Implicit Homotopy Perturbation Method for MHD Non-Newtonian Nanofluid Flow with Cattaneo-Christov Heat Flux Due to Parallel Rotating Disks

2019 ◽  
Vol 8 (8) ◽  
pp. 1648-1653
Author(s):  
Mohamed Y. Abou-Zeid
Keyword(s):  
Heat Flux ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Tangential Velocity ◽  
Thermal Relaxation ◽  
Physical Parameters ◽  
Rotating Disks ◽  
Linear Ordinary Differential Equations ◽  
Homotopy Perturbation

This article deals with the influence of Cattaneo-Christov heat flux on MHD flow of biviscosity nanofluid between two rotating disks through a porous media. Von Karman transformations are used to transform system of partial differential equations to non-linear ordinary differential equations. This system are solved by using homotopy perturbation method. Numerical results for the behaviors of the radial, axial and tangential velocities, temperature and nanoparticles with the physical parameters of the problem are obtained. These results are depicted graphically and discussed in details. The obtained results show that the tangential velocity increases with the increase of both the stretching and rotation parameters. Moreover, it is found that the stretching and thermal relaxation parameters increase the temperature, while they increase or decrease the nanoparticles concentration. Comparison between the obtained results and those obtained by other researchers is made during this study.

scholarly journals Homotopy Perturbation Method for Thin Film Flow and Heat Transfer over an Unsteady Stretching Sheet with Internal Heating and Variable Heat Flux

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
I-Chung Liu ◽  
Ahmed M. Megahed
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Flow And Heat Transfer ◽  
Variable Heat ◽  
Variable Heat Flux

We have analyzed the effects of variable heat flux and internal heat generation on the flow and heat transfer in a thin film on a horizontal sheet in the presence of thermal radiation. Similarity transformations are used to transform the governing equations to a set of coupled nonlinear ordinary differential equations. The obtained differential equations are solved approximately by the homotopy perturbation method (HPM). The effects of various parameters governing the flow and heat transfer in this study are discussed and presented graphically. Comparison of numerical results is made with the earlier published results under limiting cases.

scholarly journals Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 40 ◽  
Author(s):  
Shumaila Javeed ◽  
Dumitru Baleanu ◽  
Asif Waheed ◽  
Mansoor Shaukat Khan ◽  
Hira Affan
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Fractional Order Differential Equations ◽  
Homotopy Perturbation ◽  
The Given ◽  
Ordinary Derivative

The analysis of Homotopy Perturbation Method (HPM) for the solution of fractional partial differential equations (FPDEs) is presented. A unified convergence theorem is given. In order to validate the theory, the solution of fractional-order Burger-Poisson (FBP) equation is obtained. Furthermore, this work presents the method to find the solution of FPDEs, while the same partial differential equation (PDE) with ordinary derivative i.e., for α = 1 , is not defined in the given domain. Moreover, HPM is applied to a complicated obstacle boundary value problem (BVP) of fractional order.

scholarly journals Homotopy Perturbation Method

2017 ◽  
pp. 24-61
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Homotopy Perturbation ◽  
Wide Range ◽  
Transfer Problems

The homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.

Application of He’s Homotopy Perturbation Method to Stiff Systems of Ordinary Differential Equations

2008 ◽  
Vol 63 (1-2) ◽  
pp. 19-23 ◽  
Author(s):  
Mohammad Taghi Darvishi ◽  
Farzad Khani
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Stiff Systems ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear

We propose He’s homotopy perturbation method (HPM) to solve stiff systems of ordinary differential equations. This method is very simple to be implemented. HPM is employed to compute an approximation or analytical solution of the stiff systems of linear and nonlinear ordinary differential equations.

Sign in / Sign up

Export Citation Format

Share Document