Quasi-linearization, non-linear boundary value problems and optimization
TL;DR: In this paper, a quasi-linearization technique was used to solve non-linear differential equations of the two-point boundary value type encountered in chemical engineering, which can be used to overcome the boundary value difficulties in the calculus of variation.
About: This article is published in Chemical Engineering Science.The article was published on 1966-02-01. It has received 26 citations till now. The article focuses on the topics: Boundary value problem & Mixed boundary condition.
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TL;DR: In this paper, the mathematical methods for optimising the effects of heat processing food products are reviewed in relation to microbial destruction, nutrient destruction, cooking value and loss of quality, and some data are presented for the kinetics of the various thermal effects.
124 citations
Cites methods from "Quasi-linearization, non-linear bou..."
...…1970), where only one variable is being optimized; steepest ascent method (hill climbing) (Storey, 1962; Storey & Rosenbrock, 1967) (multivariable); quasi-linearisation (Lee, 1966, 1967) (multivariable); calculus of variations (Katz, 1960) (multivariable); and ‘dynamic programming’ (Fan, 1966)....
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TL;DR: In this article, a new technique is presented which, for the parameter study of a problem, enables one to transform the boundary value problem to the initial value problem and different criteria for testing of uniqueness and multiplicity respectively are discussed.
103 citations
TL;DR: In this paper, the maximum principle theory was used to optimize thiamin retention during sterilization of a conduction-heating canned food, and the optimal retort temperature profile determined by this procedure improved the retention by more than 2%.
Abstract: The maximum principle theory (Pontryagin et al., 1962) was used to optimize thiamin retention during sterilization of a conduction-heating canned food. The optimal retort temperature Profile determined by this procedure improved thiamin retention by more than 2%, as Compared with other methods, and showed that a single solution for the temperature profile exists. This optimization method may be applicable to other processes in which retention of nutrients or other characteristics is to be improved.
93 citations
TL;DR: In this paper, the stagnation point flow and heat transfer of a ferrofluid toward a stretching sheet in the presence of viscous dissipation were investigated with three types of ferroparticles: magnetite, cobalt and Mn-Zn.
Abstract: This paper investigates stagnation point flow and heat transfer of a ferrofluid toward a stretching sheet in the presence of viscous dissipation. Three types of ferroparticles: magnetite (Fe 3O 4 ), cobalt ferrite (CoFe 2O 4), and Mn-Zn ferrite (Mn-ZnFe 2O 4) are considered with water and kerosene as conventional base fluids. Numerical solutions to the resulting ordinary differential equations are obtained by using an implicit finite-difference method with quasi-linearization technique. The effects of controlling parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are investigated. It is found that kerosene-based ferrofluids have higher skin friction and Nusselt numbers than water-based ferrofluids. The numerical results of skin friction are compared with the available data for special cases and are found to be in good agreement.
54 citations
TL;DR: In this paper, a transient analysis of the problem of non-catalytic gas-solid reaction based on the particle-pellet model, which considers the particulate nature of the pellet and includes the external transport resistances, is presented.
39 citations