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- Combustion theory (2)
- Microwave heating (1)
- Microwave heating; Thawing; Stefan problem; Maxwell's equations; Semi-analytical solutions (1)
- Reaction-diffusion equations catalytic pellet singularity theory Hopf bifurcations semi-analytical solutions Arrhenius law (1)
- Reaction–diffusion equations; Cubic autocatalysis; Michaelis–Menten kinetics; Singularity theory; Hopf bifurcations; Semi-analytical solutions (1)
Articles 1 - 4 of 4
Full-Text Articles in Physics
Microwave Thawing Of Cylinders., Tim Marchant
Microwave Thawing Of Cylinders., Tim Marchant
Tim Marchant
Microwave thawing of a cylinder is examined. The electromagnetic field is governed by Maxwell's equations, where the electrical conductivity and the thermal absorptivity are both assumed to depend on temperature. The forced heat equation governs the absorption and diffusion of heat where convective heating occurs at the surface of the cylinder, while the Stefan condition governs the position of the moving phase boundary. A semi-analytical model, which consists of ordinary differential equations, is developed using the Galerkin method. Semi-analytical solutions are found for the temperature, the electric-field amplitude in the cylinder and the position of the moving boundary. Two examples, …
Asymptotic Solitons For A Third-Order Kortweg-De Vries Equation, Tim Marchant
Asymptotic Solitons For A Third-Order Kortweg-De Vries Equation, Tim Marchant
Tim Marchant
Solitary wave interaction for a higher-order version of the Korteweg–de Vries (KdV) equation is considered. The equation is obtained by retaining third-order terms in the perturbation expansion, where for the KdV equation only first-order terms are retained. The third-order KdV equation can be asymptotically transformed to the KdV equation, if the third-order coefficients satisfy a certain algebraic relationship. The third-order two-soliton solution is derived using the transformation. The third-order phase shift corrections are found and it is shown that the collision is asymptotically elastic. The interaction of two third-order solitary waves is also considered numerically. Examples of an elastic and …
Semi-Analytical Solutions For One - And Two-Dimensional Pellet Problems., Tim Marchant
Semi-Analytical Solutions For One - And Two-Dimensional Pellet Problems., Tim Marchant
Tim Marchant
The problem of heat and mass transfer within a porous catalytic pellet in which an irreversible first–order exothermic reaction occurs is a much–studied problem in chemical–reactor engineering. The system is described by two coupled reaction–diffusion equations for the temperature and the degree of reactant conversion. The Galerkin method is used to obtain a semi–analytical model for the pellet problem with both one– and two–dimensional slab geometries. This involves approximating the spatial structure of the temperature and reactant–conversion profiles in the pellet using trial functions. The semi–analytical model is obtained by averaging the governing partial differential equations. As the Arrhenius law …
Cubic Autocatalysis With Michaelis - Menten Kinetics: Semi-Analytical Solutions For The Reaction - Diffusion Cell, Tim Marchant
Cubic Autocatalysis With Michaelis - Menten Kinetics: Semi-Analytical Solutions For The Reaction - Diffusion Cell, Tim Marchant
Tim Marchant
Cubic-autocatalysis with Michaelis–Menten decay is considered in a one-dimensional reaction–diffusion cell. The boundaries of the reactor allow diffusion into the cell from external reservoirs, which contain fixed concentrations of the reactant and catalyst. The Galerkin method is used to obtain a semi-analytical model consisting of ordinary differential equations. This involves using trial functions to approximate the spatial structure of the reactant and autocatalyst concentrations in the reactor. The semi-analytical model is then obtained from the governing partial differential equations by averaging. The semi-analytical model allows steady-state concentration profiles and bifurcation diagrams to be obtained as the solution to sets of …