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A compact finite difference scheme for solving a three‐dimensional heat transport equation in a thin film
Author(s) -
Dai Weizhong,
Nassar Raja
Publication year - 2000
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/1098-2426(200009)16:5<441::aid-num3>3.0.co;2-0
Subject(s) - microscale chemistry , heat equation , convection–diffusion equation , mathematics , partial differential equation , finite difference method , ftcs scheme , diffusion equation , time derivative , finite difference scheme , parabolic partial differential equation , mathematical analysis , fourier transform , derivative (finance) , finite difference , numerical solution of the convection–diffusion equation , differential equation , finite element method , thermodynamics , physics , mixed finite element method , ordinary differential equation , differential algebraic equation , mathematics education , economy , service (business) , financial economics , economics
Heat transport at the microscale is of vital importance in microtechnology applications. The heat transport equation differs from the traditional heat diffusion equation in having a second‐order derivative of temperature with respect to time and a third‐order mixed derivative of temperature with respect to space and time. In this study, we develop a high‐order compact finite difference scheme for the heat transport equation at the microscale. It is shown by the discrete Fourier analysis method that the scheme is unconditionally stable. Numerical results show that the solution is accurate. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 441–458, 2000