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

Abstract

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.

Global mathematical correlations for heat pipe and nanofluid based thermal energy storage system: Dimensional analysis approach

“…Azad et al 12 developed global correlations based on nondimensional numbers to determine the minimum amount of liquid phase change material to begin the natural convection and its corresponding Rayleigh number. Száva et al 13 studied the heat transfer in rectangular hole beams by using modern dimensional analysis (MDA).…”

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

“…The boundary condition at x = 0 corresponds to the temperature of the base which is measured experimentally (Dirichlet) and at x = L, the boundary condition corresponds to the equality between the heat transfer due to conduction and the heat transfer by convection from the cross-section surface to the surrounding air (Fourier). All variables that can have an influence on the heat transfer in the beam with rectangular-hole section were are analysed in the afore-mentioned references [55][56][57][58][59][60].…”

“…In order to reduce the number of dimensionless variables n , ... , j , j 1 = π , which will form the Model Law, the method of de-doubling the dimensions was used (here: de-doubling the lengths), according the principles given in [32,33]. All variables that can have an influence on the heat transfer in the beam with rectangularhole section were are analysed in the afore-mentioned references [55][56][57][58][59][60].…”

“…The numerical simulation of the thermal behavior was performed in ABAQUS, both for the structural elements performed at the 1:1 and 1:2 scales [58,60,61]. Figures 6-9 show the modeling results of the uncovered prototype, respectively coated with heat-resistant paint [58].…”

Modern Dimensional Analysis Involved in Polymers Additive Manufacturing Optimization

“…Faced with these shortcomings, the improved method, hereinafter referred to as MDA , [ 16 , 17 , 85 , 86 , 87 , 88 , 89 , 90 , 91 ], comes to offer a solution, which practically eliminates all these shortcomings, becoming a unitary, safe and particularly accessible method for any researcher. The net advantages of MDA , successfully applied over the years and by the authors in the works [ 18 , 22 , 23 , 26 , 28 , 92 , 93 ], were presented in other work [ 16 , 17 , 22 , 26 ].…”