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.

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 “add nine six times”.  Therefore it is irrational to contend that dimensioned parameters can be multiplied, but cannot be added.  (Fourier was a world class mathematician, and it is more than likely that he knew that multiplication is repeated addition, and that his view of dimensional homogeneity is irrational.)

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 inhomogeneous, 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 inhomogeneous 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/DT (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 qconv 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 qconv 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)

qconv = 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 kwall/twall, 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/h1 + twall/kwall+ 1/h2 )                                                                                                 (12)

DTtotal = DT1 + DTwall + DT2                                                                                                    (13)

Nu = a Reb Prc                                                                                                                          (14)

q = a(k/D)Reb PrcDT                                                                                                               (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 article is entitled “An Alternate View of Dimensional Homogeneity, and Its Impact on Engineering Science”,

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 = hDT and DT = f{q}.

Based on q = hDT.                                              Based on DT = f{q}.

U = 1/(1/h1 + t/k + 1/h2)                                DTtotal = DT1 + DTwall + DT2                     (1)

DTtotal = 320 – 200 = 120                               DTtotal = 320 – 200 = 120                          (2)

h1 = .40(DT1).33                                              DT1 = 1.99q.75                                            (3)

twall/kwall = .05                                                DTwall = .05q                                              (4)

h2 = .80(DT2).50                                              DT2 = 1.16q.667                                          (5)

U = 1/(1/.4(DT1).33 +.05 + 1/.8(DT2).50)         120 = 1.99q.75  + .05q + 1.16q.667              (6)

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, DT1, and DT2), 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 DT1 and DT2 were proportional to q—ie if h1 and h2 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 DT2{q} in Table 1 is so highly nonlinear that it includes a region in which dq/dDT2 is negative, the relationship between q and DT2 is probably described graphically in the form q vs DT2.  The problem might have more than one solution, and operation might be thermally unstable in the region in which dq/dDT2 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 qout vs (T2 + DT2{qout}).  Note that (T2 + DT2{qout) is the temperature of the interface that adjoins Fluid 2, and qout is the heat flux out of that interface.

·   On the same chart, use the given information to plot qin vs (T­1 - DT1 - DTwall).  Note that (T­1 - DT1 - DTwall) is the temperature of the interface that adjoins Fluid 2, and qin 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/dDT2 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 DT2 is replaced by a chart of h vs DT2, 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 = elastice and on s = f{e}.

In the elastic region:

·   s = Eelastice is a proportional equation, and Eelastic 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 Eelastic.

Because both s = Eelastice and s = ce are proportional equations, and because c and Eelastic are numerically equal, the solution of elastic problems based on s = ce is identical to the solution based on s = Eelastice.   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{e} rather than s = Esecante.

In the inelastic region, E is the variable Esecant.  Because s = Esecante 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 = Esecante.

The solution of a stress/strain problem using s = Ee.

Determine the strain in the bar.

Given:

·   The stress in the bar is 45,000 kg/cm2.

·   Ebar = f{e} is described in Figure 1.

Analysis

The analysis based on s = Ebare is not difficult, but it is time-consuming, and there is a considerable likelihood of error.

Solve the above problem using s = f{e}.

Given:

·   The stress in the bar is 45,000 kg/cm2.

·   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, 4th 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,  3rd edition, translation by Cohen, I. B. and Whitman, A. M., 1999, p. 460, University of California Press

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

Updated on October 12, 2018

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.

1.    Book entitled The New Heat Transfer.

c.     Reviews.

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

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 International Journal of the Japanese Society of Mechanical Engineering.  It was just as timely and important in 1994 as it had been in 1964.)