Modelling and analysis of heat transfer through 1D complex granular system

Abstract

This article demonstrates the solution to the problem of the passage of air through the external wall barrier and the influence of the materials type and its layer arrangement on heat conductivity, in respect of building heat losses. It shows how the temperature changes inside the wall barriers and in a room while the external temperature changes. Also, this article presents the mathematical model based on fractional differential equation describing the analysed phenomenon.

Fractional oscillator equation – Transformation into integral equation and numerical solution

“…(30) and (36). We introduce the homogeneous grid of nodes (with the constant time step Dt ¼ b=n, where n þ 1 is a number of nodes): 0 ¼ t 0 < t 1 < Á Á Á < t i < t iþ1 < Á Á Á < t n ¼ b, and t i ¼ i Dt.…”

“…Over the last decade, it has been demonstrated that many physical systems can be modelled more accurately by applying fractional differential equation rather than classical differential equations [18,19,21,29,30]. One of the new directions in fractional calculus and its applications is to investigate the numerical solutions of fractional differential equations, containing composition of the left and the right derivatives [2,3,5,[7][8][9][10]13,20,27,31].…”

Archives of Foundry Engineering

“…Modelling the phenomenon of heat transfer in the porous materials is a complicated problem. For modelling this phenomenon one can apply the mathematical models using the fractional derivatives [7][8][9]. The usefulness of models with fractional order derivatives in modelling the thermal processes in porous materials is described in [8].…”

Simulation of granular in two dimensions: The effect of particle velocity on rigid wall boundary

“…The granular simulation is a particles based simulation [5][6]. The arrangement, number, and size of particle allow to describe and analyze various physical phenomena besides discrete properties, such as heat transfer [7], landslide flow [8], and industrial application [9]. The granular analysis can also combine with other methods such as computational fluid dynamics [10].…”