The purpose of this paper is to devise a new model of heat conduction for a body which istotally insulated at its boundary. The essence of the new model is modification of the Fourier law insuch a way that the resulti...The purpose of this paper is to devise a new model of heat conduction for a body which istotally insulated at its boundary. The essence of the new model is modification of the Fourier law insuch a way that the resulting heat conduction problem will be fonnulated as an initial value problemwith a nonstandard partial differential equation. The values of normal derivatives of the heat fiuxto various orders for all tmies (t> 0) will be detemined by the governing partial differential equa-tion and the values of normal derivatives of fluxes at the initial time (t=0). We study the properitesof this model and demonstrate its validity for a simple onedimensional case of a thin bar insulatedat both ends.展开更多
文摘The purpose of this paper is to devise a new model of heat conduction for a body which istotally insulated at its boundary. The essence of the new model is modification of the Fourier law insuch a way that the resulting heat conduction problem will be fonnulated as an initial value problemwith a nonstandard partial differential equation. The values of normal derivatives of the heat fiuxto various orders for all tmies (t> 0) will be detemined by the governing partial differential equa-tion and the values of normal derivatives of fluxes at the initial time (t=0). We study the properitesof this model and demonstrate its validity for a simple onedimensional case of a thin bar insulatedat both ends.
