Application And Numerical Algorithm Of The Fractional Dual-Phase-Lagging Heat Conduction Model

Nanotechnology is becoming increasingly the frontier field in fundamental and applied research.Nanoscale heat transfer has shown many characteristics that are different from those familiar at the macroscale.Obtaining accurate temperature distributions in nanoscale structures is critical to fundamentally understand heat transfer in nanoscale electrical and mechanical devices and in thermal processing of nanoscale materials.Effective thermal management is very important to further miniaturization and improvement of the power density and performance of next-generation electron and optoelectronic devices.Recently,fractional calculus has been successfully used to modulate several models in heat conduction and other media and has gained importance in heat conduction and thermoelastic problems.Hence,the new theoretical and numerical methods for solving fractional heat conduction models have gained increasing attention.The main aim of this thesis is to develop a new nanoscale heat transfer model based on the fractional dual-phase-lagging heat conduction equation with the temperature-jump boundary condition.And seeking a suitable thermal lagging perfect contact interfacial condition between layers can lead to obtain an energy estimation for the fractional dual-phase-lagging heat conduction equation with the temperature-jump boundary condition and this thermal lagging interfacial condition in multi-layered nanoscale thin films.From a mathematical point-of-view,the regularity(well-posedness)of the proposed fractional dual-phase-lagging heat conduction models is analyzed.Furthermore,we develop the Crank-Nicolson type finite difference schemes for solving the fractional dual-phase-lagging heat conduction models.By the discrete energy method,we prove the proposed numerical algorithms are unconditional stability and convergence in maximum norm.Finally,we show the applicability of the fractional dual-phase-lagging heat conduction models and the significant influence of the fractional orders.A new system of the theoretical analysis and the numerical method for the fractional dual-phase-lagging heat conduction is set up.