Shell-and-Tube Heat Exchanger Design (HE2): Sample Answer with Worked Iteration

For information and reference only – not to be submitted as your own work.

This heat exchanger design sample shows how a student might structure the calculation for the shell-and-tube heat exchanger HE2 design project, following Option 1 (HE2 designed alone). The brief’s flow-diagram values are not reproduced on the question page, so every input below is illustrative and must be replaced with your own figures. For the reasoning behind each step, read how to approach the heat exchanger design project.

Planning table

Percentages are suggestions only; check your brief for the marking scheme.

1. Illustrative inputs and assumptions

Water is placed on the tube side because it is the fouling-prone, higher-pressure stream and the velocity can be controlled by the pass count. The oil is on the shell side (Kern, 1950; Towler and Sinnott, 2022).

2. Energy balance

The duty is fixed from the oil side: Q = ṁ_oc_p,o(T_in − T_out) = 10.0 × 2,500 × 40 = 1.000 × 10⁶ W.

The water outlet follows from the same duty: ΔT_w = Q / (ṁ_wc_p,w) = 10⁶ / (12.0 × 4,200) = 19.84 K, so the water leaves at 39.84 °C.

3. LMTD and correction factor

For counter-current flow, ΔT₁ = 90 − 39.84 = 50.16 K and ΔT₂ = 50 − 20 = 30.00 K. The log-mean difference is (50.16 − 30.00) / ln(50.16 / 30.00) = 39.22 K.

For one shell pass and an even number of tube passes, R = (90 − 50) / 19.84 = 2.016 and P = 19.84 / (90 − 20) = 0.2834. The standard 1–2 expression (Bergman et al., 2017) gives F = 0.906, so the corrected mean difference is 0.906 × 39.22 = 35.52 K. An F value this far above 0.8 means the temperature profile is practical.

4. Iteration on the overall coefficient

The design used 19.05 mm OD tubes with 15.75 mm ID (1.65 mm wall), 4.88 m per pass, triangular pitch p_t = 1.25 × OD = 23.8 mm, and four tube passes. Four passes were chosen because two passes gave a water velocity of about 0.8 m/s, below the 1–2.5 m/s guidance on the question page. Check the tube dimensions against the standard-tube table in your brief.

4.1 Trial 1: assumed U = 400 W/m²·K

Required area A = Q / (U F ΔT_lm) = 10⁶ / (400 × 35.52) = 70.4 m². Area per tube = π × 0.01905 × 4.88 = 0.2921 m², so 241 tubes are needed, rounded up to 244 (a multiple of four passes), giving 61 tubes per pass.

Tube side. Velocity u = (12.0 / 995) / (61 × π × 0.01575² / 4) = 1.01 m/s. Re = ρud/μ = 19,879 and Pr = c_pμ/k = 5.69. Dittus–Boelter for a heated fluid, Nu = 0.023 Re^0.8 Pr^0.4 (Dittus and Boelter, 1985), gives Nu = 126.7, so h_i = 126.7 × 0.59 / 0.01575 = 4,745 W/m²·K.

Shell side. The bundle diameter is D_b = D_o(N_t/K₁)^1/n₁, with K₁ = 0.175 and n₁ = 2.285 for four passes on a 1.25 triangular pitch (Towler and Sinnott, 2022; confirm against your table). That gives D_b = 0.453 m. A clearance of 50 mm for a split-ring floating head (read from the brief’s chart or formula; 50 mm is assumed here) gives a shell diameter D_s = 0.503 m.

Taking baffle spacing B = 0.4 D_s = 0.201 m, the equivalent diameter is d_e = 1.10 (p_t² − 0.917 D_o²) / D_o = 13.5 mm. The cross-flow area is A_s = (p_t − D_o) D_s B / p_t = 0.0202 m², so G_s = 494.3 kg/m²·s and the shell-side velocity is 0.59 m/s.

Re_s = G_sd_e/μ = 5,572 and Pr = 22.2. The Kern-type correlation Nu = 0.36 Re^0.55 Pr^1/3 (Kern, 1950; Towler and Sinnott, 2022), with the viscosity-ratio term of Sieder and Tate (1936) taken as 1, gives Nu = 116.3 and h_o = 116.3 × 0.135 / 0.0135 = 1,161 W/m²·K.

The overall coefficient, referred to the outside area, is the sum of resistances: 1/U = 1/h_o + R_f,o + D_o ln(D_o/D_i) / 2k_w + R_f,iD_o/D_i + D_o/(D_ih_i). The calculated U is 627 W/m²·K, an error of +56.8% against the assumed 400. That is outside 0 to +20%, so the trial is rejected.

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4.2 Iteration table

Each trial repeats the steps above with a new assumed U. The values below were calculated from the same equations (illustrative figures).

Trial 3 passes by only 0.1 percentage points, which is too fragile if any input shifts slightly, so trial 4 is adopted. The coefficients rise with each trial because fewer tubes raise both velocities.

5. Final design check (trial 4)

With 152 tubes (38 per pass), the tube-side velocity is 1.63 m/s, Re = 31,911, Pr = 5.69 and h_i = 6,929 W/m²·K. On the shell side D_b = 0.368 m, D_s = 0.418 m, B = 0.167 m, A_s = 0.01399 m², G_s = 714.9 kg/m²·s, Re_s = 8,058 and h_o = 1,422 W/m²·K.

This gives U = 1 / 0.001356 = 737 W/m²·K and ε = (737 − 650) / 650 × 100 = +13.4%, which lies within the accepted 0 to +20% window. The shell-side film is the controlling resistance at about 52% of the total, which is typical when oil is the shell fluid.

The installed area is 152 × π × 0.01905 × 4.88 = 44.4 m². The area needed at the calculated U is 10⁶ / (737 × 35.52) = 38.2 m², a margin of 16%. The shell is slender (4.88 m long for a 0.418 m diameter, a ratio of about 11.7), so a student could discuss a shorter tube length with more tubes, in line with TEMA (2019) practice.

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6. Summary of the design (Option 1, illustrative)

For Option 2, the HE1 energy balance and the mixing condition (the two water outlets combining to the target temperature) would be added before step 2, giving m₁, m₂, m₃ and T₁, T₂, T₃. The rest of the method is unchanged.

When your own figures are ready, you can send your brief through the assignment submission page, or see the wider engineering assignment support available. Reference lists can also be checked with the citation and referencing check.

References

Bergman, T.L., Lavine, A.S., Incropera, F.P. and DeWitt, D.P. (2017) Fundamentals of heat and mass transfer. 8th edn. Hoboken, NJ: John Wiley & Sons.

Dittus, F.W. and Boelter, L.M.K. (1985) ‘Heat transfer in automobile radiators of the tubular type’, International Communications in Heat and Mass Transfer, 12(1), pp. 3–22.

Kern, D.Q. (1950) Process heat transfer. New York: McGraw-Hill.

Sieder, E.N. and Tate, G.E. (1936) ‘Heat transfer and pressure drop of liquids in tubes’, Industrial & Engineering Chemistry, 28(12), pp. 1429–1435.

Tubular Exchanger Manufacturers Association (TEMA) (2019) Standards of the Tubular Exchanger Manufacturers Association. 10th edn. Tarrytown, NY: TEMA.

Towler, G. and Sinnott, R. (2022) Chemical engineering design: principles, practice and economics of plant and process design. 3rd edn. Oxford: Butterworth-Heinemann.