Control of the Thermal Fractal Diffusion of Tightly Compressed Heterogeneous Layers of Thin Plates

Wei Qiao,Jie Sun,Shu-Tang Liu

doi:10.1155/2014/672547

Abstract

As the thermal conductivity of thin plates composed of tightly compressed heterogeneous layers varies continuously in the form of an exponential function, we present a nonlinear dynamical model of the fractal growth of thermal diffusion. We also analyze the quantitative relationship between the probability of growth and the disturbance term, predict the control action of the environmental disturbance term on fractal growth, and use Matlab simulation to verify the control effectiveness of thermal fractal diffusion. The results facilitate the selection of appropriate control areas and control parameters for the thermal diffusion variable coefficients. In addition, variation in the fractal dimension reflects the influence of environmental disturbance on the complex process of thermal fractal diffusion.

Highlights

Fractal theory has attracted considerable research interest [1,2,3,4,5,6,7,8], with the diffusion-limited aggregation (DLA) [9] model proposed by Witten and Sander receiving particular attention
As the thermal conductivity of thin plates composed of tightly compressed heterogeneous layers varies continuously in the form of an exponential function, we present a nonlinear dynamical model of the fractal growth of thermal diffusion
As the thermally conductive effects of thin plates consisting of homogeneous layers have extensive applications in the field

Summary

Introduction

Fractal theory has attracted considerable research interest [1,2,3,4,5,6,7,8], with the diffusion-limited aggregation (DLA) [9] model proposed by Witten and Sander receiving particular attention. Shen [12] used an improved DLA model to effectively control fractal thermal diffusion using a two-dimensional constant coefficient. Zhang and Liu [13] interpreted the thermal conductivity of homogeneous material as a constant and examined methods of controlling the thermal diffusion fractal growth of thin plates under conditions of environmental disturbance. Contrary to the assumptions of many researchers [14,15,16,17,18], changes in thermal source, pressure, and many other external factors in real and complex environments affect the aggregation growth process of fractal diffusion, resulting in a fractal growth morphology that is complicated, variable, and difficult to predict. Constructing an environmental disturbance term that comprises a forced item with a polynomial form and a source item with a circular designated area enables us to predict and control the thermal fractal diffusion of thin plates made of homogeneous layers

Thermal Diffusion System of the Nonhomogeneous Layers of Thin Plates

Conclusion