Abstract
The present study addresses the problem of ignition of a single sodium droplet, which is an important issue for the nuclear facilities safety. The study follows the approach of previous works and extends the results of those papers to the case of radiative heat loss. The contribution of the thermal radiation is taken into account based on the P‐1 approximation for thermal radiation transfer. An extension of solutions of the existing model is obtained in the presence of radiative heat loss for ignition time and critical temperature by exploiting the sensitivity of the process to large chemical activation energy. Different qualitative effects of varying the dimensionless convective heat loss parameter with ignition time and critical temperature are presented in the graphs. The results show that the inclusion of additional heat sink mechanism, that is, radiative heat loss, causes significant delays in the ignition time and reduces the critical temperature with respect to results of previous studies.
Highlights
There are many investigations on thermal ignition in the literature
The results show that the inclusion of additional heat sink mechanism, that is, radiative heat loss, causes significant delays in the ignition time and reduces the critical temperature with respect to results of previous studies
The problem of interest focuses on the effect of thermal radiation on ignition of a single sodium droplet with initial radius rs and ambient temperature T0 in an oxidizing atmosphere with T∞ ≤ T0 the behaviour of the droplet radius squared is still linear with time under certain conditions
Summary
The one of utmost concern is that of ignition of sodium droplet because of its extensive use as a working fluid in the design of nuclear facilities. Basic research on droplet combustion has been conducted, some questions that arose from these previous works suggest the need for further studies, Grosan and Pop 1 , Morewitz et al 2. The tendency of the square of the droplet radius is reproduced by imposing the quasisteady regime QSR for the gas International Journal of Mathematics and Mathematical Sciences phase. Sodium droplet temperature T is assumed spatially uniform but temporally varying because of its high thermal conductivity λ which is characterized by low vapour pressure
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