Application of scaled nonlinear conjugate-gradient algorithms to the inverse natural convection problem

2013 ◽  
Vol 28 (1) ◽  
pp. 159-185 ◽  
Author(s):  
Jeff C.-F. Wong ◽  
Bartosz Protas
Keyword(s):  
Natural Convection ◽  
Conjugate Gradient ◽  
Conjugate Gradient Algorithms ◽  
Gradient Algorithms ◽  
Nonlinear Conjugate Gradient ◽  
Convection Problem ◽  
Natural Convection Problem

scholarly journals A new conjugate gradient algorithms using conjugacy condition for solving unconstrained optimization

2021 ◽  
Vol 24 (3) ◽  
pp. 1647
Author(s):  
Aseel M. Qasim ◽  
Zinah F. Salih ◽  
Basim A. Hassan
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Conjugacy Condition ◽  
Simple Modification ◽  
Conjugate Gradient Algorithms ◽  
Gradient Algorithms ◽  
Nonlinear Conjugate Gradient ◽  
Nonlinear Conjugate Gradient Methods

The primarily objective of this paper which is indicated in the field of conjugate gradient algorithms for unconstrained optimization problems and algorithms is to show the advantage of the new proposed algorithm in comparison with the standard method which is denoted as. Hestenes Stiefel method, as we know the coefficient conjugate parameter is very crucial for this reason, we proposed a simple modification of the coefficient conjugate gradient which is used to derived the new formula for the conjugate gradient update parameter described in this paper. Our new modification is based on the conjugacy situation for nonlinear conjugate gradient methods which is given by the conjugacy condition for nonlinear conjugate gradient methods and added a nonnegative parameter to suggest the new extension of the method. Under mild Wolfe conditions, the global convergence theorem and lemmas are also defined and proved. The proposed method's efficiency is programming and demonstrated by the numerical instances, which were very encouraging.

The Effect of Thermal Wall Properties on Natural Convection in Inclined Rectangular Cells

1982 ◽  
Vol 104 (1) ◽  
pp. 111-117 ◽  
Author(s):  
B. A. Meyer ◽  
J. W. Mitchell ◽  
M. M. El-Wakil
Keyword(s):  
Heat Transfer ◽  
Cell Wall ◽  
Natural Convection ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Conductive Heat ◽  
Numerical Work ◽  
Aspect Ratios ◽  
Convection Problem ◽  
Natural Convection Problem

The effects of cell wall thickness and thermal conductivity on natural convective heat transfer within inclined rectangular cells was studied. The cell walls are thin, and the hot and cold surfaces are isothermal. The two-dimensional natural convection problem was solved using finite difference techniques. The parameters studied were cell aspect ratios (A) of 0.5 and 1, Rayleigh numbers (Ra) up to 105, a Prandtl number (Pr) of 0.72 and a tilt angle (φ) of 60 deg. These parameters are of interest in solar collectors. The numerical results are substantiated by experimental results. It was found that convection coefficients for cells with adiabatic walls are substantially higher than those for cells with conducting walls. Correlations are given for estimating the convective heat transfer across the cell and the conductive heat transfer across the cell wall. These correlations are compared with available experimental and numerical work of other authors.

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