EBOOK - The Nature of Motive Force (Heat and Mass Transfer) (Achintya Kumar Pramanick)

I was always very curious about how one gets around to preparing a book and so perhaps as a reader you are as well. Mark Twain takes me into his confidence with the words: ‘‘…there ain’t nothing more to write about, and I am rotten glad of it, because if I’d’a’ knowed what trouble it was to make a book I wouldn’t’a’ tackled it, and ain’t a-going to no more.’’ In contemporary practice portraying a prelude many not haveargumentum ad hominemmuch in vogue.
But in the entire gamut of my reading experience, I never laid hands on any treatise without going through the very pursuit of the author first. On the same ground, it remains almost a compelling choice for me to insinuate what inspires me. I plead to exempt me from the egalitarian fallacyof trying to make all persons alike.
Every true research is but autobiographical and so is the following monograph. At a personal level, trying the best to be very meticulous and carping on almost every aspect that crops up in my way even results in imperfect performance, and thus further suffering a setback of dilemma on decision. Riding on the lacuna of my habit of witnessing ill decision and the stigma of a perfectionist, I was prompted to compose my first scientific writing [1] while I was a second-year undergraduate student in 1991, of a 4-year Mechanical Engineering degree program at the National Institute of Technology Durgapur, India, formerly recognized as Regional Engineering College Durgapur.

After many years of latency, in January 2007, I submitted my doctoral thesis [2] haunted by my way of dogma and dilemma and by June 2007 I defended. In 2009, my doctoral thesis was selected only in the group of top five by the Prigogine prize selection committee for the best doctoral thesis in thermodynamics and hence my work could not see the delightful sun of scrutiny by a wide range of readers.
Today, I continue to regard that my scientific approach has not been well circulated, especially among physicists. Until in January 2012, when I got a call from Adrian Bejan to publish a book chapter [3], I did not get a pat on my back. By now I got older and somewhat more immuned and case hardened about what other people would think of my preparation and presentation. Granted by Heaven, maybe I can afford to toy myself with the fascinating idea of writing a book. Jonathan Swift has rightly pointed out that, ‘‘if a Writer would know how to behave himself with relation to Posterity; let him consider in old Books, what he finds, that he is glad to know; and what Omissions he most laments.’’
The essay by Sadi Carnot [4], about a quarter of a century earlier than the terminology adopted by Thomson [5], is a milestone example of how the proponent of a new theory has no choice but to misuse the language of old theory [6].
Thus, without a constant misuse of language there cannot be any discovery, any progress [7]. Tuesdell [8, 9] addressed the celebrated failure of thermodynamics in the nineteenth century, accursed by misunderstanding, irrelevance, and retreat. In the spreaded span of the late twentieth century to the beginning of the twenty-first century, through the constructal theory (fourth law of thermodynamics) [10–12] proposed by Bejan, a consistent brilliant progress has been made in the unified description of nature as well as artificial (engineered) systems. Leib and Yngvason, [13] for the first time in the history of thermodynamics, made it scholarly possible to realize the concept of entropy purely on a macroscopic basis, in contrast with the system theoretic approach of thermodynamics by Haddad et al. [14].
In company with these recent developments, the present treatise is a systematic development and application of a new theory of motive force (power), long due after Carnot [15, 16]. The former faint ideas of the author, which go by the label ‘‘heuristic’’ [17] and ‘‘method of synthetic constraint’’ [18], are formally forged into a generalized formulation recognized as a natural tendency and hence perhaps may be regarded as a law of nature.

1 Introduction ........................................ 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Aim and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 General Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1 Law of Motive Force. . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2 Conservation Principle. . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.3 Variational Formulation . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.4 Fermat’s Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.5 Constructal Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.3.6 Entropy Generation Minimization . . . . . . . . . . . . . . . . . 22
1.3.7 Method of Intersecting Asymptotes . . . . . . . . . . . . . . . . 24
1.3.8 Principle of Equipartition . . . . . . . . . . . . . . . . . . . . . . . 28
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2 Conductive Heat Transport Systems....................... 47
2.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.2 A Physical Principle in Heat Transport . . . . . . . . . . . . . . . . . . 49
2.3 The Physical Basis for Extremum Heat Transfer . . . . . . . . . . . . 51
2.4 Temperature Distribution and Heat Transfer from
an Insulated Wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.5 Insulation on Plane Surface with Static Wall Temperature
Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.6 Insulation on Cylindrical Surface with Static
Wall Temperature Condition . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.7 Insulation on Cylindrical Surface with Dynamic
Wall Temperature Condition . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.8 Law of Motive Force, Tangent Law, Fermat’s Principle,
and Constructal Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.9 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3 Conjugate Heat Transport Systems........................ 67
3.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2 The Physical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3 Optimization with Assumed Variation of Heat
Transfer Coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.4 Optimization with Unknown Variation of Convective
Heat Transfer Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.5 Bounds of Insulation Volume . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.6 Insulation with Tapered Profile . . . . . . . . . . . . . . . . . . . . . . . . 77
3.7 Law of Motive Force and Commonality of Nature
of Optimizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.8 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4 Fluid Flow Systems................................... 83
4.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 Elemental Fermat Type Flow . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3 Integral Fermat Type Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.4 First Geometrical Construct in a Shear Flow. . . . . . . . . . . . . . . 94
4.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5 Natural Heat Engine.................................. 101
5.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.2 The Physical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3 Control Volume Formulation of a Single
Thermoelectric Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.4 Control Volume Formulation for the Complete
Thermoelectric Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.5 Consequences of Equipartitioned Joulean Heat . . . . . . . . . . . . . 115
5.6 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6 Real Heat Engine..................................... 121
6.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2 The Physical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.3 The Optimization Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.4 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

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I was always very curious about how one gets around to preparing a book and so perhaps as a reader you are as well. Mark Twain takes me into his confidence with the words: ‘‘…there ain’t nothing more to write about, and I am rotten glad of it, because if I’d’a’ knowed what trouble it was to make a book I wouldn’t’a’ tackled it, and ain’t a-going to no more.’’ In contemporary practice portraying a prelude many not haveargumentum ad hominemmuch in vogue.
But in the entire gamut of my reading experience, I never laid hands on any treatise without going through the very pursuit of the author first. On the same ground, it remains almost a compelling choice for me to insinuate what inspires me. I plead to exempt me from the egalitarian fallacyof trying to make all persons alike.
Every true research is but autobiographical and so is the following monograph. At a personal level, trying the best to be very meticulous and carping on almost every aspect that crops up in my way even results in imperfect performance, and thus further suffering a setback of dilemma on decision. Riding on the lacuna of my habit of witnessing ill decision and the stigma of a perfectionist, I was prompted to compose my first scientific writing [1] while I was a second-year undergraduate student in 1991, of a 4-year Mechanical Engineering degree program at the National Institute of Technology Durgapur, India, formerly recognized as Regional Engineering College Durgapur.

After many years of latency, in January 2007, I submitted my doctoral thesis [2] haunted by my way of dogma and dilemma and by June 2007 I defended. In 2009, my doctoral thesis was selected only in the group of top five by the Prigogine prize selection committee for the best doctoral thesis in thermodynamics and hence my work could not see the delightful sun of scrutiny by a wide range of readers.
Today, I continue to regard that my scientific approach has not been well circulated, especially among physicists. Until in January 2012, when I got a call from Adrian Bejan to publish a book chapter [3], I did not get a pat on my back. By now I got older and somewhat more immuned and case hardened about what other people would think of my preparation and presentation. Granted by Heaven, maybe I can afford to toy myself with the fascinating idea of writing a book. Jonathan Swift has rightly pointed out that, ‘‘if a Writer would know how to behave himself with relation to Posterity; let him consider in old Books, what he finds, that he is glad to know; and what Omissions he most laments.’’
The essay by Sadi Carnot [4], about a quarter of a century earlier than the terminology adopted by Thomson [5], is a milestone example of how the proponent of a new theory has no choice but to misuse the language of old theory [6].
Thus, without a constant misuse of language there cannot be any discovery, any progress [7]. Tuesdell [8, 9] addressed the celebrated failure of thermodynamics in the nineteenth century, accursed by misunderstanding, irrelevance, and retreat. In the spreaded span of the late twentieth century to the beginning of the twenty-first century, through the constructal theory (fourth law of thermodynamics) [10–12] proposed by Bejan, a consistent brilliant progress has been made in the unified description of nature as well as artificial (engineered) systems. Leib and Yngvason, [13] for the first time in the history of thermodynamics, made it scholarly possible to realize the concept of entropy purely on a macroscopic basis, in contrast with the system theoretic approach of thermodynamics by Haddad et al. [14].
In company with these recent developments, the present treatise is a systematic development and application of a new theory of motive force (power), long due after Carnot [15, 16]. The former faint ideas of the author, which go by the label ‘‘heuristic’’ [17] and ‘‘method of synthetic constraint’’ [18], are formally forged into a generalized formulation recognized as a natural tendency and hence perhaps may be regarded as a law of nature.

1 Introduction ........................................ 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Aim and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 General Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1 Law of Motive Force. . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2 Conservation Principle. . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.3 Variational Formulation . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.4 Fermat’s Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.5 Constructal Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.3.6 Entropy Generation Minimization . . . . . . . . . . . . . . . . . 22
1.3.7 Method of Intersecting Asymptotes . . . . . . . . . . . . . . . . 24
1.3.8 Principle of Equipartition . . . . . . . . . . . . . . . . . . . . . . . 28
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2 Conductive Heat Transport Systems....................... 47
2.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.2 A Physical Principle in Heat Transport . . . . . . . . . . . . . . . . . . 49
2.3 The Physical Basis for Extremum Heat Transfer . . . . . . . . . . . . 51
2.4 Temperature Distribution and Heat Transfer from
an Insulated Wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.5 Insulation on Plane Surface with Static Wall Temperature
Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.6 Insulation on Cylindrical Surface with Static
Wall Temperature Condition . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.7 Insulation on Cylindrical Surface with Dynamic
Wall Temperature Condition . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.8 Law of Motive Force, Tangent Law, Fermat’s Principle,
and Constructal Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.9 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3 Conjugate Heat Transport Systems........................ 67
3.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2 The Physical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3 Optimization with Assumed Variation of Heat
Transfer Coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.4 Optimization with Unknown Variation of Convective
Heat Transfer Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.5 Bounds of Insulation Volume . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.6 Insulation with Tapered Profile . . . . . . . . . . . . . . . . . . . . . . . . 77
3.7 Law of Motive Force and Commonality of Nature
of Optimizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.8 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4 Fluid Flow Systems................................... 83
4.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 Elemental Fermat Type Flow . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3 Integral Fermat Type Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.4 First Geometrical Construct in a Shear Flow. . . . . . . . . . . . . . . 94
4.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5 Natural Heat Engine.................................. 101
5.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.2 The Physical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3 Control Volume Formulation of a Single
Thermoelectric Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.4 Control Volume Formulation for the Complete
Thermoelectric Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.5 Consequences of Equipartitioned Joulean Heat . . . . . . . . . . . . . 115
5.6 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6 Real Heat Engine..................................... 121
6.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2 The Physical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.3 The Optimization Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.4 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

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Chuyên mục: C. Bài giảng C. Bài giảng chuyên ngành Nhiệt Lạnh (Heat and Refrigeration) C. Bài giảng kỹ thuật