Self-ignition of dust cloud in a hot gas

  • Saad A. El-Sayed
Technical Paper


A dust cloud autoignition in a hot gas is investigated based on the thermal explosion theory. A mathematical model that contains the energy equations for both particle and gas is used. The critical ignition conditions using the different forms of criticality in different planes of the solution have been presented analytically for both steady-state and transient conditions. The convection and radiation heat losses are used in this work. The critical conditions have been presented in mathematical expressions. A direct integration of the governing equations of the problem using the Runga–Kutta method of a high order for different planes is presented. The analysis showed that the critical ignition temperatures and ignition time values of the convection and radiation heat loss case are lower than those obtained for the case of convection heat loss only. The effect of ambient temperature, gas temperature, dimensionless characteristic parameters, and initial particle temperature on the critical ignition conditions is investigated. It was found that the ignition delay time, τ*, increases with decreasing gas temperature and increasing ambient temperature, θa.


Dust cloud autoignition Thermal explosion theory Critical conditions Ignition times Analytical and numerical solutions 

List of symbols


Frequency factor (m/s)


Specific heat (J/kg K)


Diameter (m)


Activation energy (J/kg)


Heat transfer coefficient (W/m2 K)


Thermal conductivity (W/m K)


Arrhenius rate constant (s−1)


Mass (kg)


Number of particles in the cloud


Heat of the reaction (J/kg)


Universal gas constant (J/kg K)


Surface area (m2)


Temperature (K)

Subscripts and superscripts


Ambient temperature


Cloud or vessel


Cloud surrounding









Greek letters


Density (kg/m3)


Dimensionless temperature = RT/E


Cloud–particle density = heat transfer coefficient ratio × cloud–particle surface area ratio = \(h_{\text{cs}} S_{\text{c}} /Nh_{\text{pg}} S_{\text{p}}\)


Modified dimensionless Semenov number or reaction exothermicity for the convection heat loss case = \(\rho_{\text{g}} A_{\text{n}} QY_{\text{o}} R/Nh_{\text{pg}} E\)


Modified dimensionless Semenov number or reaction exothermicity for the radiation heat loss case = \(\rho_{\text{g }} A_{\text{n}} QY_{\text{o}} R^{4} S_{\text{p}} / \sigma \varepsilon S_{\text{v}} h_{\text{pg}} E^{4}\)


Dimensionless time = \(\rho_{\text{g}} A_{\text{n}} S_{\text{p}} QY_{\text{o}} R/m_{\text{p}} c_{\text{pp}} E\)


Stefan–Boltzmann constant = 5.67 × 10 −8 W m−2 K−4




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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Mechanical Power EngineeringDept-Zagazig UniveristyAl-SharkiaEgypt

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