Application of dimensional analysis in sorption modeling of the styryl pyridinium cationic dyes on reusable iron based humic acid coated magnetic nanoparticles

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

The paper aims to use Modern Dimensional Analysis to study the heat transmission through a rectangular bar with a hole. The problem is very important for monitoring a structure, made of such bars, to protect it from fire. The original part of the work is represented by the application of this nonconventional method in the field of heat transfer in bars of rectangular-tubular section. During system heating, the properties of the material change dramatically at high temperatures, which can lead to the collapse of the entire system. The Laws of the Model, further applied to the two sets of independent variables, provide the complete sets of dimensionless variables, which cannot be offered by any of the classical methods (such as Geometric Analogy, Theory of Similarity, and Classical Dimensional Analysis). The validation of the method was made experimental on both unprotected structural elements and those thermally protected with layers of intumescent paints, widely used in the field of fire protection. Finite Element Method was too applied to obtain the field of temperature in order to validate the model.

Experimental Validation of Model Heat Transfer in Rectangular Hole Beams Using Modern Dimensional Analysis

Based on the Szirtes’ modern dimensional analysis (MDA), the authors apply the theory to a real structure in order to validate by experimental measurements its applicability. After a presentation of the basic elements of the model law (ML), deduced for two relevant cases, the authors conceived the set of prototypes and models, based on the case of an actual construction pillar, physically performed at scales of 1:1, 1:2, and 1:4. The combination of these structural elements, made at different scales, resulted in three sets of prototypes and models. In this paper, taking into consideration the ML for two relevant cases, the following are presented: the original test stand of these structural elements; block diagram of the original electronic heating and control system; the basic considerations regarding the particularity of this heating system from the point of view of heat transfer; measurement data, obtained for both nonthermally protected elements and for those protected with layers of intumescent paints. In the last part of the paper, the values obtained by rigorous direct measurements with those offered by the ML on the elements considered as prototypes and models are compared. Almost identical values were obtained from the direct measurements with those provided by the ML, thus resulting in the validation of these laws. The same thermal regimes were applied to all these structural elements, with registration of every parameter related to these thermal regimes. Depending on the role of a structural element within a certain set (prototype-model), some of the measurement data were considered as data acquired directly through measurements, and others served as reference elements for those for which we had to obtain through the model law. In the last part of the paper, the sizes obtained by rigorous direct measurements are compared with those offered by the model law on the elements considered as prototypes and models. Identical practical values of the quantities were obtained from the direct measurements with those provided by the model law, thus resulting in the validation of these laws.