scholarly journals A Direct Optimization Algorithm for Problems with Differential-Algebraic Constraints: Application to Heat and Mass Transfer

2020 ◽  
Vol 10 (24) ◽  
pp. 9027
Author(s):  
Paweł Drąg
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Control Function ◽  
Differential Algebraic Equations ◽  
Sequential Optimization ◽  
Multiple Shooting ◽  
Optimization Approach ◽  
Algebraic Equations ◽  
Direct Optimization ◽  
Optimization Task

In this article, an optimization task with nonlinear differential-algebraic equations (DAEs) is considered. As a main result, a new solution procedure is designed. The computational procedure represents the sequential optimization approach. The proposed algorithm is based on a multiple shooting parametrization method. Two main aspects of a generalized parametrization approach are analyzed in detail: a control function and DAE model parametrization. A comparison between the original and modified DAEs is made. The new algorithm is applied to solve an optimization task in heat and mass transfer engineering.

scholarly journals An α-Model Parametrization Algorithm for Optimization with Differential-Algebraic Equations

2022 ◽  
Vol 12 (2) ◽  
pp. 890
Author(s):  
Paweł Dra̧g
Keyword(s):  
Optimization Algorithm ◽  
Numerical Optimization ◽  
Differential Algebraic Equations ◽  
Multiple Shooting ◽  
Small Range ◽  
Algebraic Equations ◽  
New Approach ◽  
Highly Nonlinear ◽  
Special Cases ◽  
Wide Range

An optimization task with nonlinear differential-algebraic equations (DAEs) was approached. In special cases in heat and mass transfer engineering, a classical direct shooting approach cannot provide a solution of the DAE system, even in a relatively small range. Moreover, available computational procedures for numerical optimization, as well as differential- algebraic systems solvers are characterized by their limitations, such as the problem scale, for which the algorithms can work efficiently, and requirements for appropriate initial conditions. Therefore, an αDAE model optimization algorithm based on an α-model parametrization approach was designed and implemented. The main steps of the proposed methodology are: (1) task discretization by a multiple-shooting approach, (2) the design of an α-parametrized system of the differential-algebraic model, and (3) the numerical optimization of the α-parametrized system. The computations can be performed by a chosen iterative optimization algorithm, which can cooperate with an outer numerical procedure for solving DAE systems. The implemented algorithm was applied to solve a counter-flow exchanger design task, which was modeled by the highly nonlinear differential-algebraic equations. Finally, the new approach enabled the numerical simulations for the higher values of parameters denoting the rate of changes in the state variables of the system. The new approach can carry out accurate simulation tests for systems operating in a wide range of configurations and created from new materials.

A Technique for the Direct Optimization of Dynamic Systems Described by Differential-Algebraic Equations

2007 ◽  
Author(s):  
Brian C. Fabien
Keyword(s):  
Optimal Control ◽  
Dynamic Systems ◽  
Differential Algebraic Equations ◽  
Time Interval ◽  
Algebraic Equations ◽  
Direct Optimization ◽  
Programming Technique ◽  
Piecewise Constant ◽  
Infinite Dimensional ◽  
Parameter Identification Problems

This paper presents a method for the optimization of dynamic systems described by index-1 differential-algebraic equations (DAE). The class of problems addressed include optimal control problems and parameter identification problems. Here, the controls are parameterized using piecewise constant inputs on a grid in the time interval of interest. In addition, the differential-algebraic equations are approximated using a Rosenbrock-Wanner (ROW) method. In this way the infinite dimensional optimal control problem is transformed into a finite dimensional nonlinear programming problem (NLP). The NLP is solved using a sequential quadratic programming technique. The paper shows that the ROW method discretization of the DAE leads to (i) a relatively small NLP problem, and (ii) an efficient technique for evaluation the function, constraints and gradients associated with the NLP problem. The paper also investigates a state mesh refinement technique that ensures a sufficiently accurate representation of the optimal state trajectory. Two nontrivial examples are used to illustrate the effectiveness of the proposed method.

Heat and mass transfer analysis in unsteady titanium dioxide nanofluid between two orthogonally moving porous coaxial disks: a numerical study

2015 ◽  
Vol 93 (3) ◽  
pp. 290-299 ◽  
Author(s):  
Muhammad Farooq Iqbal ◽  
Kashif Ali ◽  
Muhammad Ashraf
Keyword(s):  
Mass Transfer ◽  
Titanium Dioxide ◽  
Heat And Mass Transfer ◽  
Numerical Study ◽  
Titanium Dioxide Nanoparticles ◽  
Direct Method ◽  
Fluid Velocity ◽  
Algebraic Equations ◽  
Electrically Conducting ◽  
Linear Algebraic Equations

Study of heat and mass transfer in an unsteady hydromagnetic viscous electrically conducting incompressible water-based nanofluid (containing titanium dioxide nanoparticles) between two orthogonally moving porous coaxial disks with suction and viscous dissipation effects. A combination of iterative and a direct method is employed for solving the sparse systems of linear algebraic equations arising from the finite difference discretization of the quasi-linearized self-similar ordinary differential equations. It has been noticed that the rate of mass transfer at the disks decreases with the permeability Reynolds number; either the disks are approaching or receding. Moreover, the external magnetic field remarkably reduces the fluid velocity and therefore may be used as a controlling agent for the flow.

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