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

Gálfi, Botond-Pál; Şova, D.; Szavá, Ioan

doi:10.3390/math9161875

Cited by 14 publications

(25 citation statements)

References 34 publications

(68 reference statements)

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“…. , n dimensionless variables were set, based on the MDA method indicated in [32,33] was already shown by the authors in the case of the beam with circular section [31]. Therefore, only the differences that occur at the beam with rectangular-hole section will be hereafter presented.…”

Section: Methods and Modelmentioning

confidence: 99%

“…As shown in the case of a beam with a circular section [31], the variables, in the case of the rectangular hole beam, are divided into:…”

Section: Methods and Modelmentioning

confidence: 99%

“…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.…”

Section: Kmentioning

confidence: 99%

“…Based on Szirtes theory [31,32], which was applied in the present study, MDA offers the most complete and also the simplest Model Law for the studied phenomenon. The method is based on the exclusion of irrelevant physical variables.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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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.

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Section: Methods and Modelmentioning

confidence: 99%

“…As shown in the case of a beam with a circular section [31], the variables, in the case of the rectangular hole beam, are divided into:…”

Section: Methods and Modelmentioning

confidence: 99%

Section: Kmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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“…al. [21] developed a model based approach of heat transfer mechanism of a nonlinear mechanical system with in depth knowledge. It helps to study how the heat is transferred from a cylindrical type of structure.…”

Section: Dynamics Of Mechanical System-a Literature Reviewmentioning

confidence: 99%

Analytical Study of Series Solutions for the ‘Nonlinear Mechanical System’ with Stability Analysis

Chakraborty¹,

Bhattacharjee²,

Roy³

et al. 2022

YMER

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Any mechanical system can easily be analyzed with the help of proper designing or modeling. All kinematical constrains are also been considered at the time of modeling. Generally the traditional dynamical differential equations are solved to predict the nature of the system. In this work, some typical types of dynamical mechanical system in taken into consideration and further the dynamical equations are being solved using ‘Series Solutions Technique’ for the analysis of the nonlinear system. The solution is consisting of two sections. Using frequency response analysis via simulation, which section of the solution is more suitable or effective for the designing purpose has also been explained in detail. Finally, the local stability analysis of the entire system is studied in detail with proper numerical simulation. Keywords: Nonlinearity, Series Solution, Stability Analysis, Phase Portrait, Frequency Response Function.

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

Kalbande,

Vinchurkar,

Nandanwar

et al. 2023

Env Prog and Sustain Energy

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This research article presents the development of a mathematical model for a nanofluid‐based thermal energy storage (TES) system. The main objective of the study is to establish global correlations among various performance parameters of the TES system. The TES system considered in this research employs Al2O3/Soybean oil as the heat transfer fluid (HTF), and heat pipes are integrated to enhance heat transfer between the HTF and the phase change material. The mathematical model developed in this study is based on the Buckingham‐pi theorem. The derived correlations encompass the Nusselt number, stored energy, and thermal efficiency. Validation of the model is conducted for the Nusselt number, and a regression analysis is performed to assess the accuracy level of the mathematical model. Using the derived mathematical models, several key parameters of the TES unit are calculated. The convective heat transmission coefficient is determined to be 364.07 W/m2K, indicating the efficiency of heat transfer within the system. The thermal efficiency is found to be 89.10%, which provides insights into the overall effectiveness of the TES unit. Additionally, the thermal storage capacity of the TES unit is calculated as 3425.68 kJ, representing the amount of energy that can be stored and retrieved by the system. By equating the dimensions of variables within an equation, it becomes possible to deduce the relationship between the unknown parameters and the known quantities. This enables estimation of the unknown parameters even when direct measurements are unavailable, thereby providing a useful method for obtaining crucial information in data‐limited scenarios.

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

Cited by 14 publications

References 34 publications

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

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

Analytical Study of Series Solutions for the ‘Nonlinear Mechanical System’ with Stability Analysis

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

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