Students will learn how exchanger flow arrangement affects the temperature driving force, required heat-transfer area, and estimated equipment purchase cost. They will calculate the countercurrent log-mean temperature difference and the chart coordinates (R) and (S), obtain the correction factor (FT), and apply Seider's fixed-head exchanger cost correlation. They will also check the correlation's valid area range and distinguish purchase cost from installed capital cost.

MATLAB lets students carry their chart reading through the area and cost calculations, then plot how both estimates change over a range of hypothetical (FT) values. Students must interpret the plot, judge whether the proposed exchanger arrangement is appropriate, and identify information the preliminary cost model does not capture. They communicate their reasoning in a short design note that reports their calculations, assumptions, and recommended next design check.

This activity was developed for Process Design I, an upper-level undergraduate chemical engineering course at Howard University. It is designed for pairs during an 80-minute class, though students can complete it individually as an assignment. The activity fits after students have encountered energy balances, heat-exchanger duty, the log-mean temperature difference, and basic shell-and-tube configurations. It introduces or reinforces preliminary equipment cost estimation. Students use a correction-factor chart to size an exchanger, then use MATLAB and a correlation from Seider et al. textbook to estimate its purchase cost and examine how the correction factor affects that estimate.

Students should be able to work consistently with engineering units and distinguish an equipment purchase-cost estimate from the full installed capital cost. The supplied MATLAB starter script supports students with limited programming experience. Other instructors can adapt the activity by changing the stream conditions or extending the cost comparison to other exchanger types.

Students should be able to open and run sections of a MATLAB .m script, assign values to variables, use basic arithmetic and the built-in log and exp functions, and inspect results in the Command Window. The starter script introduces the vector calculations and plotting used for the sensitivity analysis, so prior experience with those steps is helpful but not required. No specialized toolbox is needed.

This is a 60–70 minute classroom activity completed in pairs. Before class, the instructor distributes the activity handout and MATLAB student script. Students first sketch the hot and cold stream temperature changes, calculate the countercurrent log-mean temperature difference and the ratios R and S, and read FT from the chart in the handout. They then complete the script to calculate exchanger area with and without the correction factor and estimate the fixed-head exchanger purchase cost using Seider's correlation.

Students use MATLAB to check the correlation's valid area range and plot how area and purchase cost respond to hypothetical values of FT. They finish with a short design note explaining the cost difference, whether the proposed arrangement is appropriate, and what remains to be checked before selecting equipment. An optional extension compares fixed-head, U-tube, and floating-head purchase costs. The calculations and plots could also be made in a spreadsheet or Python. MATLAB was chosen because students can edit a readable script, run it in sections, and use array calculations to explore the effect of an assumption immediately.

The cost and heat-transfer methods are drawn from Seider, W. D., Lewin, D. R., Seader, J. D., Widagdo, S., Gani, R., and Ng, K. M. (2017), Product and Process Design Principles: Synthesis, Analysis, and Evaluation, 4th ed., Wiley, Sections 12.2 and 16.5.

Handout for Heat Exchanger pricing assignment (Microsoft Word 2007 (.docx) 123kB Sep25 26)
MATLAB Code for Students (Matlab File 4kB Sep25 26)

Have students run the MATLAB script one section at a time and check their R, S, and chart reading before calculating cost. Common errors include reversing hot and cold temperature differences, using `log10` instead of MATLAB's natural-log function `log`, and entering area in m² when Seider's cost correlation requires ft². Accept small differences in FT due to chart reading if students use their value consistently. Reinforce that a very low FT calls for reconsidering the exchanger arrangement, and that the calculated Cp is an equipment purchase cost on the textbook's reference-index basis.

Assessment should consider the completed MATLAB script, labeled plot, and short design note. Students meet the goals when they calculate R, S, FT, area, and purchase cost correctly; check units and the correlation's valid range; and explain how the correction affects their design recommendation.

Seider, W. D., Lewin, D. R., Seader, J. D., Widagdo, S., Gani, R., and Ng, K. M. (2017). Product and Process Design Principles: Synthesis, Analysis, and Evaluation, 4th ed. Wiley. Section 12.2 provides the temperature-correction method; Section 16.5 provides the exchanger purchase-cost correlations.