2. (35 points) You are working on designing a heat exchanger to meet the following specification given. A shell-and-tube heat exchanger (one shell passes, two tube passes) will be used to heat 500 kg/h of pressurized water from 44C to 150C with 1000 kg/h of pressurized water entering the exchanger at 200C. The overall heat transfer coefficient for the proposed heat exchanger is 250 W/m.K. The heat exchanger surfaces are unfinned, and fouling is negligible. (a) Draw a sketch of the heat exchanger design (b) Use Table A.6 to find the specific heat of the water in the cold stream at the mean temperature, (C) Use Table A.6 and iterate to find the outlet temperature of the water in the hot stream and the specific heat the mean temperature. (d) Using the e-NTU approach, find the number of transfer units (NTU) for this heat exchanger. (e) Calculate the heat exchanger surface area (m) required to meet the design specifications given. Surface Tension, Expansion Coff- cient, B-107 (K) 9-10 Temper ature, T(K) CM (Nm) 75.5 75.3 748 74.3 73.7 -68.05 -32.74 46.04 114.1 1740 273.15 275 280 285 290 727 71.7 70.9 70,0 69.2 227.5 276.1 320.6 3619 400.4 295 300 305 310 315 TABLE A.6 Thermophysical Properties of Saturated Water Specific Heat of Specific Thermal Volume Vapor Heat Viscosity Conductivity Prandi Tempera (m/kg) ization, (kJ/kg-K) ( Nm') (W/mK) Number fure, T Pressure, (K) p(bars),10 (kJ/ke My10M, 10 ks 10 k10 Pr Pr. 273.15 0.00611 1.000 206,3 2502 4,217 1.854 1750 8.02 569 18.2 12.99 0.815 275 0.00697 1.000 181.7 2497 4.211 1.855 1652 8.09 574 18.3 12.22 0.817 280 0.00990 1.000 130.4 2485 4.198 1.858 1422 8.29 582 186 10.26 0.825 285 0.01387 1.000 99.4 2473 4.189 1.861 1225 8.49 590 18.9 8.81 0.833 290 0.01917 .001 69.7 2461 4.184 1.864 1080 8.69 598 19.3 7.56 0.841 295 0.026171.002 51.94 2449 4.181 1.868 959 8.89 606 19.5 6.62 0,849 300 0.03531 1.003 39.13 2438 4.179 1.872 855 9.09 613 19,6 5.83 0.857 305 0.04712 1.005 29.74 2426 4.178 1.877 769 9.29 620 20.1 5.20 0.865 310 0.06221 1.007 22.93 2414 4,178 1.882 695 9.49 628 20.4 4.62 0.873 315 0.08132 1.009 17.82 2402 4.179 1.888 631 9.69 634 20.7 4.16 0.883 320 0.1053 1.011 13.98 2390 4.180 1.895 577 9.89 640 21.0 3.77 0.894 325 0.1351 1.013 11.06 2378 4.182 1.903 528 10.09 645 21.3 3.42 0.901 330 0.1719 1,016 8.82 2366 4.184 1911 489 10.29 650 21.2 3.15 0.908 335 1.018 7.09 2354 4.186 1920 453 10.49 656 22.0 2.88 0.916 340 0.2713 1.021 5.74 2342 4.188 1.930 420 10.69 660 223 2.66 0.925 345 0,3372 1.024 4,683 2329 4.191 1.941 389 10.89 664 226 2.45 0.933 350 0.4163 1.027 3.846 2317 4.195 1.954 365 11.09 668 23.0 2.29 0.942 355 0.5100 1.030 3.180 2304 1.968 343 11.29 671 233 2.14 360 0.951 0.6209 1.034 2.645 2291 4.203 1.983 324 11.49 674 23.7 2.02 0.960 365 0.7514 1.038 2.212 2278 4.209 1.999 306 11.69 677 24.1 1.91 0.969 370 0.9040 1.041 1.861 2265 4,214 2.017 289 11.89 679 24.5 1.80 373.15 1.0133 1.044 1.679 0.978 2257 4.217 2.029 279 12.02 680 24.8 1.76 0.984 1.0815 1.045 1.574 2252 4.220 2.036 274 12.09 681 24.9 1.70 0.987 380 1.2869 1.049 1.337 2239 4.226 2057 260 12.29 683 25.4 385 1.61 0.999 1.5233 1.053 1.142 2225 4.232 2,080 248 12.49 685 25.8 1.53 1.004 390 1.794 1.058 0.980 2212 4239 2104 237 12.69 686 26,3 400 2.455 1.47 1.013 1.067 0.731 2183 4.256 2.158 217 13.05 688 27.2 410 3.302 1.34 1.033 1,077 0.553 2153 4278 2.221 200 13.42 688 28.2 420 4.370 1.088 0.425 1.24 1.054 2123 4.302 2.291 185 13.79 688 29.8 430 5,699 1.16 1.075 1.099 0.331 2091 4.331 2.369 173 14.14 685 30.4 1.09 1.10 Appendix A. Thermophysical Properties of Matter 68.3 67.5 66,6 65.8 64.9 436.7 471.2 504.0 535 5 566.0 320 325 330 335 340 0.2167 595.4 6242 4.199 64.1 63.2 623 61.4 60,5 6523 6979 59.5 58.9 58.6 57.6 56,6 375 345 350 355 360 365 370 373.15 375 380 385 190 400 410 707.1 728.7 750.1 761 788 814 841 896 952 1010 55.6 53.6 51.5 420 1003 472 430 TOOT Viscosity Surface Tension, Expansion Coeffi- cient, B,. 10 (K) 9, 10 TABLE A.6 Continued Specific Volume Tempera- (m/ka) ture, T Pressure (K) phars) w: 10 440 7.333 1.110 0.261 450 9.319 1.123 0.208 460 11.71 1.137 0.167 470 14.55 1.152 0.136 480 17.90 1.167 0.111 Temper (N/m) Heat of Vapor ization, hy (kJ/kg) 2059 2024 1989 1951 1912 2.46 4.40 15.19 43.1 42.9 40.7 38.5 36.2 490 500 510 520 530 21.83 26.40 31.66 37.70 44.58 1.184 1.203 1.222 1.244 1.268 0.0922 0,0766 0.0631 0.0525 0.0445 1870 1825 1779 1730 1679 Specific Heat (kJ/kg.) 436 2.56 4.44 2.68 4.48 2.79 4.53 2.94 4.59 3.10 4,66 3.27 4.74 3.47 4.86 3.70 4.95 3.96 5.08 4.27 5.24 4,64 5.43 5.09 5.68 5.67 6.00 6,40 33.9 316 293 26.9 245 540 Appendix A. Thermaphral Properties of Matter 52.38 61.19 71.08 82.16 94.51 1.296 1.323 1.355 1.392 1.433 550 Thermal Conductivity Prandt (Ns/m) (W/ mK) Number My 10 H, 109 kp-10 kg10 Pr Pr, 162 14.50 682 31.7 104 1.12 152 14.85 678 33.1 0.99 143 673 346 0.95 1.17 136 15.54 667 363 0.92 1.20 129 15.88 660 38.1 0.89 1.23 124 16.23 651 401 0.57 1.23 118 16.59 642 42.3 0.86 1.28 113 16.95 631 44.7 0:35 1.31 108 17.33 621 47.5 0.84 1.35 104 17.72 608 506 0.85 1.39 101 18.1 594 540 0.86 1.43 97 186 580 583 0.87 1.47 94 19.1 563 63.7 0.00 152 91 19.7 548 76.7 0.94 1.59 88 20.4 528 76,2 0.99 1.68 84 21.5 513 81 1.05 1.84 81 22.7 197 92.9 1.14 2.15 77 24.1 167 103 130 2.60 72 25.9 444 114 1.52 1.46 70 27.0 430 121 1.65 420 67 28.0 412 130 20 48 64 30.0 392 141 2.7 6,0 59 32.0 367 155 4.2 9.6 54 370 331 178 12 26 45.0 238 238 0.0375 0.0317 0.0269 0.0228 0.0193 | S wuwwwwmnnnn = $s 1622 1564 1499 1429 1353 IIIIIIIII 560 570 580 1181888 8888 88888 88888 8893 22.1 19.7 17.3 15.0 128 520 600 610 620 1083 123.5 1373 159.1 169.1 1.482 1.541 1.612 1.705 1.778 0.0163 0,0137 0.0115 0.0094 0.0085 1274 1176 1068 941 858 6,41 7.00 7.85 9.35 10.6 7.35 8.75 11.1 154 10.5 84 03 45 35 LIIT 625 18.3 1.856 1.935 2.075 2.31 3.170 640 645 630 179.7 6.15 190.9 202.7 215.2 647.3 221.2 "Adapted from Reference 22 "I hur 10 N/m Critical temperature 0.0075 0.0066 0.0057 0.0045 0.0032 126 16.4 26 90 781 03 560 361 0 22:1 27.6 42 26 13 0.5 0.1 0.0