Of all the messages we have tried to convey in this long text, the most important is to
recognize the key role of the equations of change…They can be used to determine velocity,
pressure, temperature, and concentration profiles, as well as the fluxes of momentum,
energy, and mass, even in complicated time-dependent systems. They are applicable to
turbulent systems, and even when complete a priori solutions prove infeasible, simplify the
efficient use of data through dimensional analysis.
All laws of physics including laws for heat transfer problems as distilled into
Eq. (196) are expressed in terms of governing equations.
1 That is, governing
equations for a system determine changes in the system inclusively. This is the
Bird–Stewart–Lightfoot message that their equations of change serve as the organizing principle of the subject of transport phenomena, and solutions to the equations of change determine every detail of the system that they govern.
Moreover, Eq. (196) with the addition of Eq. (197) inclusively determines all
details of change requiring no independent use of the second law because of the
addition of Eq. (197) guarantees all predictive details to satisfy the second law.
This is the scientific methodology handed down by Galileo and Newton. The
methodological program has been so successful in physics and chemistry that the
idea that all changes in nature are determined by such governing equations has been
ingrained in our worldview. Such presupposition leads to philosophical determinism: if governing equations inclusively describe all changes, then surely all changes
are predetermined as Laplace had concluded, “An intellect which at a certain
moment would know all forces that set nature in motion, and all positions of all
items of which nature is composed, if this intellect were also vast enough to submit
these data to analysis, it would embrace in a single formula the movements of the
greatest bodies of the universe and those of the tiniest atom; for such an intellect
nothing would be uncertain and the future just like the past would be present before
its eyes.” Such a universe is a causally closed universe. This is what Poincare noted,
“…in the deterministic hypothesis there is only a single possibility” of spontaneous
nonreversible process.
10.3 Energy Analysis and Exergy Analysis
For problems of reversible-like processes involving shaft work, as Poincare pointed
out, there are other possibilities, in fact, infinite possibilities. We can consider the
case in terms of energy equation for a control volume to be derived from the first law
Z
cv
@ eq
ð Þ
@t
dV þ
Z
cs
eq ~ V Á ^ ndA ¼ _
Q À _
W
ð191Þ
1
The important exception from this rule is the first and the second laws of thermodynamics; this
exception was first pointed out in [5].
10.2 Heat Transfer Phenomena are Described by Governing Equations
281
recognize the key role of the equations of change…They can be used to determine velocity,
pressure, temperature, and concentration profiles, as well as the fluxes of momentum,
energy, and mass, even in complicated time-dependent systems. They are applicable to
turbulent systems, and even when complete a priori solutions prove infeasible, simplify the
efficient use of data through dimensional analysis.
All laws of physics including laws for heat transfer problems as distilled into
Eq. (196) are expressed in terms of governing equations.
1 That is, governing
equations for a system determine changes in the system inclusively. This is the
Bird–Stewart–Lightfoot message that their equations of change serve as the organizing principle of the subject of transport phenomena, and solutions to the equations of change determine every detail of the system that they govern.
Moreover, Eq. (196) with the addition of Eq. (197) inclusively determines all
details of change requiring no independent use of the second law because of the
addition of Eq. (197) guarantees all predictive details to satisfy the second law.
This is the scientific methodology handed down by Galileo and Newton. The
methodological program has been so successful in physics and chemistry that the
idea that all changes in nature are determined by such governing equations has been
ingrained in our worldview. Such presupposition leads to philosophical determinism: if governing equations inclusively describe all changes, then surely all changes
are predetermined as Laplace had concluded, “An intellect which at a certain
moment would know all forces that set nature in motion, and all positions of all
items of which nature is composed, if this intellect were also vast enough to submit
these data to analysis, it would embrace in a single formula the movements of the
greatest bodies of the universe and those of the tiniest atom; for such an intellect
nothing would be uncertain and the future just like the past would be present before
its eyes.” Such a universe is a causally closed universe. This is what Poincare noted,
“…in the deterministic hypothesis there is only a single possibility” of spontaneous
nonreversible process.
10.3 Energy Analysis and Exergy Analysis
For problems of reversible-like processes involving shaft work, as Poincare pointed
out, there are other possibilities, in fact, infinite possibilities. We can consider the
case in terms of energy equation for a control volume to be derived from the first law
Z
cv
@ eq
ð Þ
@t
dV þ
Z
cs
eq ~ V Á ^ ndA ¼ _
Q À _
W
ð191Þ
1
The important exception from this rule is the first and the second laws of thermodynamics; this
exception was first pointed out in [5].
10.2 Heat Transfer Phenomena are Described by Governing Equations
281