@article{ajme2020841,
author={Adiutori, Eugene F.},
title={A Critical Appraisal of Modern Engineering Science, and the Changes Required by the Appraisal Conclusions},
journal={American Journal of Mechanical Engineering},
volume={8},
number={4},
pages={144--153},
year={2020},
url={http://pubs.sciepub.com/ajme/8/4/1},
issn={2328-4110},
abstract={Until the nineteenth century, engineering science was founded on a view of dimensional homogeneity that *required* the following: • Parameters *must not* be multiplied or divided. • Dimensions *must not* be assigned to numbers. • Equations *must* be dimensionless. This view made it *impossible *to create equations such as the laws of modern engineering science. Modern engineering science is founded on Fourier¡¯s radically different nineteenth century view of dimensional homogeneity. His view *allows* the following, and makes it possible to create the laws of modern engineering science: • Parameters *may* be multiplied or divided. • Dimensions *may *be assigned to numbers. • Equations *may or may not* be dimensionless*.** *Fourier did *not* prove the validity of his radically different view of dimensional homogeneity. He merely stated* *that his view of dimensional homogeneity ¡°*is the equivalent of the fundamental lemmas which the Greeks have left us without proof¡±.* Presumably, his colleagues accepted his *unproven* view because he solved problems they were unable to solve. A critical appraisal of Fourier¡¯s *unproven* view of dimensional homogeneity results in the following conclusions: • Parameters *cannot* rationally be multiplied or divided. Only the *numerical values* of parameters can rationally be multiplied or divided. • Dimensions *cannot* rationally be assigned to numbers. If dimensions could be assigned to numbers, *any* equation could be regarded as dimensionally homogeneous. • Equations are *inherently* dimensionless and dimensionally homogeneous because symbols in parametric equations can rationally represent *only* numerical value. The changes required by the appraisal conclusions result in a much simpler engineering science because parameters such as material modulus and heat transfer coefficient are *abandoned*. They are abandoned because problems are readily solved *without* them, and because when dealing with nonlinear behavior (as in the inelastic region and in various forms of convection heat transfer), they are *extraneous variables* that *greatly* complicate solutions. Examples in the text demonstrate how to solve problems without using parameters such as material modulus or heat transfer coefficient.},
doi={10.12691/ajme-8-4-1}
publisher={Science and Education Publishing}
}