The use of Dimensional Analysis and Optimization of Pneumatic Drilling Operations and Operating Parameters

Thermal Scaling of Transient Heat Transfer in a Round Cladded Rod with Modern Dimensional Analysis

“…• the direct analysis of the differential relations that describe the phenomenon, in order to establish the dimensionless groups, does not always allow the unitary establishment of the complete set of these dimensionless groups; • also, the classical methodology (CDA) is usually cumbersome and non-unitary, allowing different researchers to obtain different sets of dimensionless variables; • in order to obtain these dimensionless groups, the authors of different works use, based on the application of Buckingham's theorem, either the normalization of the terms of the differential relations related to the phenomenon describing the phenomenon, or a rather arbitrary and unambiguous combination of variables involved in describing the phenomenon of the main measure (dimensions), which takes place in each author according to his own logic, so it is a non-unitary approach to the phenomenon. Thus, based on these approaches, different sets of dimensionless variables may result, which may even represent combinations of those deduced by other authors [36,[38][39][40][41][42][43][44][45][46][47]. • the classical methodology, i.e., CDA, presupposes from the very beginning a deep knowledge of the phenomenon and of the differential relations that govern the phenomenon, which for an ordinary researcher represents an impediment; • the classical methodology, including those presented in the papers [22,23,25,[27][28][29][30], does not explicitly allow highlighting from the very beginning of the set of independent variables or dependent variables, but applies a hard-to-follow (and often unexplained) logic of how these two sets were chosen; • the involvement from the very beginning, in approaching with the help of the dimensional analysis of the phenomenon, of some very complicated differential relations whose analysis will eventually lead to the establishment of these dimensionless groups, discourages the vast majority of researchers/engineers from using a safe, unified, and simple way to approach the problem, as will happen with MDA;…”

“…The author of the paper [44] uses the choice of independent and dependent variables but applies the standard methodology for determining exponents by solving the system of linear equations, which describes the phenomenon.…”

Modern Method to Analyze the Heat Transfer in a Symmetric Metallic Beam with Hole

“…Based on a careful analysis of the phenomenon, according to the research works [21,24,[30][31][32][33][42][43][44][45][46][47][48][49][50][51][52][53][54], the set of variables that describe the heat transfer in beams of tubular-rectangular cross-sectional area are: heat, heat rate, time, density (steel, air, paint/insulating material), constant-pressure specific heat of air, specific heat capacity (steel, air), thermal conductivity (steel, paint coat), thermal diffusivity of air, velocity normal to the plane where the shear stress is developed and its gradient, dynamic viscosity of air, kinematic viscosity of air, Prandtl number of air, Reynolds number of air, convection heat transfer coefficient, thickness of the paint volume of beam or paint coat, cross-sectional area of the beam, lateral area (x-z) of the beam, lateral area (x-y) of the beam, beam's dimensions, shape factor, cross-sectional perimeter, gravitational acceleration, temperature variation, coefficient of volume expansion (steel, air), Nusselt number, Grasshoff number along x direction, Péclet number, Biot number, Stanton number, Fourier number. All these variables and the measurement unities are presented in the section Nomenclature.…”

“…New results concerning the MDA are presented in [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. In the case of the bar covered with a foaming layer (intumescent paint), heat transfer is performed by:…”

Modern Dimensional Analysis Involved in Polymers Additive Manufacturing Optimization

“…However, in a series of works, these principles of Geometric Analogy, Similitude Theory, and CDA , are applied to thermal phenomena [ 70 , 71 , 72 ] and to aspects of engineering [ 41 , 73 , 74 ], respectively. Many researches have presented the advantages of Modern Dimensional Analysis ( MDA )applied to this type of problems [ 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 ].…”