An Analytical Study on the Performance and Feasibility of Converting a Combined Gas or Gas Propulsion System to a Combined Gas Turbine–Electric and Steam System for a Type 22 Frigate
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors propose and study the conversion of a gas turbine ship power plant to a combined gas and steam power plant. Their approach is thorough enough, including calculations for the assessment of their proposal from a technical point of view, selection of the required equipment for the realization of the conversion, as well as estimatinon of their weight and size.
This reviewer has the opinion that the paper needs major revision. A significant remark is that, while the authors describe how to calculate the required heat exhanger area A by eq. (14), results about this quantity are missing!
There is also a lot of remarks, questions to be asked and points to be clarified for the potential reader. These are given below.
1) Page 5: It is not clear why minT8=250 deg while the allowable temperature due to dew point is 135 deg.
2) Page 5: The authors check that pinch point temperature difference is above zero. If I anderstand well, they do not define ΔTpp for example to be 10 deg. In addition, is the location of Pinch Point checked after the calculation? Are the authors sure that the relevant temperature difference is ΔTpp=(T7-T2) and not (T4-T3) in some cases? Please provide some clarifications on the operations concerning the pinch point.
3) In eq. (6) m should be mw.
4) The text provides the information that the boiler mass is 2060kg for p=20bar (also the condenser mass is 800kg, why?). What kind of correlation has been used to estimate the weight of the boiler with respect to the steam pressure? There is a whole curve in Fig. 10. How the information on boiler mass in this plot has been produced? In addition, add the value of 2671kg in the plot for p=40bar.
5) The fact that the power of the main engine is reduced as a side effect of using a steam boiler due to back pressure change is mentioned somewhere. However, it has not been taken into account in the calculations. It has been assumed to be constant and equal to the nominal value. Have I understood well?
6) The description of the procedure to estimate heat transfer area A is not clear. First of all, is eq. (13) valid for a phase-changing heat exchanger? The formulas for and values of NTU for the economizew, superheater LQB, HQB parts of the heat exchanger are different? Various A are calculated and then are summed? A (or better Ao?) seems to be calculated from eq. (14), where Uo is required. For the latter eq. (17) is used given in the appendix. However, this formula requires Ai and Ao. Please explain the procedure or the assumptions missing. In addition, provide the correlation used for hi and ho.
7) There are no explicit conclusions in the text under a relevant title. They are rather in the last paragraph of section 3.2 System weight and size. The structure of the text has to be revised. Furthermore, it is claimed in this last paragraph that the overall weight of the system is 7360kg. How this has been estimated?
8) Q in eq. (1) and (2) could have a subscript B, i.e QB due to Boiler, while in eq. (6) it could be QC due to Condenser.
9) Section 2.4 should be renumbered to 2.3.
10) It is not clear how eq. (15) is used. This reviewer thinks that section '2.3 Heat Exchanger Dimensioning' should be thoroughly rewritten. It is not clear!
11) The thoughts in lines 181-183, page 6 are the reasoning for defining the low pressure of the cycle. This reasoning should be mentioned in line 121-123, page 4, where reference t the low pressure of the cycle is made.
Comments on the Quality of English LanguageThe use of English language is generally of a good level. Minor editing is required.
Author Response
Comment 1: Page 5: It is not clear why minT8=250 deg while the allowable temperature due to dew point is 135 deg.
Response 1: The temperature of 250 degrees is our suggestion to stay clear of the sulphur dioxide dew point of 135 degrees. The necessary clarification was made in lines 175-179.
Comment 2: Page 5: The authors check that pinch point temperature difference is above zero. If I anderstand well, they do not define ΔTpp for example to be 10 deg. In addition, is the location of Pinch Point checked after the calculation? Are the authors sure that the relevant temperature difference is ΔTpp=(T7-T2) and not (T4-T3) in some cases? Please provide some clarifications on the operations concerning the pinch point.
Response 2: The minimum ΔTpp=(T7-T2) we have set is 0. For every heat exchanger configuration presented in this paper, we checked that this is true. Text was slightly altered just after equation 2 to reflect this.
T4-T3 is of no concern, since T4 is the exhaust gas initial temperature, which is given by the ST40M functioning parameters (502 degrees), and T3 was a parameter we fixed, at 400 degrees.
Comment 3: In eq. (6) m should be mw.
Response 3: Eq 6 was modified. We also modified m in eq 3 since it uses the same parameter as eq 6.
Comment 4: The text provides the information that the boiler mass is 2060kg for p=20bar (also the condenser mass is 800kg, why?). What kind of correlation has been used to estimate the weight of the boiler with respect to the steam pressure? There is a whole curve in Fig. 10. How the information on boiler mass in this plot has been produced? In addition, add the value of 2671kg in the plot for p=40bar.
Response 4: The way the mass is calculated has been clarified in the heat exchanger dimensioning section (lines 280-292). In the same part, it is explained that the condenser mass was calculated using proportionality, and that it is considered fixed, regardless of the maximum steam pressure.
The weight values were removed from the figure and listed in full in a new table (Table 3).
Minor modifications were made in the writing to reflect these changes.
Comment 5: The fact that the power of the main engine is reduced as a side effect of using a steam boiler due to back pressure change is mentioned somewhere. However, it has not been taken into account in the calculations. It has been assumed to be constant and equal to the nominal value. Have I understood well?
Response 5: Yes, the effect of backpressure wasn't factored in because to calculate its actual impact we would have to analyze the performance of the ST40M, which is not the purpose of this paper. It is mentioned in the text (lines 311-312) that we consider pressure drops of less than 5% to have no significant effect.
Comment 6: The description of the procedure to estimate heat transfer area A is not clear. First of all, is eq. (13) valid for a phase-changing heat exchanger? The formulas for and values of NTU for the economizew, superheater LQB, HQB parts of the heat exchanger are different? Various A are calculated and then are summed? A (or better Ao?) seems to be calculated from eq. (14), where Uo is required. For the latter eq. (17) is used given in the appendix. However, this formula requires Ai and Ao. Please explain the procedure or the assumptions missing. In addition, provide the correlation used for hi and ho.
Response 6: Eq. (13) is valid for all four boiler sections, including for phase change. The only difference is that CR = 0, and thus a limit needs to be calculated to obtain the modified formula for NTU for the boiler section, which was omitted (the clarification has now been added to the manuscript).
Eq. (14) has been changed to generalize the formula. An additional sentence was added to explain the difference between Uo and Ui. Also, in the same paragraph, it is mentioned that these areas are calculated for each section, then summed at the end.
Eq. (16) is used after an initial value for the area Ao was obtained with the initial assumptions for Uo, in order to obtain a more accurate Uo. The area Ai is derived from Ao from simple geometry. Clarifications were added in the appendix section to reflect this, along with explanations on how hi and ho were obtained.
Comment 7: There are no explicit conclusions in the text under a relevant title. They are rather in the last paragraph of section 3.2 System weight and size. The structure of the text has to be revised. Furthermore, it is claimed in this last paragraph that the overall weight of the system is 7360kg. How this has been estimated?
Response 7: The results and discussoins section has been split in two: 3. Results and 4. Conclusions, with no subsections.
The overall weight was shown to be obtained from the mass of the boiler, turbine and condenser.
Comment 8: Q in eq. (1) and (2) could have a subscript B, i.e QB due to Boiler, while in eq. (6) it could be QC due to Condenser.
Response 8: The subscripts were added accordingly
Comment 9: Section 2.4 should be renumbered to 2.3.
Response 9: The section was renumbered
Comment 10: It is not clear how eq. (15) is used. This reviewer thinks that section '2.3 Heat Exchanger Dimensioning' should be thoroughly rewritten. It is not clear!
Response 10: The pressure drop is used as a guideline to determine how the boiler should be dimensioned. Eq. (15) is actually fully dependent on W, which gives a minimum for this value due to the imposed 5% condition and the free-flow area condition.
Sentences in the paragraphs following eq. 15 were slightly altered to improve understanding. If the section is still unclear, please specify which sentences are problematic.
Comment 11: The thoughts in lines 181-183, page 6 are the reasoning for defining the low pressure of the cycle. This reasoning should be mentioned in line 121-123, page 4, where reference t the low pressure of the cycle is made.
Response 11: Can you please provide more information about the connection between the two ideas? We are unsure what is missing in lines 121-123 (now shifted to lines 145-147). The 0.07 bar pressure was a design choice.
Reviewer 2 Report
Comments and Suggestions for AuthorsTOPIC:
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The manuscript "Analytical study on the performance and feasibility of converting a COGOG propulsion system to COGES for a Type 22 frigate" investigates the technical feasibility of upgrading a cruise gas turbine of a COGOG propulsion system of a frigate to a COGES system. It is proposed to exploit the hot exhaust gases leaving one of the cruise gas turbines as the energy source of a Rankine cycle, which in turn propels an electric generator.
The proposed combined cycle is compared in terms of efficiency to a system where the Rankine cycle is replaced by a recovery system that runs with hot-air.
A preliminary design of the Rankine cycle is proposed. A sensitivity analysis for the efficiency and size/weight of the combined cycle is carried out: the maximum pressure of the cycle is varied in the range 10 - 70 bar.
According to the Authors, "It was concluded that a system operating at a maximum steam pressure of 20 bar could increase the thermal efficiency of a cruise engine by 9.7% while adding a mass of 7.4 tons to the frigate. These findings suggest that upgrading to a COGES system could substantially improve the cruise range of the vessel."
REMARKS:
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1. In the Introduction it is stated that "A more energy efficient set up for each COGOG cruise engine are the COGES (combined gas turbine-electric and steam)..." and "They allow reclaiming some of the heat energy of the residual gases that leave the gas turbine and converting it into electric power (in the case of the COGES system)....". This would suggest that the original propulsion system would be changed from [gas turbine --> shaft power] to [gas turbine --> electric generator --> electric engine --> shaft power]. Yet, I could find no mention to the efficiency and space occupation of the additional generators and electric engines. Furthermore, the needs of electric power onboard are not addressed: does the additional electric power provided by the steam turbine match these needs? This, in turn, has implications on the need of maintaining, substituting or eliminating the existing electric generators and on the associated space occupation and weight. The Authors must be more specific in the presentation of the proposed layout. A block diagram would be beneficial.
2. Eq. (16): the power output "P" << for the COGES system (is) the sum between the engine’s and steam turbine’s power output >>. I wonder why the efficiency of the electric generator [and that of the electric engine, if the generated electric power is used for propulsion, though this does not seem the case] has been disregarded.
3. The manuscripts lacks of a section "Concluding Remarks". The material on lines 355 -- 369 could serve to this purpose.
4. Line 202: adiabatically --> iso-entropically
5. Line 227: constant --> parameter
6. The preliminary design of the Rankine cycle and of the ancillary devices has been reviewed and seems flawless.
7. It must be EXPLICITLY stated whether the proposed design refers to the upgrade of a single cruise engine or to both cruise engines. I would suggest to clarify this issue in the Introduction. Furthermore, it must be EXPLICITLY declared whether the auxiliary devices to be installed if both cruise engines would be upgraded could be accommodated onboard.
8. Eq. (15) returns a dimensionless pressure drop (actual pressure drop scaled by the inlet pressure). This should be explicitly declared when first addressing equation (15).
9. The intake and the discharge seawater temperatures into/from the condenser are not specified. Though, the discharge temperature should be regulated to limit the thermal pollution (as is the case for land sources, see e.g. the "Protocol on the Protection of the Marine Environment of the Black Sea from Land-Based Sources and Activities" issued from the "Commission on the Protection of the Black Sea Against Pollution").
MINOR GRAMMATICAL ISSUES:
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1. Line 54: highspeed --> high-speed
2. Line 162: be --> by
3. Line 164: faze --> phase
4. Line 320: operating and higher maximum --> operating at higher maximum
Comments on the Quality of English Language
The quality of English language is adequate. A minor grammar- and spell-check is required.
Author Response
Comment 1: In the Introduction it is stated that "A more energy efficient set up for each COGOG cruise engine are the COGES (combined gas turbine-electric and steam)..." and "They allow reclaiming some of the heat energy of the residual gases that leave the gas turbine and converting it into electric power (in the case of the COGES system)....". This would suggest that the original propulsion system would be changed from [gas turbine --> shaft power] to [gas turbine --> electric generator --> electric engine --> shaft power]. Yet, I could find no mention to the efficiency and space occupation of the additional generators and electric engines. Furthermore, the needs of electric power onboard are not addressed: does the additional electric power provided by the steam turbine match these needs? This, in turn, has implications on the need of maintaining, substituting or eliminating the existing electric generators and on the associated space occupation and weight. The Authors must be more specific in the presentation of the proposed layout. A block diagram would be beneficial.
Response 1: Thank you for pointing this out. To make this analysis more grounded in real life applications, we now consider that the additional power generated using a COGES arrangement is used to power the auxiliary systems of the ship, in order to reduce the fuel consumption of the ship's power generators.
To reflect this, changes were made throughout the paper as follows:
- The impact of the findings was modified in the abstract in lines 23-26
- Clarifications about the differences in COGES and COGAS systems have been made in lines 77-80
- The aim of the study is pointed out again in the last part of the introduction
- The beginning of the results section was reorganized and rewritten
- The conclusion section was rewritten
Comment 2: Eq. (16): the power output "P" << for the COGES system (is) the sum between the engine’s and steam turbine’s power output >>. I wonder why the efficiency of the electric generator [and that of the electric engine, if the generated electric power is used for propulsion, though this does not seem the case] has been disregarded.
Response 2: This has been adjusted according to the response to comment 1. The paragraph on efficiency in the results section was removed.
Comment 3: The manuscripts lacks of a section "Concluding Remarks". The material on lines 355 -- 369 could serve to this purpose.
Response 3: Split the last chapter by adding a conclusions section
Comment 4: Line 202: adiabatically --> iso-entropically
Response 4: changed accordingly
Comment 5: Line 227: constant --> parameter
Response 5: changed accordingly
Comment 6: The preliminary design of the Rankine cycle and of the ancillary devices has been reviewed and seems flawless.
Response 6: -
Comment 7: It must be EXPLICITLY stated whether the proposed design refers to the upgrade of a single cruise engine or to both cruise engines. I would suggest to clarify this issue in the Introduction. Furthermore, it must be EXPLICITLY declared whether the auxiliary devices to be installed if both cruise engines would be upgraded could be accommodated onboard.
Response 7: In line with the response for comment 1, modifications were made to explicitly state that the upgrade is proposed for a single engine. Lines 415-419 in the conclusion section mention the possibility of upgrading a second engine.
Comment 8: Eq. (15) returns a dimensionless pressure drop (actual pressure drop scaled by the inlet pressure). This should be explicitly declared when first addressing equation (15).
Response 8: It was clarified that the formula outputs the pressure drop in relation to the inlet pressure in %
Comment 9: The intake and the discharge seawater temperatures into/from the condenser are not specified. Though, the discharge temperature should be regulated to limit the thermal pollution (as is the case for land sources, see e.g. the "Protocol on the Protection of the Marine Environment of the Black Sea from Land-Based Sources and Activities" issued from the "Commission on the Protection of the Black Sea Against Pollution").
Response 9: We consulted the "Commissions on the Protection of the Black Sea Against Pollution" and they stated that "The Contracting Parties shall take individually or, when necessary, jointly, all appropriate measures to prevent, reduce and control pollution of the marine environment of the Black Sea from vessels in accordance with generally accepted international rules and standards." regarding pollution from vessels. With this in mind, when we clarified this topic in our manuscript we referred to other publications on this topic.
The minor grammatical issues mentioned were addressed accordingly.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe paper entitled "Analytical study on the performance and feasibility of converting a COGOG propulsion system to COGES for a Type 22 frigate" deals with a combined gas turbine-electric and steam (COGES) system. The following issues should be addressed:
1. The English language should be improved to ensure the clarity and readability of the manuscript.
2. The abstract should have information about the key research findings.
3. The main objective of the paper must be written more clearly and concisely at the end of the introduction section.
4. A Research gap should be delivered more clearly with the directed necessity for the conducted research work. Try to make a comparative analysis or discussion with similar works.
5. The literature review should be strengthened. To ensure the completeness of the literature survey, I suggest referring also to the following papers:
Shi, H., Zheng, R., Zhang, Q., Yuan, J., Wang, R., Cheng, M., & Zou, Y. (2023). Numerical investigation of multi-nozzle ejector device with inclined nozzles for marine gas turbine. Brodogradnja: An International Journal of Naval Architecture and Ocean Engineering for Research and Development, 74(4), 1-16.
Tuswan, T., Sari, D. P., Muttaqie, T., Prabowo, A. R., Soetardjo, M., Murwantono, T. T. P., ... & Yuniati, Y. (2023). Representative application of LNG-fuelled ships: a critical overview on potential GHG emission reductions and economic benefits. Brodogradnja: An International Journal of Naval Architecture and Ocean Engineering for Research and Development, 74(1), 63-83.
Gospić, I., Martić, I., Degiuli, N., & Farkas, A. (2022). Energetic and ecological effects of the slow steaming application and gasification of container ships. Journal of marine science and engineering, 10(5), 703.
6. The term "engine" should be replaced with "gas turbine".
7. The term "residual gas" should be replaced with " exhaust gas".
8. The statement (lines 91-94) is incorrect and opposite to the arrangement of the exhaust system shown in Figures 7 and 8.
9. The saturation temperature for water at 0.07 bar is 39 degrees Celsius, not 40, (line 127).
10. Instead of "boiler outlet temperature" it should be "superheat vapor temperature" (line 132).
11. In Figures 5 and 6, the dependence of fluid temperature on the heat transfer area (not temperature evolution) should be shown. The dependence of fluid temperature on the heat transfer area has an exponential character (not straight lines as are shown, that is correct only if fluid temperature is constant).
12. Instead of thermal energy, it should be heat flux (in line 159).
13. Instead of specific latent heat of vaporization, it should be specific heat vaporization (in line 164),
14. Since specific heat capacities of hot water in the economizer as well as vapor in the superheater depend on the temperatures, in Equation (2) corresponding specific heats must be given as differences of specific enthalpies.
15. In conclusion please explain how your work advances the present state of knowledge. Please, be more effective in the conclusion paragraph.
16. It is highly recommended to highlight the novelty of the paper. The novelty of the research should be more clearly addressed and discussed.
Comments on the Quality of English Language
Moderate editing of the English language is required.
Author Response
Comment 1: The English language should be improved to ensure the clarity and readability of the manuscript.
Response 1: Several lines in the text were changed to improve clarity. If needed, please mention specific sentences where the clarity is still an issue.
Comment 2: The abstract should have information about the key research findings.
Response 2: The key findings were reformulated at the end of the abstract.
Comment 3: The main objective of the paper must be written more clearly and concisely at the end of the introduction section.
Response 3: The last part of the introduction section has been rewritten (lines 109-138).
Comment 4: A Research gap should be delivered more clearly with the directed necessity for the conducted research work. Try to make a comparative analysis or discussion with similar works.
Response 4: A paragraph was added in lines 420-425 in the conclusion to address this.
Comment 5: The literature review should be strengthened. To ensure the completeness of the literature survey, I suggest referring also to the following papers:
Shi, H., Zheng, R., Zhang, Q., Yuan, J., Wang, R., Cheng, M., & Zou, Y. (2023). Numerical investigation of multi-nozzle ejector device with inclined nozzles for marine gas turbine. Brodogradnja: An International Journal of Naval Architecture and Ocean Engineering for Research and Development, 74(4), 1-16.
Tuswan, T., Sari, D. P., Muttaqie, T., Prabowo, A. R., Soetardjo, M., Murwantono, T. T. P., ... & Yuniati, Y. (2023). Representative application of LNG-fuelled ships: a critical overview on potential GHG emission reductions and economic benefits. Brodogradnja: An International Journal of Naval Architecture and Ocean Engineering for Research and Development, 74(1), 63-83.
Gospić, I., Martić, I., Degiuli, N., & Farkas, A. (2022). Energetic and ecological effects of the slow steaming application and gasification of container ships. Journal of marine science and engineering, 10(5), 703.
Response 5: We integrated references to these publications in a paragraph at the end of the introduction section as additional ways to increase the overall frigate's efficiency alongside the conversion to a COGES system (lines 113-124).
Comment 6: The term "engine" should be replaced with "gas turbine".
Response 6: changed accordingly
Comment 7: The term "residual gas" should be replaced with " exhaust gas".
Response 7: changed accordingly
Comment 8: The statement (lines 91-94) is incorrect and opposite to the arrangement of the exhaust system shown in Figures 7 and 8.
Response 8: Can you please elaborate on why the arrangement is wrong? We have reviewed the lines mentioned and we believe they are consistent with our analysis.
Comment 9: The saturation temperature for water at 0.07 bar is 39 degrees Celsius, not 40, (line 127).
Response 9: Changed accordingly; Calculation for the condenser were made using the correct value of 39 degrees, the wrong number only appeared in the manuscript. An additional comment was made for the entry temperature of the boiler
Comment 10: Instead of "boiler outlet temperature" it should be "superheat vapor temperature" (line 132).
Response 10: changed accordingly
Comment 11: In Figures 5 and 6, the dependence of fluid temperature on the heat transfer area (not temperature evolution) should be shown. The dependence of fluid temperature on the heat transfer area has an exponential character (not straight lines as are shown, that is correct only if fluid temperature is constant).
Response 11: Figures 5 and 6 are simplified illustrations that help to visualise the heat transfer process; no calculations are made based on these figures. The captions have been modified to reflect this.
Comment 12: Instead of thermal energy, it should be heat flux (in line 159).
Response 12: changed accordingly
Comment 13: Instead of specific latent heat of vaporization, it should be specific heat vaporization (in line 164),
Response 13: changed accordingly
Comment 14: Since specific heat capacities of hot water in the economizer as well as vapor in the superheater depend on the temperatures, in Equation (2) corresponding specific heats must be given as differences of specific enthalpies.
Response 14: When doing the calculations the difference in specific heat capacity was taken into account. We added "w" and "s" as a subscript in order to make it more clear.
Comment 15: In conclusion please explain how your work advances the present state of knowledge. Please, be more effective in the conclusion paragraph.
Response 15: This issue was addressed in the paragraph mentioned in the answer to comment 4.
Comment 16: It is highly recommended to highlight the novelty of the paper. The novelty of the research should be more clearly addressed and discussed.
Response 16: This issue was addressed in the paragraph mentioned in the answer to comment 4.
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThe manuscript has been significantly improved and my comments duly addressed.
Author Response
Thank you for the feedback!
Reviewer 3 Report
Comments and Suggestions for Authors
I thank the authors for addressing my comments. However, the following issues should be addressed:
In the marine waste heat recovery steam generators (WHRSG, or marine utilization boilers on the exhaust gas), exhaust gases stream through a duct (which is mainly a rectangular cross-section, as shown in Figures 7 and 8) around tube bundles economizer, evaporator, and superheater where no baffles exist (which is characteristic for a classic shell and tube exchanger like that shown in Figures 4).
For that reason, it is very important that instead of the shell side, you use the duct side, as well as the ejected baffles that do not exist in WHRSG (because of the unacceptable pressure drop of exhaust gas that consequently decreases gas turbine efficiency|).
My remark concerning Figures 5 and 6 should be accepted due to the preservation of paper quality. Your statement about fluid temperature evaluation makes no sense. The title of Figures 5 and 6 should be the dependence of the fluid temperature on the heat transfer area.
Comments on the Quality of English LanguageModerate editing of the English language is required.
Author Response
Thank you for the clarifications!
Comment 1: In the marine waste heat recovery steam generators (WHRSG, or marine utilization boilers on the exhaust gas), exhaust gases stream through a duct (which is mainly a rectangular cross-section, as shown in Figures 7 and 8) around tube bundles economizer, evaporator, and superheater where no baffles exist (which is characteristic for a classic shell and tube exchanger like that shown in Figures 4).
For that reason, it is very important that instead of the shell side, you use the duct side, as well as the ejected baffles that do not exist in WHRSG (because of the unacceptable pressure drop of exhaust gas that consequently decreases gas turbine efficiency|).
Response 1: Between lines 95-98 we stated that through the duct (representing the shell-side) the exhaust gases pass around the tube bundles which contain the water/steam. We clarified that the shell-side is represented by the duct to eliminate this misunderstanding. We also now mentioned clearly that in a WHRSG there are no baffles.
Comment 2: My remark concerning Figures 5 and 6 should be accepted due to the preservation of paper quality. Your statement about fluid temperature evaluation makes no sense. The title of Figures 5 and 6 should be the dependence of the fluid temperature on the heat transfer area.
Response 2: The purpose of Figures 5 and 6 is to provide a visual representation of the statements between lines 164-170 (for figure 5) and 215-216 (for figure 6). Similar illustrations were seen in different academic publications. Changing them to show the dependence of the fluid temperature on the heat transfer area does not match with the purpose of those sections.
