Possibilities Arising From The Heat Loss And Production

When the heat flux and the heat production fluxes are graphically represented in a plot of heat flux against temperature, the following three cases can arise.

  1. The heat production is less than the heat lost.
  2. The heat production is the same as the heat lost.
  3. The heat production is greater than the heat lost.

Each of these cases are shown in figure 2.

[Figure 2 - Plot of the thermal fluxes]
Figure 2 - Plot of the thermal fluxes against temperature

Curve A, curve B and curve C are the heat gain curves. The straight line that crosses the curves is the heat loss.

Curve A

The reactants enter into the system at a low temperature and because the heat production curve lies above the heat loss curve they proceed to heat up until the temperature reaches the Tstable temperature. Because this temperature is said to be a stable temperature, then no further self-heating will take place with the temperature remaining constant around the stable temperature. If the reactants in the system are now heated by some external source (e.g. Bunsen burner), then the temperature within the system will rise. If the temperature reaches Tignition, which is an unstable point, and becomes greater than Tignition then the system becomes unstable and thermal runaway will occur. If however the external heat source is removed, then the reactants should begin to drop in temperature and return back to Tstable, where the system will become stable again.

Curve B

This is the most important of the three curves in figure 2. The three temperatures Tstable, Tcritical, and Tignition are all at the same temperature. The heat loss curve is tangential to the heat gain curve. The temperature of the reactants in the system will slowly rise up to the critical temperature; at which point a rapid acceleration of the temperature will occur resulting in a thermal explosion.

Curve C

As can be seen from figure 2, this curve is always going to have a heat gain flux that is always exceeding the heat loss flux. Therefore at whatever temperature the reactants are in the system, then a thermal explosion will take place.

It is also possible to alter the range of explosion limits. This can be achieved in a number of ways, with the two most likely to be examined are shown in figure 3 and figure 4. In figure 3 it can be seen that by altering the ambient temperature Ta (which is also the wall temperature for Semenov's Model) in an increasing manor, the heat loss line moves away from the heat gain curves which results in the greater range in which explosion will occur. The second method for increasing the explosion range is shown in figure 4. The ambient temperature Ta is kept at the same temperature, but the vessel dimensions are altered (e.g. for a circular or cylindrical vessel increasing the radius will decrease the gradient of the heat loss line, moving it away from the heat gain curve). This is the same, as altering the heat transfer coefficient in equation 2, reducing the coefficient will increase the explosion range.

[Figure 3 - Effect of altering the ambient temperature]
Figure 3 - Effect of altering the ambient temperature Ta to Ta*
The lighter heat loss line is the case of the original temperature.
The darker heat loss line is the resultant of altering the ambient temperature

[Figure 4 - Effect of reducing the heat transfer coefficient]
Figure 4 - Effect of reducing the heat transfer coefficient from h to h*

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