Simple and accurate approach for solving of nonlinear heat convective-radiative equation in fin by using the collocation method and comparison with HPM and VIM

Collocation Method (CM) such as analytical technique, which does not need small parameters is here used to evaluate the analytical approximate solutions of the nonlinear heat transfer equation. The obtained results from Collocation Method are compared with other analytical techniques such as Homotopy Perturbation Method (HPM) and Variation Iteration Method (VIM). Also, boundary value problem (BVP) is applied as a numerical method for validation. The results reveal that the Collocation Method is very effective, simple and more accurate than other techniques. Also, it is found that this method is a powerful mathematical tool and can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering especially at some heat transfer equations

Transverse magnetic field on Jeffery–Hamel problem with Cu–water nanofluid between two non parallel plane walls by using collocation method

An analysis has been performed to study the problem of magneto-hydrodynamic (MHD) Jeffery–Hamel flow with nanoparticles. The governing equations for this problem are reduced to an ordinary form and is solved using collocation method (CM) and numerically by fourth order Runge–Kutta technique. Also, Velocity fields have been computed and shown graphically for various values of physical parameters. The objective of the present work is to investigate the effect of the semi angles between the plates, Reynolds number, magnetic field strength and nanoparticles volume fraction on the velocity field. As an important outcome, Increasing Reynolds numbers leads to reduce velocity and excluded backflow in convergent channel

Semi-analytical method for solving non-linear equation arising of natural convection porous fin

In the present study, the problem of non-linear model arising in heat transfer through the porous fin in a natural convection environment is presented and the homotopy perturbation method is employed to obtain an approximate solution, which admits a remarkable accuracy