An Efficient Meshless Numerical Method for Heat Conduction Studies in Particle Aggregates

Abstract

A new meshless numerical approach for studying heat conduction in particulate systems was developed that allows the efficient computation of the temperature distribution and the effective thermal conductivity in particle aggregates. The incorporation of the discretization-corrected particle strength exchange operator in meshless local Petrov–Galerkin calculations is suggested here, which was shown to perform better than previously tested trial functions, regarding the speed of convergence and accuracy. Moreover, an automated algorithm for node refinement was developed, which avoids the necessity for user intervention. This was quite important in the study of particle aggregates due to the appearance of multiple points of contact between particles. An alternative approach for interpolation is also presented, that increased the stability of the methods and reduced the computational cost. Test case models, commercial computational fluid dynamics software, and experimental data were used for validation. Heat transport in various aggregate morphologies was also studied using sophisticated aggregation models, in order to quantify the effect of aggregate fractal dimension on the nanofluid conductivity, targeting eventually the optimization of heat transfer applications. A trend of effective conductivity enhancement upon reduction of the fractal dimension of the aggregate was noted.

Modelling Thermal Conduction in Nanoparticle Aggregates in the Presence of Surfactants

“…In studies conducted thus far [ 10 , 19 ], the morphology of the aggregates is considered to have the typical characteristics of particle–particle, particle–aggregate, and aggregate–aggregate clustering. Thus, descriptive models such as Diffusion-limited Aggregation (DLA), Diffusion-limited Cluster Cluster Aggregation (DLCCA), Reaction-limited Aggregation (RLA), and Ballistic Aggregation (BA) are widely used to describe the process of aggregation for various suspended nanoparticles, and the morphology of the nanofluid [ 35 , 36 ]. The majority of the established aggregation models mostly study spherical particles, and this particle geometry was used in the present work as a reference base.…”

“…Approaches to field functions and their derivatives are made using the Discretisation-Corrected Particle Strength Exchange (DC PSE) method [ 34 ], which has been shown to provide stable and fast solutions to such problems, and the integration is performed in cubic sectors around each node. The numerical method that was developed [ 35 ] for calculating temperature distribution and effective conductivity can be extended to calculations for a three-phase system, like the one encountered here.…”

Solución Analítica de la Distribución de Temperaturas en un Medio Homogéneo Debido a un Cable Eléctrico con Forma de Onda Rectangular

“…Finalmente, haciendo uso de las propiedades de la función delta de Dirac para integrar la expresión dada por (10) y reemplazando en (11), la solución analítica para la distribución de temperaturas adimensional en un sólido homogéneo infinito causada por una generación de calor en forma de onda rectangular está dada por…”

“…Por otro lado, a pesar de que los métodos puramente numéricos han permitido avanzar en la solución de muchos problemas relevantes para la ingeniería [11,12], estos métodos sólo ofrecen soluciones aproximadas (que deben ser validadas) y generalmente requieren de computadoras con alta capacidad de procesamiento, lo cual por supuesto, implica una inversión económica considerable [13]. A diferencia de las soluciones puramente numéricas, las soluciones analíticas permiten profundizar nuestro entendimiento de los fenómenos de transferencia de calor y nos ofrecen ecuaciones explícitas simples que pueden ser usadas para determinar la conductividad térmica o la capacidad calorífica de un material, parámetros esenciales para el diseño óptimo de los equipos eléctricos [14,15] exactas, elegantes, versátiles y porque pueden servir de referencia para validar los resultados de los métodos puramente numéricos.…”

An Improved 2D Meshfree Radial Point Interpolation Method for Stress Concentration Evaluation of Welded Component

“…In recent years, meshfree methods are attracting more and more interests in computational mechanics for its advantages such as good self-adaptability. With the rapid development of meshfree techniques, various problems in science and engineering have been solved by meshfree methods [12][13][14][15]. Meshfree methods have been great potential topics and trends in computational mechanics.…”