Loading...
Analysis of heat transfer and thermal stability in a slab subjected to Arrhenius kinetics
Author(s)
Legodi, Annah Mokganyetji Kgotlelelo
Date Issued
2010
Type
Thesis
Publisher
Cape Peninsula University of Technology
Abstract
Development of safe storage for reactive combustible materials to prevent possible
human and environmental hazards as well as ensure and enhance industrial safety can
significantly benefit from mathematical modelling of systems. In the recent past,
models with varying degrees of sophistication have been developed and applied to the
problem of predicting thermal criticality conditions, temperature and concentration
profiles of such system.
In this thesis, a model showing the temperature history of an nth order exothermic
oxidation reaction in a slab of combustible material with variable pre-exponential
factor, taking the consumption of the reactant into account in the presence of a
convective heating and oxygen exchange at the slab surface with the ambient is
presented Both transient and steady state problems are tackled The critical regime
separating the regions of explosive and non-explosive paths of a one step exothermic
chemical reaction is determined The governing nonlinear partial differential
equations are solved numerically by method of lines (MOL), with finite difference
schemes used for the discretisation of the spatial derivatives. Moreover, both fourth
order Runge-Kutta numerical integration coupled with shooting methods and
perturbation techniques together with a special type of Hermite-Pade series
summation and improvement method were employed to tackle the steady state
problem. The crucial roles played by the boundary conditions in determining the
location ofthe maximum heating were demonstrated.
In chapter one, the relevant applications together with previous published work on
the problem were highlighted The basic mathematical theory and equations needed to
tackle the problem were derived in Chapter two. In chapter three, the transient model
problem was formulated, analysed and discussed. The steady state problem was
formulated and solved in Chapter four. Furtherwork and concluding remarks were
highlighted in Chapter five.
human and environmental hazards as well as ensure and enhance industrial safety can
significantly benefit from mathematical modelling of systems. In the recent past,
models with varying degrees of sophistication have been developed and applied to the
problem of predicting thermal criticality conditions, temperature and concentration
profiles of such system.
In this thesis, a model showing the temperature history of an nth order exothermic
oxidation reaction in a slab of combustible material with variable pre-exponential
factor, taking the consumption of the reactant into account in the presence of a
convective heating and oxygen exchange at the slab surface with the ambient is
presented Both transient and steady state problems are tackled The critical regime
separating the regions of explosive and non-explosive paths of a one step exothermic
chemical reaction is determined The governing nonlinear partial differential
equations are solved numerically by method of lines (MOL), with finite difference
schemes used for the discretisation of the spatial derivatives. Moreover, both fourth
order Runge-Kutta numerical integration coupled with shooting methods and
perturbation techniques together with a special type of Hermite-Pade series
summation and improvement method were employed to tackle the steady state
problem. The crucial roles played by the boundary conditions in determining the
location ofthe maximum heating were demonstrated.
In chapter one, the relevant applications together with previous published work on
the problem were highlighted The basic mathematical theory and equations needed to
tackle the problem were derived in Chapter two. In chapter three, the transient model
problem was formulated, analysed and discussed. The steady state problem was
formulated and solved in Chapter four. Furtherwork and concluding remarks were
highlighted in Chapter five.
Additional information
Thesis (MTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2010
File(s)![Thumbnail Image]()
Loading...
Name
Analysis of heat transfer & thermal stability.pdf
Size
1.71 MB
Format
Adobe PDF
Checksum
(MD5):0db77ffc6e033173ac02c89d7ead26b3