Author
Michael F. Malone
Bio: Michael F. Malone is an academic researcher from Pennsylvania State University. The author has contributed to research in topics: Coordinate system & Partial differential equation. The author has an hindex of 1, co-authored 1 publications receiving 75 citations.
Papers
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TL;DR: In this article, the authors present a technique for the analysis of unsteady, two-dimensional diffusive heat-or mass-transfer problems characterized by moving irregular boundaries, including an immobilization transformation and a numerical scheme.
75 citations
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TL;DR: A review of the current knowledge on phase-change phenomena, with particular focus on phase change problems from solid to liquid or to gas, can be found in this article, where the authors consider one-dimensional conduction heat transfer problems for the development of solution methods.
Abstract: Publisher Summary Melting and freezing are important processes and these processes have played a decisive role in the formation of the Earth. This phase-change phenomena have become an indispensable part of many processes, such as, manufacturing of glass, crystals, and metal alloys; continuous casting of ingots, fabrics, and wires; food preservation and cryopreservation of biological cells; and desalination of seawater and freezing-out separation processes. This chapter reviews the current knowledge on phase-change phenomena, with particular focus on phase-change problems from solid to liquid or to gas. Because of their simplicity, one-dimensional, phase-change problems involving conduction heat transfer are the most frequently used model problems for the development of solution methods. This chapter begins with the consideration of such one-dimensional methods, either exact or approximate, which have been widely used in the literature. The substantial information about the physics of phase-change processes that can, in fact, be learned from studies of these simple models is discussed. The multidimensional conduction phase-change problems as well as the additional physics attributable to geometrical complexities are also reviewed.
169 citations
TL;DR: In this paper, four Galerkin finite-element methods are tested for solving the free-boundary problem that describes steady solidification, and they differ in the solution method used to account for the unknown shape of the melt/solid interface, in the interphase condition (either balance of heat flux or equilibrium of temperature) distinguished for locating the interface, and in the technique used for solving systems of algebraic equations that result from the finite element approximation.
129 citations
TL;DR: In this paper, a mathematical model of heat and moisture transfer in a infinite slab undergoing immersion frying was solved using a three step procedure: a coordinate transformation of the partial differential equations, application of the finite difference method of Crank-Nicolson to produce a series of nonlinear algebraic equations, and Gauss-Seidel iteration for solution of the equations.
121 citations
TL;DR: In this article, the authors deal with the on-line partial differential equation model-based predictive control of the sublimation front position, assuming two strategies based on various availability of measurement used in the feedback loop.
81 citations
TL;DR: In this article, the primary and secondary drying stages of the freeze-drying of pharmaceutical crystalline and amorphous solutes in vials are constructed and presented in a dynamic and spatially multi-dimensional mathematical model.
Abstract: Dynamic and spatially multi-dimensional mathematical models of the primary and secondary drying stages of the freeze-drying of pharmaceutical crystalline and amorphous solutes in vials, are constructed and presented in this work. The models account for the removal of free and bound water and could also provide the geometric shape of the moving interface and its position. It is proved that the temperature of the moving interface can not be constant if the flux of heat flow to the sides of the vial is not zero. It is also proved that the slope of the free surface (moving interface) at the edge of the vial is always curved downward. The numerical solution of the nonlinear partial differential equations of the models would allow model simulations that could indicate design conditions, operating conditions, and control strategies that could provide high drying rates and could lead to a series of novel experiments in freeze-drying.
70 citations