50
R. S. Lebelo and O. D. Makinde
transfer in engineering and industrial products manufacturing [1, 2]. Examples of heat
transfer applications include, among others, heavy oil recovery, storage of cellulose
materials, solids combustion, biomass and coal pyrolysis, waste incineration, and
coal gasification [3]. Furthermore, ignorance of heat transfer and thermal stability
applications during the manufacturing of industrial products using reactive materials
may lead to bending or deformation and decolorization those products [4].
Combustible materials are those that react spontaneously with oxygen because
of exothermic chemical reaction [5]. This study considers a two-step exothermic
chemical reaction like the one occurring in methane combustion. Heat transfer is
considered in a stockpile whose materials are reactive. An example can be a stockpile of wood or hay, and the study is modelled in a cylindrical pipe, such as the
one carried out in [6]. The investigation of heat transfer in stockpiles was conducted
experimentally in [7, 8], where physical properties like the material’s coarseness,
surface area thereof, its humidity and the surrounding temperature were studied. In
this study, a theoretical approach is conducted where the thermo-physical parameters including the reaction rate and activation energy, which are embedded on the
governing differential equation, are analyzed. The analysis is carried out by varying
selected parameters to see how they affect temperature profiles during combustion.
Transient heat analysis for exothermic chemical reaction in two-step was studied
in [9], where the combustion process was modelled in a rectangular slab and coupled
convective and radiative boundary conditions were applied. The analysis considered
a temperature dependent thermal conductivity, and the reactant diffusion was also
included, but in this case, a constant thermal conductivity is observed. In [10] the
analysis was conducted in a spherical domain of reactive materials, where heat loss by
convection was considered. The mathematical modelling of a two-step exothermic
chemical reaction was given by Makinde et al. [11], and their investigation was
conducted with or without reactant consumption, with no extensive consideration of
the reactant consumption. The objective of this study is to investigate the transfer of
heat in a combusting stockpile of reactive materials which loses heat to the immediate
environment by convection in an exothermic chemical reaction undergoing two steps.
From the literature above, this investigation was not intensely carried out.
5.2 Mathematical Modelling
An example of a two-step exothermic chemical reaction taking place within a stockpile of combustible materials modelled in a cylindrical domain is given as Eqs. (5.1)
and (5.2):
2CH 4 + 0.22N 2 + 3(O 2 + 3.76N 2 ) → 2CO + 4H 2 O + 11.50N 2 (Step 1) (5.1)
2CO + O 2 + 3.76N 2 → 2CO 2 + 3.76N 2 (Step 2)
(5.2)
R. S. Lebelo and O. D. Makinde
transfer in engineering and industrial products manufacturing [1, 2]. Examples of heat
transfer applications include, among others, heavy oil recovery, storage of cellulose
materials, solids combustion, biomass and coal pyrolysis, waste incineration, and
coal gasification [3]. Furthermore, ignorance of heat transfer and thermal stability
applications during the manufacturing of industrial products using reactive materials
may lead to bending or deformation and decolorization those products [4].
Combustible materials are those that react spontaneously with oxygen because
of exothermic chemical reaction [5]. This study considers a two-step exothermic
chemical reaction like the one occurring in methane combustion. Heat transfer is
considered in a stockpile whose materials are reactive. An example can be a stockpile of wood or hay, and the study is modelled in a cylindrical pipe, such as the
one carried out in [6]. The investigation of heat transfer in stockpiles was conducted
experimentally in [7, 8], where physical properties like the material’s coarseness,
surface area thereof, its humidity and the surrounding temperature were studied. In
this study, a theoretical approach is conducted where the thermo-physical parameters including the reaction rate and activation energy, which are embedded on the
governing differential equation, are analyzed. The analysis is carried out by varying
selected parameters to see how they affect temperature profiles during combustion.
Transient heat analysis for exothermic chemical reaction in two-step was studied
in [9], where the combustion process was modelled in a rectangular slab and coupled
convective and radiative boundary conditions were applied. The analysis considered
a temperature dependent thermal conductivity, and the reactant diffusion was also
included, but in this case, a constant thermal conductivity is observed. In [10] the
analysis was conducted in a spherical domain of reactive materials, where heat loss by
convection was considered. The mathematical modelling of a two-step exothermic
chemical reaction was given by Makinde et al. [11], and their investigation was
conducted with or without reactant consumption, with no extensive consideration of
the reactant consumption. The objective of this study is to investigate the transfer of
heat in a combusting stockpile of reactive materials which loses heat to the immediate
environment by convection in an exothermic chemical reaction undergoing two steps.
From the literature above, this investigation was not intensely carried out.
5.2 Mathematical Modelling
An example of a two-step exothermic chemical reaction taking place within a stockpile of combustible materials modelled in a cylindrical domain is given as Eqs. (5.1)
and (5.2):
2CH 4 + 0.22N 2 + 3(O 2 + 3.76N 2 ) → 2CO + 4H 2 O + 11.50N 2 (Step 1) (5.1)
2CO + O 2 + 3.76N 2 → 2CO 2 + 3.76N 2 (Step 2)
(5.2)