scholarly journals Finite Element Solution of Unsteady Mixed Convection Flow of Micropolar Fluid over a Porous Shrinking Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Diksha Gupta ◽  
Lokendra Kumar ◽  
Bani Singh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Mixed Convection ◽  
Micropolar Fluid ◽  
Numerical Results ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Suction Parameter ◽  
Element Method

The objective of this investigation is to analyze the effect of unsteadiness on the mixed convection boundary layer flow of micropolar fluid over a permeable shrinking sheet in the presence of viscous dissipation. At the sheet a variable distribution of suction is assumed. The unsteadiness in the flow and temperature fields is caused by the time dependence of the shrinking velocity and surface temperature. With the aid of similarity transformations, the governing partial differential equations are transformed into a set of nonlinear ordinary differential equations, which are solved numerically, using variational finite element method. The influence of important physical parameters, namely, suction parameter, unsteadiness parameter, buoyancy parameter and Eckert number on the velocity, microrotation, and temperature functions is investigated and analyzed with the help of their graphical representations. Additionally skin friction and the rate of heat transfer have also been computed. Under special conditions, an exact solution for the flow velocity is compared with the numerical results obtained by finite element method. An excellent agreement is observed for the two sets of solutions. Furthermore, to verify the convergence of numerical results, calculations are conducted with increasing number of elements.

Impact of convective heat transfer and buoyancy on micropolar fluid flow through a porous shrinking sheet: An FEM approach

2021 ◽  
pp. 095440622110456
Author(s):  
Degavath Gopal ◽  
Hina Firdous ◽  
Salman Saleem ◽  
Naikoti Kishan
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Fluid Flow ◽  
Differential Equations ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Micropolar Fluid ◽  
Micropolar Fluid Flow ◽  
Element Method

This paper represents steady two-dimensional boundary layer flow of micropolar fluid flow with impact of convective heat transfer and buoyancy force investigated numerically. The shrinking velocity has been expected to fluctuate linearly with the existence of a fixed point on the sheet. With the assistance of similarity transformations, the governing partial differential equations are transformed into a set of nonlinear ordinary differential equations; these nonlinear ODEs are solved numerically by using the variational finite element method. The current numerical results are obtained from the variational finite element method and compared with the previously published literature work, with which it exists in good agreement. The impact of the flow monitoring parameters on velocity, microrotation and temperature profiles is examined graphically and discussed. The skin friction coefficient and Nusselt numbers are impacts from adjusting various values of the physical parameters and relevant features which are studied.

scholarly journals A Finite Element Simulation of the Active and Passive Controls of the MHD Effect on an Axisymmetric Nanofluid Flow with Thermo-Diffusion over a Radially Stretched Sheet

Processes ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 207 ◽  
Author(s):  
Bagh Ali ◽  
Xiaojun Yu ◽  
Muhammad Tariq Sadiq ◽  
Ateeq Ur Rehman ◽  
Liaqat Ali
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Volume Fraction ◽  
Axisymmetric Flow ◽  
Physical Parameters ◽  
Convective Boundary ◽  
Linear Partial Differential Equations ◽  
Similarity Transformations ◽  
Element Method

The present study investigated the steady magnetohydrodynamics of the axisymmetric flow of a incompressible, viscous, electricity-conducting nanofluid with convective boundary conditions and thermo-diffusion over a radially stretched surface. The nanoparticles’ volume fraction was passively controlled on the boundary, rather than actively controlled. The governing non-linear partial differential equations were transformed into a system of nonlinear, ordinary differential equations with the aid of similarity transformations which were solved numerically, using the very efficient variational finite element method. The coefficient of skin friction and rate of heat transfer, and an exact solution of fluid flow velocity, were contrasted with the numerical solution gotten by FEM. Excellent agreement between the numerical and exact solutions was observed. The influences of various physical parameters on the velocity, temperature, and solutal and nanoparticle concentration profiles are discussed by the aid of graphs and tables. Additionally, authentication of the convergence of the numerical consequences acquired by the finite element method and the computations was acquired by decreasing the mesh level. This exploration is significant for the higher temperature of nanomaterial privileging technology.

A Numerical Analysis for Cracks Emanating from a Quarter-Spherical Cavity on the Edge of an Elastic Body

2012 ◽  
Vol 499 ◽  
pp. 243-247
Author(s):  
Long Hai Yan ◽  
Bao Liang Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Elastic Body ◽  
Spherical Cavity ◽  
Numerical Results ◽  
Shielding Effect ◽  
Corner Crack ◽  
Element Method

This note is specifically concerned with cracks emanating from a quarter-spherical cavity on the edge in an elastic body (see Fig.1) by using finite element method. The numerical results show that the existence of the cavity has a shielding effect of the corner crack. In addition, it is found that the effect of boundaries parallel to the crack on the SIFs is obvious when.H/R≤3

The Semi-Discrete Finite Element Method for the Cauchy Equation

2014 ◽  
Vol 668-669 ◽  
pp. 1130-1133
Author(s):  
Lei Hou ◽  
Xian Yan Sun ◽  
Lin Qiu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Results ◽  
Cauchy Equation ◽  
The Time Domain ◽  
Nicolson Scheme ◽  
Discrete Finite Element ◽  
Better Than ◽  
Element Method ◽  
Crank Nicolson

In this paper, we employ semi-discrete finite element method to study the convergence of the Cauchy equation. The convergent order can reach. In numerical results, the space domain is discrete by Lagrange interpolation function with 9-point biquadrate element. The time domain is discrete by two difference schemes: Euler and Crank-Nicolson scheme. Numerical results show that the convergence of Crank-Nicolson scheme is better than that of Euler scheme.

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