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Analytical solutions to the semi‐discrete form of the conduction equation for non‐homogeneous media
Author(s) -
Darsi C. R.,
Quon D.
Publication year - 1966
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450440504
Subject(s) - mathematics , mathematical analysis , partial differential equation , ordinary differential equation , homogeneous , boundary value problem , differential equation , matrix (chemical analysis) , homogeneous differential equation , thermal conduction , physics , differential algebraic equation , materials science , combinatorics , composite material , thermodynamics
The partial differential equation describing transient conduction (or diffusion) in non‐homogeneous media may be approximated by a set of first order linear ordinary differential equations if the derivatives involving the space variables are replaced by finite difference expressions. A general method of obtaining a closed form solution of these equations is presented, using some operational methods of linear algebra. The solution is given in terms of a matrix, which describes the spatial distribution of physical properties in the media, and vectors describing the initial and boundary conditions.