Exterior problem of magnetic field in Darwin model and its numerical solution

2008 ◽  
Vol 24 (2) ◽  
pp. 418-434 ◽  
Author(s):  
Caixiu Liao ◽  
Lung-An Ying
Keyword(s):  
Magnetic Field ◽  
Numerical Solution ◽  
Exterior Problem

Numerical and Statistical Analysis of Dissipative and Heat Absorbing Graphene Maxwell Nanofluid Flow Over a Stretching Sheet

2021 ◽  
Vol 10 (4) ◽  
pp. 600-607
Author(s):  
A. Bhattacharyya ◽  
R. Sharma ◽  
M. K. Mishra ◽  
Ali J. Chamkha ◽  
E. Mamatha
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Numerical Solution ◽  
Physical Parameters ◽  
Nonlinear Mathematical Model ◽  
Nanofluid Flow ◽  
Maxwell Nanofluid ◽  
Highly Nonlinear ◽  
Numeric Data ◽  
The Magnetic Field

This paper is basically devoted to carry out an investigation regarding the unsteady flow of dissipative and heat absorbing hydromagnetic graphene Maxwell nanofluid over a linearly stretched sheet taking momentum and thermal slip conditions into account. Ethylene glycol is selected as a base fluid while graphene particles are considered as nanoparticles. The highly nonlinear mathematical model of the problem is converted into a set of nonlinear coupled differential equations by means of fitting similarity variables. Further, Runge-Kutta Fehlberg algorithms along with the shooting scheme are instigated to analyse the numerical solution. The variations in graphene Maxwell nanofluid velocity and temperature owing to different physical parameters have been demonstrated via numerous graphs whereas Nusselt number and skin friction coefficients are illustrated in numeric data form and are reported in different tables. In addition, a statistical method is implemented for multiple quadratic regression estimation analysis on the numerical figures of wall velocity gradient and local Nusselt number to establish the connection among heat transfer rate and physical parameters. Our numerical findings reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. The regression analysis confers that Nusselt number is more prone to heat absorption parameter as compared to Eckert number. Finally, the numerical findings are compared with those of earlier published articles under restricted conditions to validate the numerical solution. The comparison of numerical findings shows an excellent conformity among the results.

MHD squeezing flow between two parallel disks with suction or injection via Legendre wavelet-quasilinearization technique

2017 ◽  
Vol 34 (3) ◽  
pp. 892-901 ◽  
Author(s):  
Syed Tauseef Mohyud-din ◽  
Muhammad Asad Iqbal ◽  
Umar Khan ◽  
Xiao-Jun Yang
Keyword(s):  
Magnetic Field ◽  
Numerical Solution ◽  
Flow Behavior ◽  
Maximum Velocity ◽  
Squeezing Flow ◽  
Legendre Wavelets ◽  
Content Type ◽  
Parallel Disks ◽  
Suction Or Injection ◽  
Quasilinearization Technique

Purpose This paper aims to propose a method by merging Legendre wavelets method and quasilinearization technique to tackle with the nonlinearity and to get better and more accurate results. Design/methodology/approach To test the significance of the proposed scheme, the authors applied the method on the model representing magneto-hydrodynamic squeezing flow of a viscous fluid between two parallel infinite disks, where one disk is impermeable and the other is porous with either suction or injection of the fluid. For the sake of comparison, numerical solution by using RK-4 is also computed. From the graphs and tables, it is evident that the proposed method shows an excellent accordance with the numerical solution. Findings The solution converges to the numerical solution when the degree of Legendre polynomials m is increased. For m = 20 in all the three cases, for different values of S, M and A, the graphs of solutions obtained by Legendre wavelet quasilinearization technique show an excellent agreement with numerical solution. Also, it is evident from figures that suction and injection affects the velocity profile in opposite way. For suction, maximum velocity is seen to be at the center of the channel. Magnetic field can be used to regularize the flow and it stabilizes the flow behavior. Originality/value Magnetic field can be used to regularize the flow and it stabilizes the flow behavior.

Sign in / Sign up

Export Citation Format

Share Document