### 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) |
---|---|

Pages (from-to) | 1335-1343 |

Number of pages | 9 |

Journal | International Journal of Heat and Mass Transfer |

Volume | 24 |

Issue number | 8 |

DOIs | |

State | Published - Jan 1 1981 |

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### Cite this

*International Journal of Heat and Mass Transfer*,

*24*(8), 1335-1343. https://doi.org/10.1016/0017-9310(81)90184-8

**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.

Research output: Contribution to journal › Article

*International Journal of Heat and Mass Transfer*, vol. 24, no. 8, pp. 1335-1343. https://doi.org/10.1016/0017-9310(81)90184-8

}

TY - JOUR

T1 - Numerical solution of moving boundary problems by boundary immobilization and a control-volume-based finite-difference scheme

AU - Hsu, C. F.

AU - Sparrow, Ephraim M

AU - Patankar, S. V.

PY - 1981/1/1

Y1 - 1981/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0019601449&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0019601449&partnerID=8YFLogxK

U2 - 10.1016/0017-9310(81)90184-8

DO - 10.1016/0017-9310(81)90184-8

M3 - Article

AN - SCOPUS:0019601449

VL - 24

SP - 1335

EP - 1343

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

SN - 0017-9310

IS - 8

ER -