The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer

Preface to the classics edition Preface Acknowledgments Part I. The Method of Weighted Residuals: 1. Introduction 2. Boundary-value problems in heat and mass transfer 3. Eigenvalue and initial-value problems in heat and mass transfer 4. Applications to fluid mechanics 5. Chemical reaction systems 6. Convective instability problems Part II. Variational Principles: 7. Introduction to variational principles 8. Variational principles in fluid mechanics 9. Variational principles for heat and mass transfer problems 10. On the search for variational principles 11. Convergence and error bounds Author index Subject index.

The method of weighted residuals and variational principles

Univariate Nonlinear Regression. Univariate Nonlinear Regression: Special Situations. A Unified Asymptotic Theory for Nonlinear Models with Regression Structure. Univariate Nonlinear Regression: Asymptotic Theory. Multivariate Nonlinear Regression. Nonlinear Simultaneous Equations Models. A Unified Asymptotic Theory for Dynamic Nonlinear Models. References. Index.

Nonlinear Statistical Models

This paper reviews some of the research designed to lead to an increased understanding of the chemistry of the Maillard reaction, based on recent developments, and its influence on food properties like colour, flavour and nutritional value A critical analysis is given on how quality attributes associated with Maillard reaction can be predicted and controlled by kinetic modelling Multiresponse modelling (taking more than one reactant and product into consideration in the modelling process) is a powerful tool to model complicated consecutive and parallel reactions, like the Maillard reaction Such a multiresponse approach provides a major guidance in understanding the reaction mechanism An illustrative example is given

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A review of Maillard reaction in food and implications to kinetic modelling

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Nonlinear Statistical Models.

Multiresponse data are familiar outputs of experiments and processes involving multicomponent mixtures, multiple streams or multiple methods of observation. The resulting arrays of data exhibit various structures, including rectangular (no missing values), block-rectangular, and irregular (missing values with no simple pattern). Methods for modeling such data are described, emphasizing parameter estimation strategy and available software. Experiences in multiresponse modeling are then reviewed for several chemical engineering problems.

Parameter estimation from multiresponse data

The angular distribution of solute molecules, and the space‐averaged stresses in the fluid, are computed for steady shear flows of solutions of rigid dumbbells. The computation is done by Galerkin's method, with spherical harmonics as the trial functions. The stresses are tabulated for the full range of shear rates, 0⩽λhκ⩽∞, and dumbbell width/length ratios, 0⩽h⩽38. The stress components become power functions of shear rate when the latter is large. The analogy of Cox and Merz bolds better for small width/length ratios (h≐0) than for large ones.

Jan P. Sørensen

Papers

Parameter estimation from multiresponse data

Hydrodynamic Interaction Effects in Rigid Dumbbell Suspensions. II. Computations for Steady Shear Flow

Computation of forced convection in slow flow through ducts and packed beds—II velocity profile in a simple cubic array of spheres

Computation of forced convection in slow flow through ducts and packed beds—III. Heat and mass transfer in a simple cubic array of spheres

Solution of parabolic partial differential equations by a double collocation method