scholarly journals Numerical study of double-diffusive dissipative reactive convective flow in an open vertical duct containing a non-Darcy porous medium with Robin boundary conditions

2019 ◽  
Vol 119 (1) ◽  
pp. 135-147 ◽  
Author(s):  
J. C. Umavathi ◽  
O. Anwar Bég
Keyword(s):  
Porous Medium ◽  
Boundary Conditions ◽  
Convective Flow ◽  
Numerical Study ◽  
Robin Boundary Conditions ◽  
Robin Boundary ◽  
Vertical Duct ◽  
Double Diffusive

Mixed Convective Flow in a Vertical Double Passage Channel Filled with Nanofluid Using Robin Boundary Conditions

2016 ◽  
Vol 5 (4) ◽  
pp. 549-559 ◽  
Author(s):  
J. Prathap Kumar ◽  
J. C. Umavathi ◽  
B. J. Gireesha ◽  
M. Karuna Prasad
Keyword(s):  
Boundary Conditions ◽  
Convective Flow ◽  
Robin Boundary Conditions ◽  
Mixed Convective Flow ◽  
Robin Boundary

Convection in a vertical duct under the chemical reaction influence using Robin boundary conditions

2020 ◽  
Vol 15 ◽  
pp. 100440
Author(s):  
Jawali C. Umavathi ◽  
Mikhail A. Sheremet ◽  
Bernardo Buonomo ◽  
Oronzio Manca
Keyword(s):  
Boundary Conditions ◽  
Chemical Reaction ◽  
Robin Boundary Conditions ◽  
Robin Boundary ◽  
Vertical Duct

scholarly journals Diagonal Block Method for Solving Two-Point Boundary Value Problems with Robin Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Nadirah Mohd Nasir ◽  
Zanariah Abdul Majid ◽  
Fudziah Ismail ◽  
Norfifah Bachok
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Numerical Study ◽  
Boundary Value ◽  
Diagonal Block ◽  
Robin Boundary Conditions ◽  
Block Method ◽  
Step Size ◽  
Function Calls ◽  
Robin Boundary

This numerical study presents the diagonal block method of order four for solving the second-order boundary value problems (BVPs) with Robin boundary conditions at two-point concurrently using constant step size. The solution is obtained directly without reducing to a system of first-order differential equations using a combination of predictor-corrector mode via shooting technique. The shooting method was adapted with the Newton divided difference interpolation approach as the strategy of seeking for the new initial estimate. Five numerical examples are included to examine and illustrate the practical usefulness of the proposed method. Numerical tested problem is also highlighted on the diffusion of heat generated application that imposed the Robin boundary conditions. The present findings revealed that the proposed method gives an efficient performance in terms of accuracy, total function calls, and execution time as compared with the existing method.

scholarly journals An efficient adaptive grid method for a system of singularly perturbed convection-diffusion problems with Robin boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Li-Bin Liu ◽  
Ying Liang ◽  
Xiaobing Bao ◽  
Honglin Fang
Keyword(s):  
Boundary Conditions ◽  
Grid Method ◽  
Posteriori Error ◽  
Adaptive Grid ◽  
Singularly Perturbed ◽  
Robin Boundary Conditions ◽  
Euler Formula ◽  
Convection Diffusion ◽  
Backward Euler ◽  
Robin Boundary

AbstractA system of singularly perturbed convection-diffusion equations with Robin boundary conditions is considered on the interval $[0,1]$ [ 0 , 1 ] . It is shown that any solution of such a problem can be expressed to a system of first-order singularly perturbed initial value problem, which is discretized by the backward Euler formula on an arbitrary nonuniform mesh. An a posteriori error estimation in maximum norm is derived to design an adaptive grid generation algorithm. Besides, in order to establish the initial values of the original problems, we construct a nonlinear optimization problem, which is solved by the Nelder–Mead simplex method. Numerical results are given to demonstrate the performance of the presented method.

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