B50TE Heat Exchanger Design: Duty, LMTD and Tube-Side h (Reference Extract)

Modules coded B50TE (Heat Exchangers and Heat Transfer) typically ask for a justified TEMA AEU U-tube design (Tubular Exchanger Manufacturers Association, 2019) that recovers heat in a whisky-distillery setting: a hot, nearly alcohol-free by-product (pot ale) pre-heats the cold feed (wash, a roughly 9% ABV water–ethanol mixture). This extract covers the calculation spine that markers look for in the manual-check tasks: heat duty, temperature profile, LMTD with an F correction, tube-side coefficient from forced-convection correlations, and the area check. It does not reproduce any HTRI Xchanger output; the shell-side coefficient is an assumed placeholder, and your own report must use your own software results. The full brief is on our B50TE heat exchangers Assignment #1 question page.

1. Basis and assumptions (illustrative)

All values below are approximate working assumptions for demonstration, not measured data. Fluids stay liquid, the hot stream (pot ale, treated as water) is on the tube side, the wash is on the shell side, and the exchanger is modelled as identical 1-2 shells in series.

Tube geometry assumed: 19.05 mm outside diameter, 15.75 mm inside diameter, carbon-steel wall (k = 16 W/m·K), 60 tubes per pass, fouling resistance 0.0002 m²·K/W on each side, and a shell-side coefficient of 3,000 W/m²·K taken as a stand-in for the figure your software would report. The 9% ABV wash is about 7% ethanol by mass, so mixture properties are weighted estimates; in a real submission, take them from the property package and state the source.

2. Heat balance (duty)

Wash mass flow = 550/60/1000 × 975 = 8.94 kg/s. Duty Q = ṁcΔT = 8.94 × 4.10 × (70 − 35) = 1,282.5 kW. Pot ale mass flow is 8.89 kg/s, so its outlet temperature is 85 − 1,282.5/(8.89 × 4.19) = 50.6 °C.

The pot ale outlet (about 51 °C) is cooler than the wash outlet (70 °C). That is a temperature cross, which strongly limits what a single shell pass can do and drives the design decision in Section 3.

3. LMTD, correction factor and number of shells

Counter-current terminal differences are ΔT₁ = 85 − 70 = 15.0 K and ΔT₂ = 50.6 − 35 = 15.6 K, giving LMTD_cf = 15.29 K. The dimensionless groups are R = (85 − 50.6)/(70 − 35) = 0.984 and P = (70 − 35)/(85 − 35) = 0.70.

For one 1-2 shell the maximum attainable P at this R is 0.591, so P = 0.70 is impossible in one AEU shell. Splitting the duty over N identical shells in series reduces the P each shell must achieve; the standard F expression (Bowman et al., 1940; Kakaç et al., 2020) then gives:

The corrected mean difference is F × LMTD_cf = 0.896 × 15.29 = 13.69 K. A sensible report would also test what happens with a different pot ale flow. With the lower flow of 400 L/min, the pot ale outlet would be about 37.7 °C and a single shell could not exceed a wash outlet of about 59.8 °C, below the 66 °C requirement. That comparison shows markers why the flow rate and shell count were chosen, not just stated.

4. Tube-side heat transfer coefficient

Tube velocity v = Q_v/(N_t × A_flow) = 0.009167/(60 × 1.948×10⁻⁴) = 0.78 m/s. Reynolds number Re = ρvd/μ = 30,197, so the flow is fully turbulent. Prandtl number Pr = c_pμ/k = 2.54.

Dittus–Boelter form (cooling fluid, n = 0.3; Bergman et al., 2011): Nu = 0.023 Re^0.8 Pr^0.3 = 116.7, so h_i = Nu k/d = 4,891 W/m²·K.

Gnielinski (Gnielinski, 2010): f = (0.79 ln Re − 1.64)⁻² = 0.0236; Nu = (f/8)(Re − 1000)Pr / [1 + 12.7 √(f/8) (Pr^2/3 − 1)] = 137.2, giving h_i = 5,750 W/m²·K. Gnielinski is about 18% higher here, which is typical because it is valid for a wider Re range and is fitted to a friction factor. Compare whichever value you use with the software figure and explain any gap (property package, wall-temperature correction, tube-side model).

Mixture note: the hot stream here is treated as water because pot ale carries little ethanol. If the wash (the water–ethanol mixture) were on the tube side, use mixture density, viscosity, conductivity and specific heat at the mean bulk temperature, not a linear average of the pure-component values, because viscosity of water–ethanol is strongly non-linear.

5. Overall coefficient and area check

Referred to the outside area: 1/U_o = 1/h_o + R_f,o + d_o ln(d_o/d_i)/(2k_w) + R_f,i d_o/d_i + d_o/(d_ih_i). With the Gnielinski value, U_o = 910 W/m²·K; with Dittus–Boelter, 880 W/m²·K.

The two correlations differ by only about 3.4% in required area because the fouling and shell-side resistances dominate. Without the F correction the same duty would appear to need only 92.2 m², about 10% too small, which is the error a marker expects you to avoid. When you compare with a software area, discuss differences in shell-side coefficient, baffle arrangement, tube-count limits and the software’s own fouling treatment.

6. Trade-offs and parameter effects

Tube count per pass sets velocity (heat transfer and fouling) against pressure drop; the wash target sets duty and the temperature cross. The table varies each individually and together at the same assumptions (3 shells, Gnielinski basis).

Change A raises velocity and h_i by 27%, but the area only falls by 4% because other resistances remain; tubes lengthen by 28% and friction loss roughly doubles. Change B cuts duty by 11% and relaxes the cross, so F rises to 0.95 and area drops by about 34%, at the price of a cooler wash. Together the effects are not additive, since the lower duty also shortens the tubes needed. All friction losses sit well inside the 50 kPa allowance before nozzle and return losses, which you should still add.

Practical comment for a report: 0.78 m/s is modest for a stream with suspended solids, so a velocity-versus-fouling argument (or a supplementary-heating option if the 66 °C minimum cannot be guaranteed) should appear in the justification.

Companion guide: how to structure a shell-and-tube design report and what markers reward. Related: engineering report writing support.

About the expert

Reviewed by Nada Ahmed. Her profile lists Thermodynamics & Heat Transfer as her field and a Bachelor’s in Mechanical Engineering from Jumeirah College.

References

• Bergman, T. L., Lavine, A. S., Incropera, F. P., & DeWitt, D. P. (2011). Fundamentals of heat and mass transfer (7th ed.). Wiley.
• Bowman, R. A., Mueller, A. C., & Nagle, W. M. (1940). Mean temperature difference in design. Transactions of the ASME, 62, 283–293.
• Gnielinski, V. (2010). G1 Heat transfer in pipe flow. In VDI heat atlas (2nd ed., pp. 691–700). Springer.
• Kakaç, S., Liu, H., & Pramuanjaroenkij, A. (2020). Heat exchangers: Selection, rating, and thermal design (4th ed.). CRC Press.
• Tubular Exchanger Manufacturers Association. (2019). TEMA standards (10th ed.). TEMA.