scholarly journals Heat transfer from convecting-radiating fin through optimized Chebyshev polynomials with interior point algorithm

2019 ◽  
Vol 9 (1) ◽  
pp. 102-110
Author(s):  
Elyas Shivanian ◽  
Mahdi Keshtkar ◽  
Hamidreza Navidi
Keyword(s):  
Heat Transfer ◽  
Chebyshev Polynomials ◽  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problem ◽  
Mathematical Formulation ◽  
Interior Point Algorithm ◽  
Equivalent Problem ◽  
One Dimensional ◽  
Fin Efficiency

AbstractIn this paper, the problem of determining heat transfer from convecting-radiating fin of triangular and concave parabolic shapes is investigated.We consider one-dimensional, steady conduction in the fin and neglect radiative exchange between adjacent fins and between the fin and its primary surface. A novel intelligent computational approach is developed for searching the solution. In order to achieve this aim, the governing equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. Additionally, heat transfer rate and the fin efficiency are reported.

Interior-Point Method for the Computation of Shakedown Loads for Engineering Systems

2010 ◽  
Author(s):  
Jaan-Willem Simon ◽  
Dieter Weichert
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problem ◽  
Specific Problem ◽  
Practical Interest ◽  
Solution Procedure ◽  
Interior Point Algorithm ◽  
Engineering Systems ◽  
Shakedown Analysis ◽  
Convex Optimization Problem

A new interior-point algorithm for the computation of shakedown loads has recently been developed by the authors. The analytical formulation is based on the statical shakedown theorem by Melan which leads to a nonlinear convex optimization problem. The algorithm’s efficiency results from the close adaption of the solution procedure to the specific problem of shakedown analysis. This paper focuses on algorithmic aspects of the proposed method. A numerical example of practical interest is used for validation purposes.

Thermal Analysis of Longitudinal Fin with Temperature-Dependent Properties and Internal heat Generation by a Novel Intelligent Computational Approach Using Optimized Chebyshev Polynomials

2019 ◽  
Vol 20 (2) ◽  
pp. 153-166 ◽  
Author(s):  
Elyas Shivanian ◽  
Ramin Kazemi ◽  
Mahdi Keshtkar
Keyword(s):  
Heat Transfer ◽  
Heat Generation ◽  
Chebyshev Polynomials ◽  
Optimization Problem ◽  
Mathematical Formulation ◽  
Internal Heat ◽  
Computational Approach ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Temperature Dependent Properties

AbstractIn this work, heat transfer in a longitudinal rectangular fin with temperature-dependent thermal properties and internal heat generation is studied and more accurate results obtained in respect of the previous investigations. The advanced heat transfer models have been used to study the effects of thermo-geometric parameters, coefficient of heat transfer and thermal conductivity parameters on the temperature distribution, heat transfer and thermal performance of the longitudinal rectangular fin. It is applied a novel intelligent computational approach for searching the solution. In order to achieve this aim, the governing equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem.

A New Predictor-corrector Infeasible Interior-point Algorithm for Linear Optimization in aWide Neighborhood

2020 ◽  
Vol 177 (2) ◽  
pp. 141-156
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Linear Optimization ◽  
Point Method ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Positive Direction ◽  
Complexity Result ◽  
Infeasible Interior Point Method ◽  
Predictor Corrector

In this paper, we propose a Mizuno-Todd-Ye type predictor-corrector infeasible interior-point method for linear optimization based on a wide neighborhood of the central path. According to Ai-Zhang’s original idea, we use two directions of distinct and orthogonal corresponding to the negative and positive parts of the right side vector of the centering equation of the central path. In the predictor stage, the step size along the corresponded infeasible directions to the negative part is chosen. In the corrector stage by modifying the positive directions system a full-Newton step is removed. We show that, in addition to the predictor step, our method reduces the duality gap in the corrector step and this can be a prominent feature of our method. We prove that the iteration complexity of the new algorithm is 𝒪(n log ɛ−1), which coincides with the best known complexity result for infeasible interior-point methods, where ɛ > 0 is the required precision. Due to the positive direction new system, we improve the theoretical complexity bound for this kind of infeasible interior-point method [1] by a factor of n . Numerical results are also provided to demonstrate the performance of the proposed algorithm.

A FULL-NEWTON STEP INFEASIBLE INTERIOR-POINT METHOD FOR LINEAR OPTIMIZATION BASED ON AN EXPONENTIAL KERNEL FUNCTION

2014 ◽  
Vol 07 (01) ◽  
pp. 1450018
Author(s):  
Behrouz Kheirfam ◽  
Fariba Hasani
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Interior Point Method ◽  
Polynomial Complexity ◽  
Linear Optimization ◽  
Interior Point Algorithm ◽  
Math Model ◽  
Newton Step ◽  
Infeasible Interior Point Method ◽  
Full Newton Step

This paper deals with an infeasible interior-point algorithm with full-Newton step for linear optimization based on a kernel function, which is an extension of the work of the first author and coworkers (J. Math. Model Algorithms (2013); DOI 10.1007/s10852-013-9227-7). The main iteration of the algorithm consists of a feasibility step and several centrality steps. The centrality step is based on Darvay's direction, while we used a kernel function in the algorithm to induce the feasibility step. For the kernel function, the polynomial complexity can be proved and the result coincides with the best result for infeasible interior-point methods.

Radiation Heat Transfer for Annular Fins of Trapezoidal Profile

1970 ◽  
Vol 92 (1) ◽  
pp. 113-116 ◽  
Author(s):  
H. H. Keller ◽  
E. S. Holdredge
Keyword(s):  
Heat Transfer ◽  
Radiation Heat Transfer ◽  
Dimensionless Group ◽  
Radiation Heat ◽  
One Dimensional ◽  
Fin Efficiency ◽  
Flat Surfaces ◽  
Dimensionless Groups ◽  
Trapezoidal Profile ◽  
Annular Fins

A one-dimensional numerical solution is obtained for the steady-state thermal behavior of annular fins of trapezoidal profile which transfer heat by conduction and radiation. The results obtained are presented as charts relating fin efficiency to the dimensionless group (rT − rB)εσTB3/k cos α, for various values of the dimensionless groups rB/(rT − rB), ZT/(rT − rB), and arctan [(ZB − ZT)/(rT − rB)]. As presented the problem is the general formulation for the problem of radiating fins with flat surfaces.

scholarly journals New complexity analysis of full Nesterov-Todd step infeasible interior point method for second-order cone optimization

2018 ◽  
Vol 28 (1) ◽  
pp. 21-38
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Interior Point Methods ◽  
Complexity Analysis ◽  
Second Order ◽  
Interior Point Algorithm ◽  
Complexity Bound ◽  
Second Order Cone ◽  
Infeasible Interior Point Method ◽  
Barrier Parameter

We present a full Nesterov-Todd (NT) step infeasible interior-point algorithm for second-order cone optimization based on a different way to calculate feasibility direction. In each iteration of the algorithm we use the largest possible barrier parameter value ?. Moreover, each main iteration of the algorithm consists of a feasibility step and a few centering steps. The feasibility step differs from the feasibility step of the other existing methods. We derive the complexity bound which coincides with the best known bound for infeasible interior point methods.

scholarly journals Transmitted Waveform Design Based on Iterative Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Bin Wang ◽  
Jinkuan Wang ◽  
Xin Song ◽  
Fengming Xin
Keyword(s):  
Mutual Information ◽  
Iterative Methods ◽  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problem ◽  
Waveform Design ◽  
Design Criterion ◽  
Cognitive Radar ◽  
Simulation Results ◽  
Transmitted Waveform

In intelligent radar, it is an important problem for the transmitted waveform to adapt to the environment in which radar works. In this paper, we propose mutual information model of adaptive waveform design, which can convert the problem of adaptive waveform design into the problem of optimization. We consider two situations of no clutter and clutter and use Newton method and interior point method to solve the optimization problem. Then we can draw the design criterion for the transmitted waveform in cognitive radar and get a greater mutual information from the simulation results. Finally, the whole paper is summarized.

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