Theory for Electrochemical Heat Sources and Exothermic Explosions: The Akbari–Ganji Method

Round 1

Reviewer 1 Report

The paper considers a timely problem for the user of lithium ion batteries, namely the possibility of their self-ignition and explosion due to exothermic reactions occurring within the piles. The subject of the study is certainly within the scope of the journal MDPI Electrochem.

Before the paper is accepted for publication, it has to be revised. Even the layout of the manuscript (e.g. different font sizes within the same sections) suggests that its contents has been subject to prompt modifications (most probably the authors tried to send the original version elsewhere, but it was rejected).

It is advisable that the authors do not act in haste and try to read their manuscript once again.

Sentences in lines 23-28 are quite general and most probably been used somewhere else than the second paragraph (lines29-36). There is no logical junction between the paragraphs. Line 24 “healing” or “heating”?

Line 30 – “to describe the exothermic reaction kinetics” (where, in what substances? – add this piece of information)

It is good that the authors review several papers from the context like in line 32, but just a simple mentioning of “electrochemical modeling of lithium-ion battery nail penetration” does not provide any information. Please either write say two sentences more, what was peculiar about that model and why you think it is relevant to the present paper, or cut out unnecessary references.

The same remark refers to the “mass citation” of several sources (line 36). Maybe this information is even trivial?

Line 41 – typo error “lithium”

Line 43 – maybe instead of “environment” there should be “surroundings” or “neighborhood”?

Try to keep the references like [11] here at the end of the sentence, in this way as they are now, they are distracting

Line 49 use a unified notation for the surname Frank-Kamenetskii in the whole text

Line 57 instead of “the same” use “these”

Lines 49-74  - this is a nice review, but again, please show the importance of these papers in the context of the present paper.

Line 118 – please add information how this nonlinear Equation (13) was derived

Lines 119-121 Too little information on the Ying-Buzu-Shu algorithm (the reader shall only learn that it is faster than the classical approaches, but what is the working principle of it? Another question: is it really so important that you solve a single nonlinear equation faster or slower, in fact for modern computers solutions of a single equation do not last longer than fractions of seconds, even for the usually slow bisection code they may be of the order of seconds. It follows you need to determine the value of theta2 once, so is it really a problem?

Lines 123-140. On the other hand, these descriptions are too long, since you do not use the derived expressions explicitly.

You can write sth. shorter, like

The nonlinear equation (5) may be effectively solved using homotopy method, as pointed out in the study by Anathaswamy et al. [11] or using the perturbation approach (Makinde et al. [10]. The expressions derived in the aforementioned papers are lengthy and the inexperienced users may encounter some convergence issues using them. Therefore we tackle the problem directly in our paper and propose to use the technique etc. etc.

The methods described in the aforementioned papers are used as reference in order to prove the correctness of our computations.

In the conclusion section do not write “This method can be 204 applied to infinite cylindrical and spherical geometries.” because you do not prove this in this paper. Rather summarize your achievements, like “we have proven that our approach based on … is equivalent to …”

“Future work shall be devoted to other geometries of practical importance like cylindrical and spherical ones”.

Generally, this paper is a good one, but you should also write sth. about its practical usefulness in the context of lithium batteries explosions.

I recommend a major revision.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

The article titled "Theory for Electrochemical Heat Sources and Exothermic Explosions: Akbari-Ganji’s Method" by Rajendran L. et. al., discusses a mathematical model for analyzing exothermic explosions in a slab involving electrochemical reactions. The authors explore the application of Akbari-Ganji's method to solve the nonlinear equation describing the temperature distribution within the slab. The paper delves into the effects of various parameters, such as the Frank-Kamenetskii parameter, activation energy, and numerical exponent, on the temperature profile. The presented results are compared with previous analytical and numerical findings, highlighting a satisfactory agreement between them.

Overall, the article presents a comprehensive theoretical exploration of exothermic explosions in electrochemical cells, offering insights into the mathematical modeling of the phenomenon and the application of Akbari-Ganji's method. The comparison with previous results and the discussion of parameter influences provides valuable insights for researchers studying exothermic reactions and thermal runaway in various contexts. I would be happy to recommend this article for publication in Electrochem journal after the authors address following critical questions-

1.     The introduction should be rewritten in a more formal way because currently it’s written in an informal way. The authors are suggested to write this part in a concise and lucid way. The authors need to be more consistent with formatting and using symbols. They have used E and e for activation energy and it’s misleading. The authors are strongly suggested to define every acronym at the first point of use.

2.     Could you explain the theoretical basis for choosing Akbari-Ganji's method as the preferred mathematical approach for solving the nonlinear equation in the context of exothermic explosions? What are the advantages of this method compared to other established techniques, such as the homotopy analysis method or perturbation methods?

3.     In the context of electrochemical cells, how does the presence of an exothermic reaction affect the cell's overall performance and safety? Can you provide a detailed explanation of how the reaction kinetics and heat generation within the cell contribute to potential hazards, and how your proposed model addresses these aspects?

4.     The article discusses the application of the Akbari-Ganji method to derive approximate analytical expressions for the temperature profile under various reaction mechanisms. How sensitive are these expressions to changes in the input parameters, such as activation energy, Frank-Kamenetskii parameter, and numerical exponent? Could you elaborate on the potential implications of parameter sensitivity on real-world scenarios?

5.     The paper emphasizes the comparison between the analytical results obtained through Akbari-Ganji's method and other existing analytical and numerical solutions. Can you provide a detailed discussion on the potential sources of discrepancies or limitations in the proposed method compared to these alternative approaches, particularly in cases of highly nonlinear or complex reaction kinetics?

6.     The study focuses on the specific geometry of a slab. How feasible would it be to extend the proposed methodology to more complex geometries commonly encountered in practical applications, such as cylindrical or spherical configurations? Are there any inherent challenges or adaptations required when applying the method to different geometries, and how might this impact the accuracy of the results?

7.     The article mentions the importance of the activation energy parameter in influencing the temperature profile. Could you elucidate the physical implications of varying the activation energy in the context of exothermic reactions? How does the activation energy parameter affect the initiation and progression of thermal runaway, and how does your model account for these effects?

8.     The work extensively references Frank-Kamenetskii's contributions to thermal explosion theory. Could you provide a deeper insight into the historical context of Frank-Kamenetskii's work and its significance in the field of exothermic reactions? How has your research built upon or extended the understanding established by Frank-Kamenetskii's theory?

9.     The article presents approximate analytical solutions for the temperature profile. In practical applications, accuracy is crucial. Could you discuss potential strategies for refining or improving the accuracy of the analytical solutions derived using Akbari-Ganji's method, especially in scenarios where experimental validation might be limited or challenging?

10.  Exothermic explosions in electrochemical cells have important safety implications. How might the insights gained from your study be practically applied to enhance the safety protocols and design considerations in industries that utilize electrochemical cells, such as energy storage or chemical processing?

A grammar check and spell check should be run throughout the article. The writing style should be more formal.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have improved their paper to much extent. In particular the weakest parts were reformulated. Of course, this manuscript might still be polished and further improved, but I think in the present paper it can be considered for publication. The main point of the paper is that the authors provided an alternative method to compute the nonlinear differential equation governing heat transfer in the considered cell (Eq.5). The method is shown to be stable and provide better accuracy than the existing ones.

The authors should comment in the text on the choice of values of parameters somewhere before Table 1, I mean how typical are the values chosen for computations. I think two significant digits after decimal points when talking about "errors" is enough (Tables 1-4).

There are some typo errors and most probably also language of the manuscript should be revised, if possible consult a native speaker.

Author Response

Please note attached document.

Reviewer 2 Report

I am satisfied with the authors response and definitely the changes/modifications have made significant improvement in the article. I am happy to recommend it for publication.

Author Response

Please refer to attached document.