@Article{NMTMA-16-511,
author = {Ji , Cui-Cui and Dai , Weizhong},
title = {Numerical Algorithm with Fourth-Order Spatial Accuracy for Solving the Time-Fractional Dual-Phase-Lagging Nanoscale Heat Conduction Equation},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2023},
volume = {16},
number = {2},
pages = {511--540},
abstract = {<p style="text-align: justify;">Nanoscale heat transfer cannot be described by the classical Fourier law
due to the very small dimension, and therefore, analyzing heat transfer in nanoscale
is of crucial importance for the design and operation of nano-devices and the optimization of thermal processing of nano-materials. Recently, time-fractional dual-phase-lagging (DPL) equations with temperature jump boundary conditions have
showed promising for analyzing the heat conduction in nanoscale. This article
proposes a numerical algorithm with high spatial accuracy for solving the time-fractional dual-phase-lagging nano-heat conduction equation with temperature jump
boundary conditions. To this end, we first develop a fourth-order accurate and unconditionally stable compact finite difference scheme for solving this time-fractional
DPL model. We then present a fast numerical solver based on the divide-and-conquer
strategy for the obtained finite difference scheme in order to reduce the huge computational work and storage. Finally, the algorithm is tested by two examples to verify
the accuracy of the scheme and computational speed. And we apply the numerical
algorithm for predicting the temperature rise in a nano-scale silicon thin film. Numerical results confirm that the present difference scheme provides ${\rm min}\{2−α, 2−β\}$ order accuracy in time and fourth-order accuracy in space, which coincides with the
theoretical analysis. Results indicate that the mentioned time-fractional DPL model
could be a tool for investigating the thermal analysis in a simple nanoscale semiconductor silicon device by choosing the suitable fractional order of Caputo derivative
and the parameters in the model.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2022-0050 },
url = {http://global-sci.org/intro/article_detail/nmtma/21587.html}
}