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Heat transfer analysis of non-Newtonian natural convective fluid flow using Homotopy Perturbation and Daftardar-Gejiji & Jafari Methods

Adeleye Olurotimi, Yinusa Ahmed

Journal of Applied Mathematics and Computational Mechanics

2019

Vol. 18, nr 2

5--18

In this paper, the analytical solution of natural convective heat transfer of a non-Newtonian fluid flow between two vertical infinite plates using the Homotopy Perturbation Method (HPM) and Daftardar-Gejiji & Jafari Method (DJM) is presented. The heat transfer problem of natural convection is observed in many engineering fields including geothermal systems, heat exchangers, petroleum reservoirs, nuclear waste reserves, etc. The problem which is modelled as fully coupled nonlinear ordinary differential equations requires special analytical techniques for its solution. The solutions are obtained using an exact analytical method: the Homotopy Perturbation Method (HPM) and a semi-analytical method: the Daftardar-Gejiji & Jafari Method (DJM). These solutions are compared with solutions obtained from the Runge-Kutta numerical method. The results are in good agreement with the numerical solutions. The effects of the Eckert number, Prandtl number and the non-Newtonian fluid viscosity parameter on the non-dimensional temperature and velocity of the fluid are investigated. The results obtained from the analytical method show that the method can be applied to predict excellent results of the problem and can be used for parametric studies of the problem. From the results, it is shown that when the Prandtl number and the Eckert number are increased, there is an increase in both temperature and fluid flow velocity.

Investigation on the Film Flow of a Third Grade Fluid on an Inclined Plane Using HPM

Azimi M., Azimi A.

Mechanics and Mechanical Engineering

2014

Vol. 18, nr 1

5--10

This work concerns the study of the thin film flow problem arising in non–Newtonian fluid mechanics using analytical approach. The governing equations are reduced to ordinary nonlinear boundary value problem by applying the transformation method. Homotopy Perturbation Method (HPM) has been applied to obtain solution of reduced nonlinear boundary value problem. The analytical solutions of the flow velocity distributions for different cases have been presented. The effect of material constant has also discussed. Finally, analytical results have been compared with numerical one obtained by forth order Runge Kutta method. High accuracy and validity are the advantages of present study.