Tools › Fluids and Heat Transfer › Heat Exchangers › Heat Exchanger Sizing and Pressure Drop › Example
Water-to-water 1-2 shell-and-tube exchanger: energy balance, LMTD with the Bowman–Mueller–Nagle F, Kern shell side, shell sized to the area, both pressure drops
| Tool | Heat Exchanger Sizing and Pressure Drop |
| Source | Bowman, R. A., Mueller, A. C., and Nagle, W. M. (1940). "Mean Temperature Difference in Design." Transactions of the ASME, Vol. 62, No. 4, pp. 283–294 (the 1-2 correction factor as mathematics); Kern, D. Q. (1950). Process Heat Transfer. McGraw-Hill, New York (shell-side method as mathematics, cited); U.S. Department of Energy (1992). DOE Fundamentals Handbook: Thermodynamics, Heat Transfer, and Fluid Flow, Volume 2 of 3. DOE-HDBK-1012/2-92 (LMTD and U_o examples used for the checks); Oak Ridge National Laboratory (1961). Heat Transfer and ΔP Design of MSRE Primary Heat Exchanger. ORNL CF-61-4-1; Segaser, C. L. (1952). Heat Exchanger Design Study for the ISHR. ORNL CF-52-10-195 (Kern shell-side pressure drops used for the checks). |
| Level | Undergraduate |
Problem
Cool 50,000 lb/h of water from 180 to 120 °F with 100,000 lb/h of water entering at 60 °F in a 1-2 shell-and-tube exchanger with 3/4 in 16 BWG tubes on a 15/16 in triangular pitch, 12 ft long, two tube passes, cold water in the tubes, carbon-steel tubes, 0.0005 h·ft²·°F/Btu fouling on each side, baffles at half the shell diameter with 25 % cut, 10 % over-design and 10 lb/in² allowable on each side. Find the duty and the cold outlet, the LMTD and F, the film coefficients, U clean and fouled, the area required, the shell diameter and tube count that provide it, and the two pressure drops.
Inputs to Enter
- Hot water 50,000 lb/h, 180 → 120 °F; cold water 100,000 lb/h, 60 °F in (outlet from the balance); water properties from IAPWS-IF97 at the mean bulk temperatures (150 °F and 75 °F)
- 1 shell pass, 2 tube passes; 0.75 in OD × 0.065 in wall tubes, PR 1.25 triangular, L 12 ft, shell-to-bundle clearance 0.5 in, pass lane 0.625 in, k_w 26 Btu/(h·ft·°F), R_f 0.0005 h·ft²·°F/Btu each side, roughness 0.00006 in
- Shell diameter, tube count and baffle spacing left blank (sized), B/D_s 0.5, cut 25 %, over-design target 10 %, allowable drops 10 lb/in² tube side and shell side, Dittus–Boelter in the tubes
Answers
- C_h = 49,990 Btu/(h·°F), C_c = 99,900 Btu/(h·°F); Q = 2,999,000 Btu/h; cold outlet 90.02 °F
- ΔT_1 = 89.98 °F, ΔT_2 = 60 °F, ΔT_lm = 73.98 °F; P = 0.2502, R = 1.999, F (Bowman 1-2 closed form) = 0.9420 (P_max for this R = 0.3822), F ΔT_lm = 69.69 °F
- Tubes (cold water): 76 tubes in 2 passes, v = 5.60 ft/s, Re = 29,370, Dittus–Boelter Nu = 180.4, h_i = 1,220 Btu/(h·ft²·°F); shell (hot water, Kern): a_s = 0.0694 ft², G_s = 720,000 lb/(h·ft²), D_e = 0.542 in, Re_s = 31,300, h_o = 1,203 Btu/(h·ft²·°F)
- U_clean = 487.4, U_fouled = 316.8 Btu/(h·ft²·°F); A_req = 135.8 ft² (clean 88.3 ft²); shell sized at 10 in ID with 76 tubes (lattice count; CTP/CL estimate 92), A_prov = 179.1 ft², over-surface 31.8 %; 27 baffles at 5 in
- ΔP tube side = 2.34 + 1.69 (returns) = 4.02 lb/in² (within 10); ΔP shell side (Kern, f = 0.2489 at Re_s 31,300, 28 crossings) = 9.45 lb/in² (within 10)
Notes
The tool's default inputs are this case; press Submit. The case is illustrative (stated on the page), not a printed example; the method is checked by test_heat_exchanger_sizing.php (653 checks) against the DOE handbook's LMTD (232 °F) and U_o (827.6) examples, the ORNL MSRE memorandum (LMTD 137 °F, TEMA 1-2 factor 0.965, tube-side Re and ΔP), the ORNL ISHR memorandum (Kern crossflow areas, Reynolds numbers, friction-chart readings and nine shell-side pressure drops within 2 %), the Bowman closed forms against the ε–NTU route and an independent numpy script, and Mason's crossflow series against a 2-D cell solution.