Abstract: The purpose of this paper is
to devise a new model of heat conduction for a body which is
totally insulated at its boundary. The essence of the new model
is modification of the Fourier law in such a way that the
resulting heat conduction problem will be formulated as an
initial value problem with a non-standard partial differential
equation. The values of normal derivatives of the heat flux to
various orders for all times (t>0) will be determined by the
governing partial differential equation and the values of normal
derivatives of fluxes of fluxes at the initial time (t=0). We
study the properties of this model and demonstrate its validity
for a simple one-dimensional case of a thin bar insulated at
both ends.
Key words:
Heat conduction Model
manuscript received on
December 24, 1994
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