The "fluid friction factor" (f) should be abandoned because it is a mathematically undesirable parameter that complicates the solution of fluid flow problems.

This article reviews profile of Joseph Fourier, a French mathematician, who was a true father of modern engineering. Concepts that engineers use every day—as fundamental as the homogeneity of equations and the heat transfer coefficient—were pioneered by Fourier. Fourier’s contributions to engineering science, many of which were presented in his 1822 book, The Analytical Theory of Heat, include the original view of dimensional homogeneity. The heat transfer science it presented has been handed down to us virtually unchanged, and has served as a model for other branches of engineering. Fourier’s contemporaries forestalled the general publication of his work for 15 years while they claimed to find fault with it. They ultimately accepted his revolutionary view of homogeneity, solely because he was able to solve many practical and theoretical problems that had never been solved. He attributed his success to the homogeneity in his equations.

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Film effectiveness (η) is used to describe the adiabatic wall temperature (TAW) which results when a colder or hotter fluid is injected into the boundary layer. Eq (1) is the defining equation for η:(1)(TMS−TAW)=η(TMS−TF)where TF and TMS refer to the temperatures of the film and mainstream fluids. Literature data indicate that η is a constant coefficient in Equation 1 only in applications where TF/TMS is restricted to a narrow band. If TF/TMS varies over a wide band, such as in gas turbines and rockets, then η is a variable in Eq 1. This article demonstrates that, in applications where TF/TMS varies over a wide band, the film effectiveness concept is neither simple nor direct, and it complicates and confuses the solution of practical problems. This article also presents a new and simple concept to replace film effectiveness. The new concept retains the TF/TMS parameter used in film effectiveness methodology, but it replaces η with TAW/TMS. The particular advantage of the new concept is that it describes TAW in a simple and direct way even if TF/TMS varies over a wide band. The end result is that, in applications such as gas turbines and rockets, the new concept is much simpler and therefore much better than the film effectiveness concept it replaces.

Conventional engineering laws are irrational for three reasons: When the laws are applied to nonlinear behavior, they have three variables to describe how two variables are related; they are founded on Fourier’s erroneous claims that dimensions can rationally be assigned to numbers, and dimensions can rationally be multiplied or divided. Until now, it has been globally accepted that parameter symbols in rational equations represent numerical value and dimension. The proposed paradigm shift requires that parameter symbols in equations represent only numerical value, and if an equation is quantitative, the dimension units that underlie parameter symbols must be specified in an accompanying nomenclature. The proposed paradigm shift results in laws and equations that are dimensionally homogeneous because they are dimensionless. The new laws are analogs of y = f{x}.The new laws state that the numerical value of parameter y is a function of the numerical value of parameter x, and the function may be proportional, linear, or nonlinear. The new laws are rational because they always have only two variables, they do not require that dimensions be assigned to numbers, and they do not require that parameter dimensions be multiplied or divided.