# Numerical solution of moving boundary problems by boundary immobilization and a control-volume-based finite-difference scheme

C. F. Hsu, Ephraim M Sparrow, S. V. Patankar

Research output: Contribution to journalArticle

69 Citations (Scopus)

### Abstract

A methodology is set forth for the numerical solution of transient two-dimensional diffusion-type problems (e.g. Heat conduction) in which one of the boundaries of the solution domain moves with time. The moving boundary is immobilized by a coordinate transformation, but the transformed coordinates are, in general, not orthogonal. Furthermore, with respect to a given control volume in the new coordinate system, mass appears to pass through the control surface which bounds the volume, and this mass movement brings about a convection-like transport of energy. The energy equation for a moving, nonorthogonal control volume is derived in general and then specialized to the transformed coordinate system associated with the immobilization of the moving boundary. A fully implicit scheme is used to discretize the control volume energy equation. The spatial derivatives are discretized by either of two schemes depending on the size of the pseudo-convection relative to the diffusion. The energy balance at the moving boundary of the solution domain is also transformed and discretized. A numerical procedure is then developed for solving the discretized energy equations. The use of the control volume formulation and the solution methodology will be illustrated for a specific physical situation in a companion paper that follows this paper in the journal.

Original language English (US) 1335-1343 9 International Journal of Heat and Mass Transfer 24 8 https://doi.org/10.1016/0017-9310(81)90184-8 Published - Jan 1 1981

### Fingerprint

immobilization
Control surfaces
Energy balance
Heat conduction
convection
energy
methodology
control surfaces
coordinate transformations
Derivatives
conductive heat transfer
formulations
Convection

### Cite this

Numerical solution of moving boundary problems by boundary immobilization and a control-volume-based finite-difference scheme. / Hsu, C. F.; Sparrow, Ephraim M; Patankar, S. V.

In: International Journal of Heat and Mass Transfer, Vol. 24, No. 8, 01.01.1981, p. 1335-1343.

Research output: Contribution to journalArticle

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