The temperature overshooting phenomenon in one-dimensional nanoscale heat conduction in thin films is studied for various boundary conditions.The results show that when ballistic heat transport strongly affects the he...The temperature overshooting phenomenon in one-dimensional nanoscale heat conduction in thin films is studied for various boundary conditions.The results show that when ballistic heat transport strongly affects the heat transport process,temperature overshooting is more likely to occur.A sudden increase of temperature on only one surface of a thin film cannot trigger temperature overshooting,while symmetric boundary temperature perturbations lead to the largest temperature overshooting.Twodimensional heat conduction is also studied in a nanoscale area.The analytic results show that Fourier’s law may severely underestimate the temperatures in nanofilms as well as in nanoareas when temperature overshooting occurs.展开更多
Four basic explicit analytical solutions of non_Fourier heat conduction equation simulating IC chip thermal condition are derived. Some other analytical series solutions can also be derived with the above_mentioned ba...Four basic explicit analytical solutions of non_Fourier heat conduction equation simulating IC chip thermal condition are derived. Some other analytical series solutions can also be derived with the above_mentioned basic solutions. Analytical solution has its own irreplaceable important meaning in theory. In addition, as the standard solution to check the accuracy, convergence and effectiveness of various numerical computational methods and their differencing schemes, grid generation ways and so on, the analytical solution is very useful also for the newly rapidly developing computational heat transfer.展开更多
基金supported by the National Basic Research Program of China(2011CB706904)
文摘The temperature overshooting phenomenon in one-dimensional nanoscale heat conduction in thin films is studied for various boundary conditions.The results show that when ballistic heat transport strongly affects the heat transport process,temperature overshooting is more likely to occur.A sudden increase of temperature on only one surface of a thin film cannot trigger temperature overshooting,while symmetric boundary temperature perturbations lead to the largest temperature overshooting.Twodimensional heat conduction is also studied in a nanoscale area.The analytic results show that Fourier’s law may severely underestimate the temperatures in nanofilms as well as in nanoareas when temperature overshooting occurs.
文摘Four basic explicit analytical solutions of non_Fourier heat conduction equation simulating IC chip thermal condition are derived. Some other analytical series solutions can also be derived with the above_mentioned basic solutions. Analytical solution has its own irreplaceable important meaning in theory. In addition, as the standard solution to check the accuracy, convergence and effectiveness of various numerical computational methods and their differencing schemes, grid generation ways and so on, the analytical solution is very useful also for the newly rapidly developing computational heat transfer.
