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2 Journal of Applied Mathematics and Computational Mechanics

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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.

Application of Daftardar-Gejiji and Jafari method to kinetic analysis of thermal inactivation of Jack bean urease

Sobamowo G., Adeleye O.

Journal of Applied Mathematics and Computational Mechanics

2018

Vol. 17, nr 2

65--76

Jack bean urease has been used as a good catalyst for hydrolysis of urea in various applications such as biotechnology and biomedical engineering. The wide range of applications require proper understanding of the thermal inactivation of the enzyme. Consequently, the theoretical analysis of the enzyme kinetic of the thermal inactivation is required. In this paper, a new iterative method proposed by Daftardar-Gejiji and the Jafari method is applied to analyse the kinetic of thermal inactivation of jack bean urease (EC3.5.1.5). The kinetics of the urease consist of three-reaction steps and included the Arrhenius equation for temperature-dependent rate constants as well as the temperature change in the initial heating period. The approximate analytical solutions are verified with results of numerical method using Runge-Kutta with the shooting method, and good agreements are established between the results of the methods. From the analytical investigation, it is established that the molar concentration of the native enzyme decreases as the time increases while the molar concentration of the denatured enzyme increases as the time increases. The time taken to reach the maximum value of the molar concentration of the native enzyme is the same as the time taken to reach the minimum value of the molar concentration of the denature enzyme. It is hoped that the information given in this theoretical investigation will assist in the kinetic analysis of thermal inactivation of the experimental results over handling rate constants and molar concentrations.