Heat exchanger designs are still considered to be an experimental challenge and most approaches developed are empirical or semi-empirical with no adequate theoretical base nor enough understanding of the underlying phenomena. Powerful CFD and topology optimization techniques haven’t brought much progress in this area so far. And this wouldn’t be a problem if existing heat exchanger designs would perform near optimum or if heat exchange didn’t play a major role in worldwide energy utilization, electronics and power utilities. But none of this is the case; it has been estimated that in more than 80% of the worldwide energy utilization heat transfer is involved. Within the electronics industry, heat transfer is still considered as a major and fundamental bottleneck, especially for high performance and high power semiconductor technologies. Several other industries face similar limitations which can generally be characterized as having a poor ratio of heat flow versus the system volume and corresponding mass, and/or having a poor thermal efficiency.

In the next section various quotes (opinions) are included from scientists themselves referring to current progression within heat exchange in which fluid flow is involved. According to Tezzit, these opinions supports the validness to question (scientifically) the quality of the second law of thermodynamics. The second section contains the references.

**Thermodynamics** **knowledge base **

**Thermodynamics**

*Thermodynamics is the kingdom also of running current history as well as polemics, not to mention verbosity. In no other discipline have the same equations been published over and over again so many times by different authors in different ill-defined notations and therefore claimed as his own by each; in no other has a single author seen fit to publish essentially the same ideas over and over again within a period of twenty years; and nowhere else is the ratio of talk and excuse to reason and result so high. In no other part of mathematical physics have so many claims and counterclaims of priority been issued by the leading creators of the subject, and in no other have these same men turned aside from research to write historical papers or long historical notes within a decade or two of their first attacks on the theory itself. Small wonder then that histories and historical papers by secondary authors and historians abound, yet the field seems ever fresh to the newcomer.* (Truesdell, 1980)

*With Clausius’ formulation of the second law of thermodynamics, the conflict between thermodynamics and dynamics became obvious. There is hardly a single question in physics that has come more often and more actively discussed than the relation between thermodynamics and dynamics. Even now, a 150 years after Clausius, the question arouses strong feelings.* (Prigogine & Stengers, 1984)

*Perhaps, after all, the wise man’s attitude towards thermodynamics should be to have nothing to do with it. To deal with thermodynamics is to look for trouble. This is not the citation of a famous scientist, but the result of a deep cogitation following mere observations. Why do we need to get involved in a field of knowledge which, within the last hundred years, has exhibited the largest number of schizophrenics and megalomaniacs, imbalanced scientists, paranoiacs, egocentrists, and probably insomniacs and sleepwalkers? *(Maugin, 1999)

*The basic equation to describe the heat transfer at the interface between a solid surface at T, and a fluid at To by the use of a heat transfer coefficient is: q=-λdT/dy=α(T_s-T_0). In most textbooks this law is referred to as Newton’s cooling law, but it is really more a definition of a than a law. As Jakob (’53) stated, this magically simple equation was a grave handicap to progress in the field of heat transfer, because for a long time it had been assumed that a is a constant, which is clearly not the case. Now, forty years later, there is no doubt that very much progress has been made in heat transfer in general, but not so in the definition and the representation of the heat transfer coefficient. Apart from the problem with the non-constant α, the second and much more challenging problem is how to define T_0. *(Hoogendoorn, Henkes, Burgers, & Lasance, 1993, p. 6)

*Every mathematician knows that it is impossible to understand any elementary course in thermodynamics.* (Arnold, Contact Geometry: the Geometrical Method of Gibbs’s Thermodynamics, 1989, p. 163)

*What is mathematics? Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap. *(Arnold, On teaching mathematics, 1998)

*Extremal principles in non-equilibrium thermodynamics. The classical law refers only to states of thermodynamic equilibrium, and local thermodynamic equilibrium theory is an approximation that relies upon it. Still it is invoked to deal with phenomena near but not at thermodynamic equilibrium, and has some uses then. But The classical law is inadequate for description of the time course of processes far from thermodynamic equilibrium. For such processes, a more powerful theory is needed, and the second entropy is part of such a theory.* (Wikipedia, pp. *Extremal principles in non-equilibrium thermodynamics*)

*The logarithmic mean temperature difference (LMTD) has caused inconveniences in several applications like equation oriented flow sheeting programs. *(Zavala-Río, Femat, & Santiesteban-Cos, 2005)

*The often used Nusselt number is critically questioned with respect to its physical meaning. *(Herwig, 2016)

*However, it is well known that optimization of thermal systems is inherently complex and ambiguous, and often controversial. In general, the ‘extrema principles’, the minimum and maximum entropy production principles (or entransy dissipation principles), are both elusive and not yet fully understood. The Second Law of Thermodynamics, and the entransy, exergy and entropy that quantifies its analysis, are sometimes subtle and thus may be confusing and misleading if not fully understood and properly accounted for, to enhance the efficacy of all devices involved in all processes to be optimized. Exhaustive research has been done by many investigators on the use of twisted tape, artificial roughness or vortex generators to enhance the heat transfer characteristics in tube heat exchangers as discussed in this review; however the areas related to outer tube geometries like conical, parabolic, frustum, etc have not yet been explored and could be the focus of new research.* (Kostic, 2017)

*The Second Law of Thermodynamics, and the entransy, exergy and entropy that quantifies its analysis, are sometimes subtle and thus may be confusing and misleading if not fully understood and properly accounted for, to enhance the efficacy of all devices involved in all processes to be optimized.* (Kostic, 2017)

*Exhaustive research has been done by many investigators on the use of twisted tape, artificial roughness or vortex generators to enhance the heat transfer characteristics in tube heat exchangers as discussed in this review; however the areas related to outer tube geometries like conical, parabolic, frustum, etc have not yet been explored and could be the focus of new research.* (Maradiya & et. al., 2018)

*In all cases, a thermal resistance can be defined, but in many practical cases, the physical significance of the definition is subject to doubt, with the exception of those definitions that incorporate the ultimate heat sink (an ambient at uniform temperature) as one of the nodes. As a consequence, the widespread notion of a universal analogy between electrical and thermal resistance hampers a correct understanding of the physics. *(Lasance, 2008)

*Over the last ten years, significant progress has been achieved in the field of thermal characterization and modelling of chip packages…….Despite the very significant progress realized over the past ten years, there are still quite challenging problems to be solved, both from an experimental and a numerical point of view.* (Lasance, 2008)

*It is unquestionable that the concept of entropy has played an essential role both in the physical and biological sciences. However, the entropy production, crucial to the second law, has also other features not clearly conceived. We all know that the main difficulty is concerned with its quantification in non-equilibrium processes and consequently its value for some specific cases is limited. […] The concept of entropy, indispensable for dealing with the subject of entropy production, is certainly one of the most abused, and misunderstood concepts in theoretical physics. *(Velasco, Javier Uribe, & Scherer Garc´ıa-Col´ın, 2011)

*My greatest concern was what to call it. I thought of calling it ‘information’, but the word was overly used, so I decided to call it ‘uncertainty’. When I discussed it with John von Neumann, he had a better idea. Von Neumann told me, ‘You should call it entropy, for two reasons: In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage.* (Neumann and Shannon, 1948)

*Despite its long history, to many, the term entropy still appears not to be easily understood. Initially, the concept was applied to thermodynamics, but it is becoming more popular in other fields. The concept of entropy has a complex history. It has been the subject of diverse reconstructions and interpretations making it very confusing and difficult to understand, implement, and interpret*. (Ribeiro, M., Henriques, T. et al., 2021)

**References**

- Arnold, V. I. (1989). Contact Geometry: the Geometrical Method of Gibbs’s Thermodynamics. Proceedings of the Gibbs Symposium: Yale University, May 15-17, 1989
- Arnold, V. I. (1998). On teaching mathematics. (T. i. 1997, Ed.) Russian Math. Surveys 53, 229–236
- Herwig, H. (2016). What Exactly is the Nusselt Number in Convective Heat Transfer Problems and are There Alternatives? 5
- Hoogendoorn, C., Henkes, R., Burgers, J., & Lasance, C. (1993). Thermal Management of Electronic Systems. Proceedings of EUROTHERM Seminar 29, 14–16 June 1993. Delft, The Netherlands
- Kostic, M. (2017). Entransy concept and controversies: A critical perspective within elusive. J. Heat Transf. 115 (2017) 340-346
- Kostic, M. (2020). Maxwell’s Demon and its Fallacies Demystified
- Kostic, M. (n.d.). The Second Law and Entropy Misconceptions Demystified
- Lasance, C. (2008). Ten Years of Boundary Condition Independent Compact Thermal Modeling of Electronic Parts A Review. Heat Transfer Engineering, 29(2):149-168 (2008)
- Maradiya, C., & et. al. (2018). The heat transfer enhancement techniques and their Thermal Performance Factor. Basic and Applied Sciences 7 (2018) 1-21
- Maugin, G. A. (1999). The Thermomechanics Of Nonlinear Irreversible Behaviors. World Scientific Publishing Co Pte Ltd.
- Neumann and Shannon (1948) Discussions, regarding what Shannon should call the “measure of uncertainty” or attenuation in phone-line signals with reference to his new information theory.
- Olla, S. (2018). From Dynamics to Thermodynamics (presentation slides). Université Paris-Dauphine-PSL Research University, CEREMADE, Supported by ANR LSD, INPAM. Warsaw
- Prigogine, I., & Stengers, I. (1984). Order Out of Chaos (March 1, 1984 ed.)
- Ribeiro, M., Henriques, T. et al., (2021) The Entropy Universe
- Truesdell, C. (1980). Tragicomical history of thermodynamics 1822-1854. Springer
- Velasco, R., Javier Uribe, F., & Scherer Garc´ıa-Col´ın, L. (2011). Entropy Production: Its Role in Non-Equilibrium Thermodynamics.
- Wikipedia. (n.d.). Extremal principles in non-equilibrium thermodynamics
- Zavala-Río, A., Femat, R., & Santiesteban-Cos, R. (2005). An analytical study of the logarithmic mean temperature difference. Revista Mexicana de Ing. Quimica, Vol. 4 201-212

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