scholarly journals Galerkin finite element study for mixed convection (TiO2–SiO2/water) hybrid-nanofluidic flow in a triangular aperture heated beneath

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Fares Redouane ◽  
Wasim Jamshed ◽  
S. Suriya Uma Devi ◽  
M. Prakash ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Finite Element ◽  
Hartmann Number ◽  
Physical Nature ◽  
Hybrid Nanofluid ◽  
Galerkin Finite Element Method ◽  
Minimal Impact ◽  
Galerkin Finite Element ◽  
Independent Analysis ◽  
Triangular Elements ◽  
Element Study

AbstractFluidity and thermal transport across the triangular aperture with lower lateral inlet and apply placed at the vertical outlet of the chamber which filled with efficient TiO2–SiO2/water hybrid nanofluid under the parametrical influence. Several parameters are tested like the numbers of Hartmann ($$0 \le Ha \le 100$$ 0 ≤ H a ≤ 100 ), Richardson ($$0 \le Ri \le 5$$ 0 ≤ R i ≤ 5 ), and Reynolds ($$10 \le Re \le 1000$$ 10 ≤ R e ≤ 1000 ) were critiqued through streamlines, isotherms, and Nusselt number ($$Nu$$ Nu ). Numerical model has to be developed and solved through the Galerkin finite element method (GFEM) by discretized with 13,569 triangular elements optimized through grid-independent analysis. The Hartmann number ($$Ha$$ Ha ), exerts minimal impact over the flow and thermal aspects while the other parameters significantly manipulate the physical nature of the flowing and thermal aspects behaviors.

scholarly journals Numerical Solution of Nonlinear Schrödinger Equation with Neumann Boundary Conditions Using Quintic B-Spline Galerkin Method

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 469 ◽  
Author(s):  
Azhar Iqbal ◽  
Nur Nadiah Abd Hamid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Spline Method ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
B Spline

This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank Nicolson and finite difference schemes are applied for nodal parameters and for time integration. Two numerical problems are discussed to demonstrate the accuracy and feasibility of the proposed method. The error norms L 2 , L ∞ and conservation laws I 1 ,   I 2 are calculated to check the accuracy and feasibility of the method. The results of the scheme are compared with previously obtained approximate solutions and are found to be in good agreement.

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