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THE CONNECTION BETWEEN SPATIAL DISCRETIZATION AND ERRORS WHEN COMPUTING LINEAL AND NON-LINEAL HEAT TRANSFER PROCESSES BY THE NETWORK SIMULATION METHOD

DOI: 10.1615/ICHMT.2008.CHT.520
14 pages

Francisco Alhama
Applied Physics Department, Universidad Politécnica de Cartagena 30202, España

Juan Pedro Luna Abad
Escuela Técnica Superior de Ingenieros Industriales, Campus Muralla del Mar, Universidad Politécnica de Cartagena, Cartagena 30203, Spain

Abstract

This communication deals with the connection between spatial discretization, the total number of volume elements or cells and the specified errors related to the application of the network simulation method. Three problems, whose analytical or semi-analytical solution is known, are studied; the lineal conduction trough a semi-infinite plate, idem trough a finite plate and the non-lineal Stefan problem −a phase-change moving-boundary problem. For the first problem, once the volume element number is chosen, each specified error value is related to the time-interval for which the NSM solution and the exact solution are close each other. For the finite slab there exists only a minimum time for each specified error; this means that only in a small initial part of the complete transient solution of the NSM the errors are out of the specified range. Finally, for the Stefan problem (solidification of a 1-D semi-infinite homogeneous medium) the error is defined by the location of the phase-change boundary. The connection between the size of the cell, the error and the time-interval is given by tables for different Stefan numbers, Stf. The range of values studied is: Stf = 0.1, 0.5, 1 and 4, N0 = 20, 40, 60 and 80.

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