scholarly journals Finite Element Analysis of Thermo-Diffusion and Multi-Slip Effects on MHD Unsteady Flow of Casson Nano-Fluid over a Shrinking/Stretching Sheet with Radiation and Heat Source

2019 ◽  
Vol 9 (23) ◽  
pp. 5217 ◽  
Author(s):  
Liaqat Ali ◽  
Xiaomin Liu ◽  
Bagh Ali ◽  
Saima Mujeed ◽  
Sohaib Abdal
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Medium ◽  
Heat Source ◽  
Numerical Solution ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Physical Parameters ◽  
Nano Fluid ◽  
Slip Effects

In this article, we probe the multiple-slip effects on magnetohydrodynamic unsteady Casson nano-fluid flow over a penetrable stretching sheet, sheet entrenched in a porous medium with thermo-diffusion effect, and injection/suction in the presence of heat source. The flow is engendered due to the unsteady time-dependent stretching sheet retained inside the porous medium. The leading non-linear partial differential equations are transmuted in the system of coupled nonlinear ordinary differential equations by using appropriate transformations, then the transformed equations are solved by using the variational finite element method numerically. The velocity, temperature, solutal concentration, and nano-particles concentration, as well as the rate of heat transfer, the skin friction coefficient, and Sherwood number for solutal concentration, are presented for several physical parameters. Next, the effects of these various physical parameters are conferred with graphs and tables. The exact values of flow velocity, skin friction, and Nusselt number are compared with a numerical solution acquired with the finite element method (FEM), and also with numerical results accessible in literature. In the end, we rationalize the convergence of the finite element numerical solution, and the calculations are carried out by reducing the mesh size.

scholarly journals Finite Element Simulation of Multiple Slip Effects on MHD Unsteady Maxwell Nanofluid Flow over a Permeable Stretching Sheet with Radiation and Thermo-Diffusion in the Presence of Chemical Reaction

Processes ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 628 ◽  
Author(s):  
Bagh Ali ◽  
Yufeng Nie ◽  
Shahid Ali Khan ◽  
Muhammad Tariq Sadiq ◽  
Momina Tariq
Keyword(s):  
Finite Element ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Numerical Solution ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Nanofluid Flow ◽  
Maxwell Nanofluid ◽  
Slip Effects

The aim of the present study is to investigate the multiple slip effects on magnetohydrodynamic unsteady Maxwell nanofluid flow over a permeable stretching sheet with thermal radiation and thermo-diffusion in the presence of chemical reaction. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations with the aid of appropriate similarity variables, and the transformed equations are then solved numerically by using a variational finite element method. The effects of various physical parameters on the velocity, temperature, solutal concentration, and nanoparticle concentration profiles as well as on the skin friction coefficient, rate of heat transfer, and Sherwood number for solutal concentration are discussed by the aid of graphs and tables. An exact solution of flow velocity, skin friction coefficient, and Nusselt number is compared with the numerical solution obtained by FEM and also with numerical results available in the literature. A good agreement between the exact and numerical solution is observed. Also, to justify the convergence of the finite element numerical solution, the calculations are carried out by reducing the mesh size. The present investigation is relevant to high-temperature nanomaterial processing technology.

scholarly journals Optimization of EDM Parameters for Production of Biomedical Materials

2021 ◽  
Vol 7 (2) ◽  
pp. 1-8
Author(s):  
Mukesh Kumar Rakesh ◽  
Dr. Syed Faisal Ahmed
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Literature Survey ◽  
Experimental Results ◽  
Physical Parameters ◽  
The Finite Element Method ◽  
Critical Areas ◽  
Cylindrical Cup ◽  
Good Agreement

The finite element method (FEM) is used for simulating complex intricate shapes of industrial sheet forming operation. Effective physical parameters, as well as the numerical solution, influence the parameters of this phenomenon and its numerical prediction of results. In this study, to investigate the influence of different embossing patterns and embossing depths on the critical areas appearing during deep-drawn of a cylindrical cup. The numerical results are found from the literature survey to be in good agreement with the experimental results and accurate thinning distributions had been predict.

scholarly journals Multiple Slip Effects on Magnetohydrodynamic Axisymmetric Buoyant Nanofluid Flow above a Stretching Sheet with Radiation and Chemical Reaction

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1171 ◽  
Author(s):  
Shahid Ali Khan ◽  
Yufeng Nie ◽  
Bagh Ali
Keyword(s):  
Thermal Radiation ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Chemical Effect ◽  
Physical Parameters ◽  
Multiple Slip ◽  
Nano Fluid ◽  
Slip Effects ◽  
Non Linear ◽  
Multiple Slips

The present article investigates the effect of multiple slips on axisymmetric magnetohydrodynamics (MHD) buoyant nano-fluid flow over a stretching sheet with radiation and chemical effect. The non-linear partial differential equations were transformed to a non-linear control equation using an appropriate similarity transformation. The governing equations were solved through the finite element method. The influence of physical parameters such as multiple slips, magnetic, thermal radiation, Prandtl number, stretching, Brownian motion, thermophoresis, Schmidt number, Lewis number and chemical reaction on the radial velocity, temperature, solutal concentration and nano-fluid volume fraction profile were investigated. We noted that the boundary layers increases in the presence of multiple slip effects whereas, the effect of thermal slip on Nusselt number increases with the increasing values of magnetic and thermal radiation. To verify the convergence of the numerical solution, the computations were made by reducing the mesh size. Finally, our results are parallel to previous scholarly contributions.

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.

scholarly journals Flow over Exponentially Stretching Sheet through Porous Medium with Heat Source/Sink

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
I. Swain ◽  
S. R. Mishra ◽  
H. B. Pattanayak
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Heat Source ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Mass Transfer Effect ◽  
Exponentially Stretching Sheet ◽  
Exponentially Stretching ◽  
Source Sink

An attempt has been made to study the heat and mass transfer effect in a boundary layer MHD flow of an electrically conducting viscous fluid subject to transverse magnetic field on an exponentially stretching sheet through porous medium. The effect of thermal radiation and heat source/sink has also been discussed in this paper. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically using a fourth-order Runge-Kutta method with a shooting technique. Graphical results are displayed for nondimensional velocity, temperature, and concentration profiles while numerical values of the skin friction local Nusselt number and Sherwood number are presented in tabular form for various values of parameters controlling the flow system.

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