Heat transfer analysis of non-Newtonian natural convective fluid flow using homotopy perturbation and Daftardar-Gejiji & Jafari methods

Abstract

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.

Analytical investigations of temperature effects on creep strain relax-ation of biomaterials using homotopy perturbation and differentialtransform methods

“…A number of studies have been carried out to establish the strength of HPM by comparing the results obtained to other methods such as Adomian Decomposition Method (ADM) [12]. Remarkably, these studies have concluded that the method is more accurate and effective than ADM. Other studies carried out with the homotopy perturbation method (HPM) include its use for the analysis of heat transfer in longitudinal fins [13], the use of HPM and collocation method (CM) for analysis of thermal performances of porous fin with temperature-dependent heat generation [14] and heat transfer analysis of non-Newtonian natural convective fluid flow using homotopy perturbation and Daftardar-Gejiji and Jafari methods [15].…”