42 79.57 79.68 79.74 79.78 79.7978.99 79.18 79.34 79.45 79.51 79.55 79.5678.76 78.94 79.10 79.21 79.28 79.32 79.3378.52 78.71 78.86 78.98 79.05 79.09 79.1178.29 78.47 78.63 78.75 78.82 78.86 78.8878.06 78.24 78.40 78.52 78.59 78.63 78.6577.83 78.00 78.16 78.29 78.36 78.41 78.4377.60 77.77 77.93 78.06 78.14 78.18 78.2177.37 77.54 77.70 77.83 77.91 77.96 77.9877.14 77.31 77.47 77.60 77.68 77.73 77.7676.92 77.08 77.24 77.37 77.46 77.51 77.5476.69 76.85 77.01 77.14 77.23 77.29 77.3276.47 76.63 76.79 76.92 77.01 77.07 77.1076.25 76.40 76.56 76.69 76.79 76.85 76.8876.03 76.18 76.33 76.47 76.57 76.63 76.6675.81 75.95 76.11 76.24 76.34 76.41 76.4475.59 75.73 75.89 76.02 76.12 76.19 76.2275.37 75.51 75.66 75.80 75.90 75.97 76.0175.16 75.29 75.44 75.58 75.68 75.75 75.7974.95 75.07 75.22 75.36 75.46 75.53 75.58
0.38 0.4
100.00 100.0099.70 99.7099.39 99.3999.09 99.0998.79 98.7999.92 98.4999.62 98.2899.32 98.0799.01 97.8598.71 97.6398.41 97.4098.11 97.1797.82 96.9497.52 96.7097.22 96.4696.93 96.2296.64 95.9796.35 95.7296.05 95.4895.77 95.2395.48 94.9795.19 94.7294.90 94.4694.62 94.2194.33 93.9594.05 93.6993.77 93.4493.49 93.1893.21 92.92
92.93 92.6692.65 92.4092.37 92.1492.10 91.8891.82 91.6291.55 91.3691.28 91.1091.01 90.8490.73 90.5890.47 90.3290.20 90.0689.93 89.8089.66 89.5589.40 89.2989.13 89.0388.87 88.7888.61 88.5288.35 88.2688.09 88.0187.83 87.7687.57 87.5087.31 87.2587.05 87.0086.80 86.7486.54 86.4986.29 86.2486.04 85.9985.79 85.7585.54 85.5085.29 85.2585.04 85.0084.79 84.7684.54 84.5184.30 84.2784.05 84.0383.81 83.7883.56 83.5483.32 83.3083.08 83.0682.84 82.8282.60 82.5982.36 82.3582.13 82.1181.89 81.8881.65 81.6481.42 81.4181.18 81.1780.95 80.94
80.72 80.7180.49 80.4880.26 80.2580.03 80.0279.80 79.7979.57 79.5679.34 79.3479.11 79.1178.89 78.8978.66 78.6678.44 78.4478.22 78.2277.99 77.9977.77 77.7777.55 77.5577.33 77.3377.11 77.1276.89 76.9076.68 76.6876.46 76.4676.24 76.2576.03 76.0375.81 75.8275.60 75.61
Dynamic Model of a Cross-Flow Heat Exchanger
This article will develop a dynamic model of a cross-flow heat exchanger from first principles, and then discretize the governing partial differential equation with finite difference approximations. It will then demonstrate how this equation can be implemented in Excel (or indeed any other math tool)
First Principles ModelingConsider liquid flowing (at mass flowrate F) through a length Δx of pipe (diameter D), subject to cooling by cross-flow air (at temperature Ta and heat transfer coefficient U)
A heat balance over time Δt gives the following.
Dividing by Δx and Δt and simplifying gives
As Δx and Δt tend to zero, we get the following parabolic partial differential equation
Equation 1
Finite Difference ApproximationA forward difference approximation for the first of temperature with respect to time is
Equation 2
A backward difference approximation for the first of temperature with respect to space is
Introduction
If you just want the Excel implementation, then click here, but I encourage you to read the rest of the article so you understand how the spreadsheet is implemented.
Equation 4
Substituting Equation 2 and 3 into Equation 1, and rearranging gives
Equation 4
We only need to know the temperature of the bar at time t (on the RHS of Equation 4) to calculate the temperature at time t + Δt (on the LHS of Equation 4).
Implementating in ExcelThis is how Equation 4 will be implemented in Excel
We will now discuss the individual steps in detail.
Step 1 - Specify your parameters, including your chosen time and space step. I've named the cells in Column C with the names in Column E. I'll use named values when entering Equation 4.
Step 2 - Create a column and row containing your space and time steps
Step 3 - Fill in your initial conditions at time t = 0 (this will be the inlet liquid temperature as specified in the parameters).
Step 4 - Insert your boundary conditions at distance x = 0 (this will be the inlet liquid temperature - the same as the initial condition).
Step 5 - Implement Equation 4 into the first empty cell (at t = Δt and x = Δx)
The techniques I've demonstrated above can be applied to many other challenges in science, engineering and math. If you have any requests, then let me know.
Step 5 - Copy this formula to all other times and positions. For my implementation, I go up to t = 1 and x = 0.4.
Dynamic Model of a Cross-Flow Heat Exchanger
This article will develop a dynamic model of a cross-flow heat exchanger from first principles, and then discretize the governing partial differential equation with finite difference approximations. It will then demonstrate how this equation can be implemented in Excel (or indeed any other math tool)
Consider liquid flowing (at mass flowrate F) through a length Δx of pipe (diameter D), subject to cooling by cross-flow air (at temperature Ta and heat transfer coefficient U)
As Δx and Δt tend to zero, we get the following parabolic partial differential equation
A forward difference approximation for the first of temperature with respect to time is
A backward difference approximation for the first of temperature with respect to space is
If you just want the Excel implementation, then click here, but I encourage you to read the rest of the article so you understand how the spreadsheet is implemented.
We only need to know the temperature of the bar at time t (on the RHS of Equation 4) to calculate the temperature at time t + Δt (on the LHS of Equation 4).
- Specify your parameters, including your chosen time and space step. I've named the cells in Column C with the names in Column E. I'll use named values when entering Equation 4.
- Create a column and row containing your space and time steps
- Fill in your initial conditions at time t = 0 (this will be the inlet liquid temperature as specified in the parameters).
- Insert your boundary conditions at distance x = 0 (this will be the inlet liquid temperature - the same as the initial condition).
- Implement Equation 4 into the first empty cell (at t = Δt and x = Δx)
The techniques I've demonstrated above can be applied to many other challenges in science, engineering and math. If you have any requests, then let me know.
- Copy this formula to all other times and positions. For my implementation, I go up to t = 1 and x = 0.4.
This article will develop a dynamic model of a cross-flow heat exchanger from first principles, and then discretize the governing partial differential equation with finite difference approximations. It will then demonstrate how this equation can be implemented in Excel (or indeed any other math tool)
If you just want the Excel implementation, then click here, but I encourage you to read the rest of the article so you understand how the spreadsheet is implemented.
- Specify your parameters, including your chosen time and space step. I've named the cells in Column C with the names in Column E. I'll use named values when entering Equation 4.
This article will develop a dynamic model of a cross-flow heat exchanger from first principles, and then discretize the governing partial differential equation with finite difference approximations. It will then demonstrate how this equation can be implemented in Excel (or indeed any other math tool)