**THE NEW ENGINEERING**

*Dear colleague, *

*The
following short narrative critically appraises conventional engineering
science, describes the new engineering science that should replace it, and demonstrates
the solution of practical problems using the new engineering. The particular advantages
of the new engineering are that it is much easier to learn because there are
fewer concepts, it is a much better way to think because there are fewer parameters,
and it greatly simplifies the solution of problems that concern nonlinear
behavior because there are fewer variables. *

*The
rest of this website concerns my publications, presentations, patents, and
narratives that relate how I have promoted the new engineering, and how the
promotion has been received. *

*Eugene
F. Adiutori *

**Fourier’s view of
dimensional homogeneity: why it is irrational, and how it impacts
conventional engineering science.**

Fourier
(1822) is generally credited with the modern view of dimensional
homogeneity. His view of dimensional
homogeneity *requires* the *creation *of parameters such as h, E, and
R so that engineering laws such as Eqs. (1) to (3)
can be dimensionally homogeneous.

q
= hDT (1)

s = Ee (2)

V = IR (3)

In
Fourier’s view of dimensional homogeneity,

·
Dimensioned
parameters *can* be multiplied and divided, but *cannot*
be added or subtracted.

·
Dimensions
*can* be assigned to numbers.

Fourier’s
view is *irrational* because it is *not possible* to multiply things that
cannot be added. Multiplication is repeated addition. Note that “six ** times** nine” means “

Fourier’s
view of homogeneity replaced the view that prevailed for more than 2000 years
prior to the publication of Fourier’s treatise, *The Analytical Theory of Heat*, published in 1822. In the 2000 year
view, scientists and engineers such as Galileo and Newton globally agreed that
dimensioned parameters *cannot* be
added, subtracted, multiplied, or divided, with the *single* exception that a dimensioned parameter *can* be divided by the same dimensioned parameter.

Until
the nineteenth century, it was not rational to multiply dimensioned
parameters. That is why Hooke’s law is a
proportion rather than an equation. And
why Newton’s second law of motion in Newton (1726) is *not* f = ma. Newton’s
contemporaries would have considered f = ma irrational because it requires the
multiplication of dimensioned parameters “m” and “a”. Newton’s second law of
motion in Newton (1726) is Proportion (4):

a
a f a is acceleration f is force (4)

Fourier
performed convective heat transfer experiments.
From data he had obtained, Fourier induced that in steady-state heat
transfer by forced convection to atmospheric air, the relationship between heat
flux q and temperature difference DT
is described by Proportion (5).

q
a DT (5)

When
Proportion (5) is transformed to an equation, arbitrary *number* “c” is introduced, as in Eq. (6).

q
= cDT (6)

Fourier
recognized that Eq. (6) is dimensionally *in*homogeneous,
and that it can rationally be transformed to a homogeneous equation *only* if it is rational to assign
dimensions to numbers, and to multiply dimensioned parameters. That is why he conceived the irrational view
that dimensions *can* be assigned to
numbers, and dimensioned parameters *can *be
multiplied.

To
*number* *c* in Eq. (6), Fourier *assigned
*the dimension of q/DT and the symbol
h, thereby transforming *number c *into
*dimensioned* *parameter* *h*, and
transforming *in*homogeneous Eq. (6)
into homogeneous Eq. (7).

q
= hDT (7)

Fourier’s irrational view of dimensional
homogeneity is the *only* reason conventional
engineering includes parameters such as h, E, and R.

(Although
Eq. (7) is usually referred to as “Newton’s law of cooling”, Adiutori (1974 and
1990) and Bejan (2013) state that Eq. (7) and h were
conceived by Fourier (1822). Also, Eq.
(7) cannot be a “law of cooling” because cooling is a *transient* phenomenon, and Eq. (7) is a *steady-state* equation.)

Rearranging
Eq. (7) results in h = q/DT, indicating that
h and q/DT are *identical and interchangeable*. In other words, parameters such as h, E, and
R are *not *fundamental. They are *created*
from other parameters. h is *created*** **from q and DT, just as Nusselt
number is *created* from h, D, and
k. Similarly, modulus E is *created* from s and e,
electrical resistance R is *created*
from V and I, etc.

Fourier (1822) offered *no proof* that it is rational to multiply dimensioned parameters,
even though it was a revolutionary change from the view held by world class
scientists and engineers for 2000 years.
The only “proof” given by Fourier in his nearly 500 page
treatise is the statement that his view of dimensional homogeneity “*is the equivalent of the fundamental lemmas
(axioms) which the Greeks have left us without proof”*. Fourier (1822)

Fourier did *not
*include the lemmas in his nearly 500 page
treatise, *nor* did he include a
reference to the lemmas, *nor* did he
include his own proof that his view of homogeneity is rational. (It seems more than likely that Fourier made
no attempt to prove that his view of homogeneity is rational because he
recognized that it is irrational.)
Presumably Fourier’s contemporaries accepted his view of dimensional
homogeneity without proof because he was able to solve numerous practical
problems his contemporaries were unable to solve.

**Why parameters such as h, E, and R should have been abandoned more than 60 years ago.**

Although Fourier is generally credited with the
modern view of dimensional homogeneity, the modern view differs from Fourier’s
view in one important way. In the modern
view, dimensions must *not* be assigned
to numbers. Langhaar
(1951) states:

*Dimensions must not be
assigned to numbers, for then any equation could be regarded as dimensionally
homogeneous.*

Parameters such as h, E, and R should have been
*abandoned* more than 60 years ago
because they *require* that dimensions
be assigned to *numbers*, in accordance
with Fourier’s view of homogeneity, but in *violation
*of the modern view expressed by Langhaar in 1951
that *“dimensions must not be assigned to numbers, for then
any equation could be regarded as dimensionally homogeneous”*.

**The real problem with parameters such as h, E, and R.**

The real problem with parameters such as h, E,
and R is that, in problems that concern nonlinear behavior, parameters such as
h, E, and R are *variables*,
and *greatly *complicate solutions.

Recall that h and q/DT are identical and interchangeable. If q is proportional to DT, q/DT
(aka h) is a *constant*. But if q is a *nonlinear* function of DT (as in free convection, boiling, and condensation), q/DT (aka h) is a *variable*. Consequently Eq. (1) contains the *two parameters* q and DT, and the *three variables*
q, DT, and q/DT (aka h).

It is self-evident that *any* nonlinear problem that can be solved with the *three* variables q, DT, and q/DT
(aka h) can also be solved with the *two *variables
q and DT, and that the *two* variable solution is *much*
simpler. And similarly
for parameters s/e (aka E) and V/I (aka R).

**Questioning the implicit assumption that mathematical expressions
can describe how different parameters are related.**

Since the time of Aristotle, it has been
implicitly assumed that mathematical expressions can describe how different
parameters are related—how stress is related to strain—how heat flux is related
to temperature difference—how electromotive force is related to electric
current.

It is axiomatic that *different* things *cannot*
be related, and therefore mathematical expressions *cannot* describe how *different*
things are related. For example,
mathematical expressions *cannot *describe
how birds are related to pencils, how cars are related to tigers, how stress is
related to strain, how heat flux is related to temperature difference, etc.

However, mathematical expressions *can *oftentimes describe how the *numerical values* of different things are
related—how the *numerical value* of
stress is related to the *numerical value*
of strain—how the *numerical value* of
heat flux is related to the *numerical
value* of temperature difference, etc.

In the new engineering, mathematical
expressions do *not* describe how
parameters are related. They describe
how the *numerical values* of
parameters are related. For example, in
the new engineering, Hooke’s law is* not*
“stress is proportional to strain”.
Hooke’s law is “the *numerical
value* of stress is proportional to the *numerical
value* of strain”.

**Parameter symbolism, dimensional homogeneity, and dimensional
analysis in the new engineering.**

In the new engineering:

·
Mathematical expressions describe how the *numerical values* of different parameters
are related. Therefore
parameter symbols *must* represent
numerical value, but *not* dimension.

·
Because parameter symbols are dimensionless,
mathematical expressions are *inherently*
dimensionless and *inherently*
dimensionally homogeneous.

·
Because mathematical expressions are *inherently* dimensionally homogeneous, it
is *not *necessary to create parameters
such as q/DT (aka h), s/e
(aka E), and V/I (aka R), and they are *abandoned*.

·
If an equation is *quantitative*, the dimension units that underlie parameter symbols *must *be specified in an accompanying
nomenclature.

·
If an equation is *qualitative*, it is not necessary to specify the dimension units
that underlie parameter symbols.

·
Because mathematical expressions are *inherently* dimensionally homogeneous,
they contain no dimensions to be analyzed, and consequently dimensional
analysis is *abandoned*.

**Replacements for parameters such as q/****D****T (aka h), ****s****/****e**** (aka E), and V/I (aka
R).**

The *only*
reason parameters such as h, E, and R are required in conventional engineering
is because it is *not possible* to have
a dimensionally
homogeneous law in the form of a proportional equation unless the coefficient
in the equation is the ratio of the two parameters in the equation. For example, Eq. (1) is a law in the form of
a proportional equation, and it is dimensionally homogeneous *only* because h is the ratio q/DT.
And similarly for Eqs.
(2) and (3).

Because parameters such as h, E, and R are
required *only* so that engineering
laws can be dimensionally homogeneous, and because equations are *inherently* dimensionally homogeneous in
the new engineering, replacements for parameters such as h, E, and R would
serve no purpose in the new engineering.
Consequently parameters such as h, E, and R are
*not *replaced.

**Replacements for laws such as Eqs. (1) to
(3).**

Comprehensive experiments indicate that q_{conv} is a function of DT, and the function may be proportional, or linear, or
nonlinear. Therefore
the law of convective heat transfer *must *indicate
that q_{conv} is a function of DT, and *must* allow that
the function may be proportional, or linear, or nonlinear. And similarly for s and e,
and for V and I.

Equation (8) indicates that the numerical value
of y is a function of the numerical value of x, and the function may be
proportional, or linear, or nonlinear.
Eq. (8) is an analog of Eqs. (9) to (11), the
laws that replace laws such as Eqs. (1) to (3). Equation (9) states that the numerical value
of heat flux is an unspecified function of the numerical value of temperature
difference, and the unspecified function may be proportional, or linear, or
nonlinear. And similarly
for Eqs. (10) and (11).

y = *f*{x} (8)

q_{conv} = *f*{DT} (9)

s = *f*{e} (10)

V = *f*{I} (11)

**Transformation from conventional engineering to the new
engineering.**

The transformation from conventional
engineering to the new engineering is quite simple. For example, to transform the convective heat
transfer section of a heat transfer text:

·
Replace Eq. (1) with Eq. (9).

·
Recognize that parameter symbols represent numerical
value, but *not* dimension.

·
Recognize that h and q/DT are *identical and
interchangeable*.

·
In all equations that explicitly or implicitly
include h, substitute q/DT
for h and for k_{wall}/t_{wall},
then separate q and DT.

For example, the transformation of Eq. (12)
results in Eq. (13), and the transformation of Eq. (14) results in Eq. (15).

U
= 1/(1/h_{1} + t_{wall}/k_{wall}+ 1/h_{2 }) (12)

DT_{total} = DT_{1} + DT_{wall} + DT_{2} (13)

Nu = a Re^{b }Pr^{c}
(14)

q = a(k/D)Re^{b}^{
}Pr^{c}DT
(15)

In the new engineering, Eqs.
(1), (12), and (14) are *abandoned*,
and are replaced by Eqs. (9), (13), and (15). And similarly for
other branches of engineering. Note that
Eqs. (12) and (13) are *identical*, and that Eq. (13) is so simple it is intuitive, whereas
Eq. (12) is far from intuitive. It is
much easier to learn how to solve problems using Eq. (13) instead of Eq.
(12). And *any* heat transfer problem that can be solved using Eq. (12) can
also be solved using Eq. (13).

If a heat transfer problem concerns
proportional behavior, it is easily solved using either Eq. (12) or Eq.
(13). If a heat transfer problem
concerns *moderately nonlinear*
behavior, the solution is quite simple if Eq. (13) is used, and considerably
more difficult if Eq. (12) is used, as demonstrated by the problem in Table 1
below. If a heat transfer problem
concerns *highly nonlinear* behavior,
the solution is quite simple if Eq. (13) is used, and *virtually impossible* if Eq. (12) is used.

*The remainder of
this narrative is a slightly modified form of several pages taken from my
article in The Open Mechanical Engineering Journal, 2018, 12: 164-174.* https://www.benthamopen.com/contents/pdf/TOMEJ/TOMEJ-12-164.pdf

**The solution of proportional and moderately nonlinear heat transfer
problems using conventional engineering and the new engineering.**

Table
1 describes the solution of a moderately nonlinear heat transfer problem that
concerns heat transfer between two fluids separated by a flat wall. The solution on the left side of Table 1 is
based on conventional engineering. The
solution on the right side is based on the new engineering. The solutions described in Table 1 are
typical of problems in which the thermal behavior of boundary layers is
described by equations (rather than charts).

**
Table 1**

** The solution
of a moderately nonlinear**

** heat transfer problem
based on q = h****D****T and ****D****T = f{q}.**

* Based on q = h**D**T.*** Based
on **

**U = 1/(1/h _{1
}+ t/k + 1/h_{2}) **

**D****T _{total}**

**h _{1} = .40(**

**t _{wall}**

**h _{2} = .80(**

**U = 1/(1/.4(****D****T _{1})^{.33
}+.05 + 1/.8(**

Note
the following in Table 1:

·
The
equations on the left side of Table 1 are *identical
*to the equations on the right side.
They differ only in form.

·
The
equation on the left side of Line 6 is much more difficult to solve than the
equation on the right side because it contains *three *unknowns (U, DT_{1}, and
DT_{2}),
whereas the equation on the right side contains *one *unknown (q).

·
The
equation on the right side of Line 6 can be solved in about a minute using
Excel and trial-and-error methodology.
It would take much longer than a minute to solve the equation on the
left side, and the likelihood of error would be much greater.

·
If
DT_{1} and DT_{2 }were proportional to
q—ie if h_{1} and h_{2} were *constants*—the equations on *both *sides of Line 6 would be simple to
solve. In other words, proportional
problems are very simple to solve whether the solution is based on q = hDT or DT
= *f*{q}.

·
The
problem in Table 1 can be solved graphically if the solution is based on DT = *f*{q} because the equation on the right side of Line 1 can be solved
graphically. The problem in Table 1 *cannot* be solved graphically if the
solution is based on q = hDT because the
equation on the left side of Line 1 *cannot*
be solved graphically.

**The solution of a highly nonlinear heat transfer problem
using the new engineering.**

If
DT_{2}{q}
in Table 1 is so highly nonlinear that it includes a region in which dq/dDT_{2} is *negative*, the relationship between q and
DT_{2} is
probably described graphically in the form q vs DT_{2}. The problem might have more than one solution,
and operation might be thermally unstable in the region in which dq/dDT_{2} is
negative. Such problems are solved quite
simply if the solution is based on q = *f*{DT}, as demonstrated by the
following:

·
Use
the given information to plot q_{out} vs (T_{2}
+ DT_{2}{q_{out}}).
Note that (T_{2} + DT_{2}{q_{out}) is the temperature of the interface that
adjoins Fluid 2, and q_{out} is the heat flux
*out of* that interface.

·
On
the same chart, use the given information to plot q_{in}
vs (T_{1} - DT_{1} - DT_{wall}). Note that (T_{1} - DT_{1} - DT_{wall}) is the
temperature of the interface that adjoins Fluid 2, and q_{in}
is the heat flux *into* that interface.

·
At
intersections of the two curves, the heat flux *into* the interface in Fluid 2 equals the heat flux *out *of that interface. Therefore intersections
are steady-state operating points *provided
*operation at the intersection is thermally stable.

·
If
an intersection is in a region in which dq/dDT_{2} is negative,
operation may be thermally unstable. To
appraise thermal stability at the intersection, inspect the chart to determine
whether a small perturbation at the intersection would shrink or grow.

·
If
a small perturbation would shrink, operation at the intersection is thermally
stable with respect to small perturbations.
(It may be thermally unstable with respect to *large *perturbations.)

·
If
a small perturbation would grow, operation at the intersection is thermally
unstable.

o If the unstable
intersection lies between two other intersections, inspection of the chart will
indicate that the instability results in hysteresis.

o If there is only
one intersection, inspection of the chart will indicate that the instability
results in undamped oscillations in temperature and heat flux.

**The solution of a
highly nonlinear heat transfer problem using conventional engineering.**

The
solution of the highly nonlinear problem above is quite simple because the
solution is based on q = *f*{DT}.
If the solution is based on q = hDT,
the chart of q vs DT_{2} is
replaced by a chart of h vs DT_{2}, and
the addition of the *variable h* adds
so much complexity that it is virtually impossible to determine the correct and
complete solution of the problem.

**The solution of
stress/strain problems in the elastic region based on ****s**** = E _{elastic}**

In
the elastic region:

·
s = E_{elastic}e
is a proportional equation, and E_{elastic}
is a dimensioned proportionality constant.

·
s = *f*{e} is the proportional equation s = ce,
and c is a dimensionless proportionality constant.

·
c
is numerically equal to E_{elastic}.

Because
both s = E_{elastic}e
and s = ce are proportional equations, and
because c and E_{elastic} are numerically
equal, the solution of elastic problems based on s
= ce is *identical *to the solution based on s = E_{elastic}e.
The only difference between the two solutions is that the symbols in one
equation represent numerical value *and*
dimension, whereas the symbols in the other equation represent numerical value
but *not *dimension.

**Why inelastic
stress/strain problems are much simpler to solve if the solution is based on ****s**** = f{**

In
the inelastic region, E is the *variable*
E_{secant}.
Because s = E_{secant}e
contains *three* variables in the
inelastic region whereas s = *f*{e} contains only *two* variables, inelastic problems are *much *simpler to solve if the solution is
based on s = *f*{e}.

The
following problem demonstrates that inelastic problems are much simpler to
solve if solutions are based on s
= *f*{e} rather than s = E_{secant}e.

**The solution of a
stress/strain problem using ****s**** = E****e****. **

Determine
the strain in the bar.

**Given:**

·
The
stress in the bar is 45,000 kg/cm^{2}.

·
E_{bar} = *f*{e} is described in Figure 1.

**Analysis**

The
analysis based on s = E_{bar}e
is not difficult, but it is time-consuming, and there is a considerable
likelihood of error.

**Solve the above
problem using ****s**** = f{**

**Given:**

·
The
stress in the bar is 45,000 kg/cm^{2}.

·
s = *f*{e} is described in Figure 2.

**Analysis
and solution:**

Inspection of Figure 2 indicates that the strain in
the bar may be .0015, .0036, or .0068. The
given information is not sufficient to determine a
unique solution.

**The
purpose of the bar problem.**

The purpose of the bar problem is to demonstrate
that it is *much* easier to solve
inelastic problems if E is *not* used
in the solution. If E is *not *used, the correct and complete
solution of the bar problem requires less than ten *seconds*, and there is virtually no chance of error. If E is*
*used, the correct and complete solution requires *much* longer than ten seconds, and there is a considerable chance of
error because the problem does not have a unique solution.

**Why
“stress/strain charts” are not charts
of stress vs strain, and why “stress/strain charts” are in precisely the form
required in the new engineering.**

Charts do *not*
describe how parameters are related.
Charts describe how the *numerical
values* of parameters are related.
Charts are in precisely the form required in the new engineering because
*both* parametric charts and parametric
equations state that the numerical value of parameter y is a function of the
numerical value of parameter x, and the function may be proportional, or
linear, or nonlinear.

For example, “stress/strain charts” describe how s, the numerical value of stress, is related to e, the numerical value of strain.
If a chart is to be *quantitative*,
the dimension units that underlie s and e *must *be
specified on the chart, or in an accompanying nomenclature. Note that if dimension units were *not *specified on Figures (1) and (2),
the charts would only be *qualitatitive*.

**Conclusion**

The
new engineering science described herein should replace conventional
engineering science because it is *much*
easier to learn and apply, and because it *greatly
*simplifies the solution of problems that concern nonlinear behavior.

**References**

Adiutori, E. F., 1974, *The New Heat Transfer*, pp. 1-14, 1-15, Ventuno
Press

Adiutori, E. F., 1990, “Origins of the Heat Transfer
Coefficient”, pp 46-50, *Mechanical
Engineering*, August issue

Bejan, Adrian, 2013, *Convection Heat Transfer*, 4^{th}
edition, p. 32, John Wiley and Sons, Inc.

Fourier,
J., 1822, *The Analytical Theory of Heat*,
Article 160, 1955 Dover edition of the 1878 English translation, The University
Press

Langhaar, H. L., 1951, *Dimensional Analysis and Theory of Models*,
p. 13, John Wiley & Sons

Newton, I., 1726, *The Principia, 3*^{rd} edition,
translation by Cohen, I. B. and Whitman, A. M., 1999, p. 460, University of
California Press

**More about the new
engineering.**

The
new engineering and its application are described in the following:

·
An
18 minute youtube video by Eugene F. Adiutori
entitled “The New Engineering”.

·
The
2017 edition of *The New Engineering*
by Eugene F. Adiutori. Hardback copies
can be purchased at bookstores (ISBN 978-0-9626220-4-5) for $49.95 (USA) or
$69.95 (international), or from Ventuno Press:

**Ventuno****
Press, 1094 Sixth Lane N., Naples, FL
34102, USA**

Eugene
F. Adiutori

Updated on October 12,
2018

**Copyright ****ã**** 2017 by Eugene F. Adiutori**

**All material on this
website may be downloaded and printed for personal use without charge, but may
not be sold, reproduced by any means, or republished, without the written
permission of the copyright owner.**

__Table of Contents__

1. Book entitled* The New Heat
Transfer. *

* *

a. Narrative on writing and
marketing *The New Heat Transfer*.

b. Downloadable copy of
the first edition published in 1974.

c. Reviews.

2. The Russian edition of *The New Heat Transfer* (published
by Mir, Moscow in 1977).

a. Narrative on the Russian
edition of *The New Heat Transfer*.

b. Downloadable copy of the
Russian edition.

3. Modern engineering—the
brainchild of Joseph Fourier (1822).

5. Published
letters and errata that concern the new engineering.

7. Talks I was invited to
give at AIChE and ASME dinner meetings.

8. My patents.

9. Narratives:

c. My 1964 paper that was
accepted for publication in the *AIChE** Journal* (but
*never* published there), and the
amazing view expressed by Professor Rohsenow. (The paper was published in ** 1994** in the