Abstract
Thermal analysis of heat exchangers is crucial in both conventional and sustainable energy systems. However, traditional (non–dimensional) methods may be inadequate in certain scenarios, such as temperature or heat maps, pinch point prediction, two–phase or trans–critical flows. These challenges can be addressed using discrete thermal analysis methods, which allow for the numerical calculation of temperature and heat maps, or effectiveness values for heat exchangers having any complex flow patterns. This research introduces the Discrete Sub–Heat Exchanger (DSHE) method and demonstrates its application to the E–type shell–and–tube heat exchangers under defined NTU and Cr conditions. According to the application results, temperature and heat maps have been calculated successfully, with numerical effectiveness values closely matching analytical ones. Finally, sensitivity and error analyses in wide NTU and Cr ranges confirm the excellent applicability of the DSHE method with acceptable analytical error rates.
Data availability
All data generated or analyzed during this study are included in this published article. No external datasets were used.
Abbreviations
- C :
-
Heat capability [W/K]
- Cr :
-
Heat capability ratio
- N p :
-
Number of tube passes
- n :
-
Number
- ntu :
-
Number of transfer units of sub–heat exchanger
- NTU :
-
Number of transfer units
- \(\dot{Q}\) :
-
Heat transfer rate [W]
- T :
-
Temperature [°C]
- e :
-
Error rate
- P :
-
Thermal effectiveness
- R :
-
Heat capability ratio
- F :
-
Correction factor
- DSHE :
-
Discrete sub – heat exchanger
- E 2 STHE :
-
E–type shell–and–tube heat exchanger having two–tube passes
- TEMA :
-
Tubular Exchanger Manufacturers Association
- SS :
-
Shell – side fluid
- TS :
-
Tube – side fluid
- LMTD :
-
Logarithmic temperature mean difference
- spmd :
-
Single program, multi data
- analy :
-
Analytical
- min :
-
Minimum
- max :
-
Maximum
- sp :
-
Sub–heat exchanger pair
- r :
-
Rate
- p :
-
Parallel
- c :
-
Counter
- j :
-
Counter
- t :
-
Tube – side
- s :
-
Shell – side
- num :
-
Numerical
- I :
-
First law
- k :
-
Iteration number
- ε :
-
Effectiveness
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**Kubilay Bayramoğlu: ** Supervisor, Writing–Reviewing and Editing. **İbrahim KAYA: ** Conceptualization, Methodology, Modelling, Visualization, Investigation. **Yasin ÜST: ** Data Curation, Writing–Original draft preparation.
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Bayramoğlu, K., Kaya, I. & Ust, Y. Discrete thermal analysis of the E–type shell–and–tube heat exchanger. Sci Rep (2026). https://doi.org/10.1038/s41598-026-35215-z
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DOI: https://doi.org/10.1038/s41598-026-35215-z
