Authors :
Ismail Abbas
Volume/Issue :
Volume 6 - 2021, Issue 7 - July
Google Scholar :
http://bitly.ws/9nMw
Scribd :
https://bit.ly/3z3TZY1
Abstract :
The ad hoc one-dimensional definition of the
scalar thermal diffusion coefficient D defined as K / Roh
C is short and inadequate to deal with the resolution of
the 2D and 3D thermal diffusion equation. We have
alternatively applied the chains of matrix B to the
solution of the 2D and 3D heat diffusion equation for
stationary solutions and time-dependent transient
solutions.
The role of 3D thermal diffusivity in the numerical
resolution of the heat equation is carefully studied
throgh the repeated variation of the main diagonal entry
of matrix B,RO in the interval [0,1]. It is obvious that
thermal diffusivity is related to RO, one of them
produces the other.
The chains of the matrix B using the 3D diffusion
coefficient combine D, dt and the Laplace operator in an
inseparable block and define a new technique to solve
the diffusion of heat in different situations.In this article,
we have applied the B chains to solve five different
examples of heat diffusion in 2D and 3D geometries for
both time-dependent and stationary conditions and the
presented digital solutions are surprisingly precise, fast
and stable
The ad hoc one-dimensional definition of the
scalar thermal diffusion coefficient D defined as K / Roh
C is short and inadequate to deal with the resolution of
the 2D and 3D thermal diffusion equation. We have
alternatively applied the chains of matrix B to the
solution of the 2D and 3D heat diffusion equation for
stationary solutions and time-dependent transient
solutions.
The role of 3D thermal diffusivity in the numerical
resolution of the heat equation is carefully studied
throgh the repeated variation of the main diagonal entry
of matrix B,RO in the interval [0,1]. It is obvious that
thermal diffusivity is related to RO, one of them
produces the other.
The chains of the matrix B using the 3D diffusion
coefficient combine D, dt and the Laplace operator in an
inseparable block and define a new technique to solve
the diffusion of heat in different situations.In this article,
we have applied the B chains to solve five different
examples of heat diffusion in 2D and 3D geometries for
both time-dependent and stationary conditions and the
presented digital solutions are surprisingly precise, fast
and stable
