We extend the well-known concept and results for lumped parameters used in the spring-like models for linear materials to Hollomon’s power-law materials.We provide the generalized stiffness and effective mass coeffic...We extend the well-known concept and results for lumped parameters used in the spring-like models for linear materials to Hollomon’s power-law materials.We provide the generalized stiffness and effective mass coefficients for the power-law Euler-Bernoulli beams under standard geometric and load conditions.In particular,our mass-spring lumped parameter models reduce to the classical models when Hollomon’s law reduces to Hooke’s law.Since there are no known solutions to the dynamic power-law beam equations,solutions to our mass lumped models are compared to the low-order Galerkin approximations in the case of cantilever beams with circular and rectangular cross-sections.展开更多
Mass transfer between a bubble and the dense phase in gas fluidized beds of Group A and Group B particles was proposed based on previous experimental results and literature data. The mass transfer coefficient between ...Mass transfer between a bubble and the dense phase in gas fluidized beds of Group A and Group B particles was proposed based on previous experimental results and literature data. The mass transfer coefficient between bubbles and the dense phase was determined by kbe = 0.21 db. A theoretical analysis of the mass transfer coefficient between a bubble and the dense phase using diffusion equations showed that the mass transfer coefficient between a bubble and the dense phase is kbe α εmf√ub/db in both three- and two-dimensional fiuidized beds. An effective diffusion coefficient in gas fluidized beds was introduced and correlated with bubble size as De = 13.3db2.7 for Group A and Group B particles. The mass transfer coefficient kbe can then be expressed as kbe = 0.492εmf√ubdb1.7 for bubbles in a three-dimensional bed and kbe = 0.576εm√ubdb1.7 for bubbles in a two-dimensional bed.展开更多
文摘We extend the well-known concept and results for lumped parameters used in the spring-like models for linear materials to Hollomon’s power-law materials.We provide the generalized stiffness and effective mass coefficients for the power-law Euler-Bernoulli beams under standard geometric and load conditions.In particular,our mass-spring lumped parameter models reduce to the classical models when Hollomon’s law reduces to Hooke’s law.Since there are no known solutions to the dynamic power-law beam equations,solutions to our mass lumped models are compared to the low-order Galerkin approximations in the case of cantilever beams with circular and rectangular cross-sections.
基金an innovation research grant(13YZ130)a Leading Academic Discipline Project(J51803)from the Shanghai Education Committeea Cultivate Discipline Fund of the Shanghai Second Polytechnic University(XXKPY1303)
文摘Mass transfer between a bubble and the dense phase in gas fluidized beds of Group A and Group B particles was proposed based on previous experimental results and literature data. The mass transfer coefficient between bubbles and the dense phase was determined by kbe = 0.21 db. A theoretical analysis of the mass transfer coefficient between a bubble and the dense phase using diffusion equations showed that the mass transfer coefficient between a bubble and the dense phase is kbe α εmf√ub/db in both three- and two-dimensional fiuidized beds. An effective diffusion coefficient in gas fluidized beds was introduced and correlated with bubble size as De = 13.3db2.7 for Group A and Group B particles. The mass transfer coefficient kbe can then be expressed as kbe = 0.492εmf√ubdb1.7 for bubbles in a three-dimensional bed and kbe = 0.576εm√ubdb1.7 for bubbles in a two-dimensional bed.
