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.

Calculation of the gradient of Tikhonov’s functional in solving coefficient inverse problems for linear partial differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander S. Leonov ◽  
Alexander N. Sharov ◽  
Anatoly G. Yagola
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Partial Differential Equations ◽  
Inverse Problems ◽  
Differential Equations ◽  
Differential Operators ◽  
The Finite Element Method ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Element Method

Abstract A fast algorithm for calculating the gradient of the Tikhonov functional is proposed for solving inverse coefficient problems for linear partial differential equations of a general form by the regularization method. The algorithm is designed for problems with discretized differential operators that linearly depend on the desired coefficients. When discretizing the problem and calculating the gradient, it is possible to use the finite element method. As an illustration, we consider the solution of two inverse problems of elastography using the finite element method: finding the distribution of Young’s modulus in biological tissue from data on its compression and a similar problem of determining the characteristics of local oncological inclusions, which have a special parametric form.

scholarly journals The Impact of Nanoparticles Due to Applied Magnetic Dipole in Micropolar Fluid Flow Using the Finite Element Method

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 520 ◽  
Author(s):  
Liaqat Ali ◽  
Xiaomin Liu ◽  
Bagh Ali ◽  
Saima Mujeed ◽  
Sohaib Abdal ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Magnetic Dipole ◽  
Thermal Stratification ◽  
Volume Fraction ◽  
Numerical Technique ◽  
The Impact ◽  
Element Method

The present work examines the effect of different magnetic nanoparticles and the heat transfer phenomena over the stretching sheet with thermal stratification and slips effect. The mixture of water (H 2 O) and ethylene glycol (C 2 H 6 O 2 ) is used as base fluid whereas the paramagnetic, diamagnetic, and ferromagnetic ferrites are taken as nanoparticles. In the presence of ferrite nanoparticles, the magnetic dipole has a significant effect in controlling the rate of heat transfer and the thermal boundary layers. By using suitable similarity transformations, the system of partial differential equations is transformed into nonlinear ordinary differential equations. The numerical solution of resulting equations is found out by using the variational finite element method. The effect of numerous emerging parameters on velocity, temperature, and micro-rotation velocity are represented graphically and analyzed numerically. It has been noticed that comparatively the diamagnetic ferrites have gained maximum thermal conductivity relative to the other nanoparticles. It was also observed that the thermal conduction of nanoparticles increases with the variation of volume fraction. Moreover, with increasing values of thermal stratification the thermal boundary layer thickness decreases and the heat transfer rate increases at the surface. Furthermore, the validation of code and the accuracy of the numerical technique has been confirmed by the assessment of current results with earlier studies.

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.

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