The influence of natural convection on the temporal development of the temperature and concentration fields for Sal’nikov's reaction,P→A→B, occurring batchwise in the gas phase in a closed vessel

The behaviour of Sal’nikov’s reaction, P → A → B, in a spherical batch reactor with the diffusion of heat and matter

“…This arrangement is suitable for studying Sal'nikov's reaction in the well-mixed limit; however, it is not suitable for cases that are not spatially uniform. This reaction has also been studied numerically in the well mixed and zero gravity extremes 24,25 as well as when natural convection is present [11][12][13][14][15] . The reaction between hydrogen and chlorine, using similar experimental techniques, has also been used as a model of Sal'nikov's reaction 24 .…”

“…The reaction between hydrogen and chlorine, using similar experimental techniques, has also been used as a model of Sal'nikov's reaction 24 . The following parameters were chosen to match those used in previous numerical studies of the di-t-butyl peroxide reaction [11][12][13][14][15] . The temperature of the wall of the spherical reactor The value of  diffusion was therefore altered by changing the radius of the reactor, L. We note that a similar variation in  diffusion could alternatively be achieved by maintaining a constant vessel radius, and altering the diffusivity, as was done by Fairlie and Griffiths 25 , who considered reaction occurring in a vessel of radius 0.0492 m with diffusivities of 3 × 10 -4 and 6 × 10 -4 m 2 s -1 .…”

“…The assumption of constant density is, of course, a considerable simplification and this should be borne in mind when interpreting the results; however, previous analytical [17][18][19] and numerical studies 24,25 of Sal'nikov's reaction occurring in the presence of purely diffusive transport processes have made the same assumption. The adoption of such an assumption also allows easier comparison with the results of numerical studies in the presence of natural convection, which have applied the Boussinesq approximation [11][12][13][14][15] , i.e. when the density is only allowed to vary in the buoyancy term of the Navier-Stokes equations.…”

“…Its inclusion arises from the standard definition of the thermal diffusivity,  = k T / ( C P ). The thermal diffusivity has been defined thus to enable comparison between the results in a purely diffusive system, with one in which convection plays a role [11][12][13][14][15] . To achieve the required form of , each term in Eq.…”

“…natural convection is induced. This convection can significantly alter the behaviour within the reactor whilst the reaction proceeds; these effects have been studied numerically recently [11][12][13][14][15] . The other case to consider is that when convection is eliminated from the unstirred vessel, so that diffusion is the only mode of heat and mass transfer in the reactor.…”