**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 several practical problems using the new engineering. The particular advantages of the new engineering are that it is
easier to learn because there are fewer parameters, and it greatly simplifies
the solution of nonlinear problems by reducing the number of variables.

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

*Eugene F. Adiutori *

**Why parameter symbols
are dimensionless in the new engineering.**

In the new engineering,
parameter symbols are *dimensionless* because engineering data describe
how the *numerical values* of parameters are related.

** **

For
example, Hooke’s data do *not* indicate that “stress is proportional to
strain”. Hooke’s data indicate that “the numerical value of stress is
proportional to the numerical value of strain”. Therefore the *correct*
symbolic expression of Hooke’s law is s
a e in which s and e
are *dimensionless*.

Data indicate that “the *numerical
value* of stress is *always* a function of the *numerical value*
of strain”. This statement is a *law* because it describes behavior, and is *always *obeyed. The correct
symbolic expression of this law is s = *f*{e} in which s and e are *dimensionless*.
This law replaces s = Ee, and makes it necessary to *abandon* E
because E is *defined* by s = Ee.

Data indicate that “the *numerical
value* of convective heat flux is *always* a function of the *numerical
value* of temperature difference”. This statement is a *law *because
it describes behavior, and is *always*
obeyed. The correct symbolic expression of this law is q = *f*{DT} in which q and DT are *dimensionless*.
This law replaces q = hDT, and makes it necessary to abandon h because h
is *defined* by q = hDT.

Data indicate that, in
resistive electrical components, “the *numerical value* of electromotive
force is *always *a function of the *numerical value* of electric
current”. This statement is a *law*
because it describes behavior, and is *always* obeyed. The correct
symbolic expression of this law is V = *f*{I} in which V and I are *dimensionless*.
This law replaces V = IR, and makes it necessary to abandon R because R is *defined
*by V = IR.

**How dimensionless parameter symbols greatly improve engineering
science.**

Dimensionless
parameter symbols result in a greatly improved engineering science by making it
necessary to replace laws such as s = Ee,
q = hDT, and V = IR with
laws such as s = *f*{e},
q = *f*{DT},
and V = *f*{I}, and to abandon parameters
such as E, h, and R. The improvements
are:

·
It
is *much* easier to learn engineering
science because the abandonment of parameters such as E, h, and R reduces the
number of concepts that must be understood and applied.

·
It
is *much* easier to solve nonlinear
problems because the abandonment of parameters such as E, h, and R reduces the
number of variables in nonlinear problems.

·
*All* parametric
equations are *inherently*
dimensionless and dimensionally homogeneous.
Therefore all parametric equations are
dimensionally acceptable.

·
Engineering
science is more rational because engineering data *and* engineering equations *and*
engineering charts describe how the *numerical
values* of parameters are related.

**How dimensionless parameters greatly simplify the solution of nonlinear
problems.**

Dimensionless
parameters greatly simplify the solution of nonlinear problems by making it
possible to abandon parameters such as h, E, and R. These parameters are undesirable because they
are *variables* in nonlinear problems.

For
example, q = hDT and h = q/DT are *identical*. Therefore h and q/DT
are identical and interchangeable. If q
is proportional to DT, q/DT (aka h) is a *constant, *and both q = hDT
and q = *f*{DT} contain the *two *variables q and DT. But if q is a *nonlinear* function of DT,
q/DT (aka h) is a *variable*, and q = hDT contains the *three *variables q, DT, and q/DT (aka h), whereas q = *f*{DT}
contains only the *two* variables q and
DT.

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 E and R.

**Dimensional homogeneity in the new engineering.**

In the new engineering, parameter symbols are
dimensionless, and therefore *all*
parametric equations are dimensionless and dimensionally homogeneous. If an equation is *quantitative*, the dimension units that underlie parameter symbols *must *be specified in an accompanying
nomenclature.

**The 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, q = hDT 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 E
and R.

Because parameters such as h, E, and R are
required *only* for the dimensional
homogeneity of engineering laws, and because equations are *inherently* dimensionally homogeneous in the new engineering,
parameters such as h, E, and R can be, and are, abandoned and *not *replaced.

*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. The article can be downloaded without charge
at https://www.benthamopen.com/tomej/. *

**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 subject of
convective heat transfer to the new engineering:

·
Replace Eq. (1) with Eq. (2).

q = hDT (1)

q = *f*{DT} (2)

·
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. (3) results
in Eq. (4), and the transformation of Eq. (5) results in Eq. (6).

U
= 1/(1/h_{1} + t_{wall}/k_{wall}+ 1/h_{2 }) (3)

DT_{total} = DT_{1} + DT_{wall} + DT_{2} (4)

Nu = a Re^{b }Pr^{c}
(5)

q = a(k/D)Re^{b}^{
}Pr^{c}DT (6)

In the new engineering, Eqs.
(1), (3), and (5) are *abandoned*, and
are replaced by Eqs. (2), (4), and 6). And similarly for
other branches of engineering. Note that
Eqs. (3) and (4) are *identical*, and that Eq. (4) is so simple it is intuitive, whereas
Eq. (3) is far from intuitive. It is
much easier to learn how to solve problems using Eq. (4) rather than Eq.
(3). And *any* heat transfer problem that can be solved using Eq. (3) can also
be solved using Eq. (4).

If a heat transfer problem concerns
proportional behavior, it is easily solved using either Eq. (3) or Eq. (4)
because both equations contain only two variables. However, if a heat transfer problem concerns *moderately nonlinear* behavior, the
solution is quite simple if Eq. (4) is used, and considerably more difficult if
Eq. (3) is used, as demonstrated by the problem in Table 1. If a heat transfer problem concerns *highly nonlinear* behavior, the solution
is quite simple if Eq. (4) is used, and *virtually
impossible* if Eq. (3) is used.

**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).

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.

** 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(**

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

If
DT_{2}{q} in
Table 1 were so highly nonlinear that it included a region in which dq/dDT_{2} is *negative*, the relationship between q and
DT_{2}
would probably be described graphically in the form q vs DT_{2}. The problem could 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}**

**on ****s**** = f{**

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.**

Just as equations *always* describe how the *numerical
values* of parameters are related, charts *always* describe how the *numerical
values* of parameters are related.

For example, “stress/strain charts” describe how the
numerical value of s is related to the numerical value of e. 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 the dimension units were *not *specified on Figures (1) and (2), the charts would 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) or Ventuno Press for $49.95.

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

Eugene
F. Adiutori

Updated on November 4,
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