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A model of binary alloy solidification (1984)

Wilson, D. G. ; Solomon, A. D. ; Alexiades, V.

Chichester [u.a.] : Wiley-Blackwell

International Journal for Numerical Methods in Engineering 20 (1984), S. 1067-1084

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ISSN: 0029-5981

Keywords: Engineering ; Engineering General

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics , Technology

Notes: A linear model for the solidification of a dilute binary alloy is presented. In this model the solidus and liquidus curves are linear. As a consequence internal energy depends linearly upon temperature and concentration. The formulation is a generalization of the well-known enthalpy method to treat a phase change problem involving coupled heat and mass transfer. Both analytic and numerical formulations are given. Results from the latter are presented and compared with an explicit solution of Rubinstein for a Stefan-like problem posed in a semi-infinite slab. Some remarks on the behaviour of the explicit solution are given.

Additional Material: 5 Ill.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/nme.1620200609

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Optimal control of a heat transfer problem with convective boundary condition (1993)

Lenhart, S. ; Wilson, D. G.

Springer

Journal of optimization theory and applications 79 (1993), S. 581-597

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ISSN: 1573-2878

Keywords: Optimal control ; heat equation ; convective boundary condition ; optimality system

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We consider the problem of controlling the solution of the heat equation with the convective boundary condition taking the heat transfer coefficient as the control. We take as our cost functional the sum of theL 2-norms of the control and the difference between the temperature attained and the desired temperature. We establish the existence of solutions of the underlying initial boundary-value problem and of an optimal control that minimizes the cost functional. We derive an optimality system by formally differentiating the cost functional with respect to the control and evaluating the result at an optimal control. We show how the solution depends in a differentiable way on the control using appropriate a priori estimates. We establish existence and uniqueness of the solution of the optimality system, and thus determine the unique optimal control in terms of the solution of the optimality system.