Integral transform ?infixing? method for nonlinear transient mass-transfer problems

A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the interval scale is relatively large, an optimization-based approach in conjunction with a dimension-adaptive sparse grid (DSG) surrogate is developed for the bounds estimation of temperature, and the heavy computational burden of repeated deterministic solutions of nonlinear transient heat transfer problems can be efficiently alleviated by the DSG surrogate. A temporally piecewise adaptive algorithm with high fidelity is employed to gain the deterministic solution of temperature, and is further developed for recursive adaptive computing of the first and second-order derivatives of temperature. Therefore, the implementation of Taylor series expansion and the construction of DSG surrogate are underpinned by a reliable numerical platform. The parallelization is utilized for the construction of DSG surrogate for further acceleration. The accuracy and efficiency of the proposed approaches are demonstrated by two numerical examples.

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- Solution Strategy for Mass Transfer Problems

Diffusion and Mass Transfer ◽

10.1201/b12923-13 ◽

2016 ◽

pp. 263-270

Keyword(s):

Mass Transfer ◽

Solution Strategy ◽

Transfer Problems

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A general real-time formulation for multi-rate mass transfer problems

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-6-2415-2009 ◽

2009 ◽

Vol 6 (2) ◽

pp. 2415-2449 ◽

Cited By ~ 6

Author(s):

O. Silva ◽

J. Carrera ◽

S. Kumar ◽

M. Dentz ◽

A. Alcolea ◽

...

Keyword(s):

Mass Transfer ◽

River Flow ◽

Breakthrough Curves ◽

Flow And Transport ◽

Multiple Processes ◽

Programming Effort ◽

Non Local ◽

Time Formulation ◽

Transfer Problems ◽

Non Equilibrium

Abstract. Many flow and transport phenomena, ranging from delayed storage observed in pumping tests to tailing in river or aquifer tracer breakthrough curves, display non-equilibrium behavior. Usually, they are modeled by non-local in time formulations, such as multi-porosity, multiple processes non equilibrium, continuous time random walk, memory functions, integro-differential equations, fractional derivatives or multi-rate mass transfer (MRMT), among others. We develop a MRMT algorithm that can be used to represent all these formulations. The method is accurate, computationally inexpensive and easy to implement in groundwater or river flow and transport codes. In fact, we present a module that can be linked to existing programs with minimal programming effort. Its accuracy is verified by comparison with existing solutions.

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Math Modeling of Vacuum Conductive Timber Drying

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1040.478 ◽

2014 ◽

Vol 1040 ◽

pp. 478-483

Author(s):

M. Goreshnev ◽

E. Litvishko

Keyword(s):

Mathematical Modeling ◽

Mass Transfer ◽

Mathematical Models ◽

Heat And Mass Transfer ◽

Block Diagram ◽

Calculated Data ◽

Math Modeling ◽

Advantages And Disadvantages ◽

Transfer Problems

The article is devoted to the mathematical modeling of vacuum conductive timber drying. Analysis of known mathematical models allowed revealing their advantages and disadvantages. The modeling block diagram based on the drying periods is proposed. Lykov’s equations have been selected to solve heat and mass transfer problems. The comparison of experimental and calculated data has been conducted.

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