Browsing by Author "MOSES, Felix Oghenerobor"

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    Thermal explosion with arrhenius kinetics in parallel plates subject to various boundary conditions
    (Department of Mathematics, Faculty of sciences, Obafemi Awolowo University, 2022) MOSES, Felix Oghenerobor
    This study formulated an energy balance equation and accompanying boundary conditions governing the thermal explosion with Arrhenius kinetics in parallel plates. It also solved the formulated energy equation using standard techniques. These were with a view to examining the effects of various boundary conditions on the thermal explosion with Arrhenius kinetics. The governing equation was formulated from the principle of conservation of energy in a system with Arrhenius kinetics under realistic conditions. The resulting steady state temperature equation which is non-linear and of second order was non-dimensionalized using appropriate dimensionless variables. Four parameters emerged; constant surface temperature, θs, Biot number, Bi, constant ambient temperature, θa and Frank-Kamenetskii number, δ. The dimensionless temperature equation was solved by integration method and variable separation technique. Effects of four different boundary conditions were examined on the temperature equation. The critical maximum temperature and the critical Frank-Kamenetskii num ber were determined for each boundary condition considered. Effects of the emerging parameters (Biot number, Bi and the dimensionless surface temperature, θs) on the critical maximum temperature and the critical Frank-Kamenetskii number were presented on tables. Graphs of the maximum temperature, θmax and Frank-Kamenetskii number, δ, were plotted using Maple 17 platform. The results showed that the maximum critical temperature increases with increasing dimensionless sur face temperature and decreasing critical Frank-Kamenetskii number for the asymmetric model. However, the maximum critical temperature decreases with increasing dimensionless surface temperature, critical Frank-Kamenetskii number and Biot number for the mixed case two model. Two special cases emerged as limiting cases; when θs → 0 and Bi → 0. The symmetric model was found to serve as limiting case to the asymmetric model while the mixed case one model serves as limiting case to the mixed case two model. The study concluded that, changing the boundary conditions of the parallel plates significantly alters the critical maximum temperature and the critical Frank-Kamenetskii number.