Browsing by Author "A. T. Cole"

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CONTINUOUS FORMULATION OF HYBRID BLOCK MILNE TECHNIQUE FOR SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS
(Mathematical Association of Nigeria (MAN), 2022-12-13) Khadeejah James Audu; Y. A. Yahaya,; J. Garba; A. T. Cole; F. U. Tafida
In most scientific and engineering problems, ordinary differential equations cannot be solved by analytic methods. Consequently, numerical approaches are frequently required. A block hybrid Milne technique was formulated in this paper in order to develop a suitable algorithm for the numerical solution of ordinary differential equations. Utilizing power series as the basis function, the proposed method is developed. The developed algorithm is used to solve systems of linear and nonlinear differential equations, and it has proven to be an efficient numerical method for avoiding timeconsuming computation and simplifying differential equations. The fundamental numerical properties are examined, and the results demonstrate that it is zero-stable and consistent, which ensures convergence. In addition, by comparing the approximate solutions to the exact solutions, we demonstrate that the approximate solutions converge to the exact solutions. The results demonstrate that the developed algorithm for solving systems of ordinary differential equations is straightforward, efficient, and faster than the analytical method.
Modelling heat and mass transfer of a CO2 binary mixture: a mathematical approach. International Journal of Mathematical Analysis and Modelling
(International Journal of Mathematical Analysis and Modelling, 2023-09-28) R. O. Olayiwola; A. T. Cole; M. D. Shehu; F. A. Oguntolu; E. E. Iyeme; A. W. Abubakar
This paper presents an analytical solutions for describing heat and mass transfer between a droplet of organic solvent and a compressed antisolvent taking into consideration the viscous energy dissipation and heat and mass transfer between the surface and the droplet by convection. The solvent and antisolvent are assumed to be fully miscible and have the same temperature. Both the initial temperature of the mixture and the initial carbon dioxide concentration are also assumed to depend on the space variable. The governing equations formulated based on the conservation of total mass, chemical species, momentum and energy were solved analytically using polynomial approximation method. The results obtained are presented graphically and discussed. The results revealed the effects of operating parameters on droplet lifetime. These results might be used for interpretation or experiments planning of the more complex real supercritical antisolvent process.
Some New Results on a Free Boundary Value Problem Related to Auto Ignition of Combustible Fluid in Insulation Materials
(International Conference on Mathematical Analysis and Optimization, 2019-03) R. O. Olayiwola; A. T. Cole; M. D. Shehu; F. A. Oguntolu; J. T. Fadepo; F. E. Okoosi
Auto ignition of combustible fluids in insulation materials is one of the major problems facing the processing industries and many developing nations because it leads to serious environmental problem. This paper presents an analytical solutions to a free boundary value problem related to auto ignition of combustible fluids in insulation materials. The aim is to ascertain whether such a system is safe or if it will undergo ignition for a particular set of conditions. The conditions for this existence of unique solution of the model is established by actual solution method. The properties of solutions is examined. The analytical solution is obtained via polynomial approximation method, which show the influence of the parameters such as the Lewis numbers and Nusselt number are presented graphically and discussed.