Industrial Mathematics: Case Studies in the Diffusion of Heat and MatterThe focus in this text is on mathematical modelling stimulated by contemporary industrial problems involving heat conduction and mass diffusion. These include continuous metal casting, laser drilling, spontaneous combustion of industrial waste, water filtration and crop irrigation. The industrial problems prove to be an excellent setting for the introduction and reinforcement of modelling skills, equation solving techniques, qualitative understanding of partial differential equations and their dynamical properties. Mathematical topics include setting up partial differential equations and boundary conditions, dimensional analysis, scaling, perturbation expansions, boundary valuer problems, Fourier series, symmetry reductions, Stefan problems and bifurcations. |
Contents
Continuous Casting | 49 |
Water Filtration | 85 |
4 | 107 |
Factory Fires | 142 |
Irrigation | 172 |
Conclusions | 189 |
| 195 | |
Other editions - View all
Industrial Mathematics: Case Studies in the Diffusion of Heat and Matter Glenn R. Fulford,Philip Broadbridge No preview available - 2001 |
Industrial Mathematics: Case Studies in the Diffusion of Heat and Matter Glenn Fulford,Philip Broadbridge No preview available - 2002 |
Common terms and phrases
a²c advection Applying the boundary arbitrary constant Arrhenius assume bifurcation diagram Boltzmann similarity solution boundary conditions C₁ C₂ chain rule Chapter coefficients concentration Consider critical value cross-section denote determine diffusion equation dimensional analysis dimensionless dimensionless variables dimensions drum equilibrium solutions equilibrium temperature first-order fluid following example Fourier series Fourier's law function given gives governing equations heat conduction heat equation heat flow heat flux Hence industry initial condition integral involving laser latent heat linear liquid mass mathematical model metal molten steel moving boundary Newton cooling nonlinear obtain ordinary differential equation parameter partial differential equation quantity sawdust scale Section semi-infinite solidified solve spontaneous ignition Stefan condition stretching transformation study problem Substituting suction potential surface techniques temperature u₁ tion transcendental equation vaporisation velocity Ξα Әс ди მე მთ მუ