Magnesium Oxychloride sorrel cement coatings was introduced as a fire control method and in order to provide a barrier system intended to prevent ignition of and spread of flame along a combustuble substrate. These can be used in warheads in the navy to prevent fire spread. A critical thickness of insulation can be identified. Beyond this thickness exists a cost thickness tradeoff. Magnesium oxychloride cement coating co-bonded with high alumina calcium aluminate cement colloidal silica can be effective. The UL 1709 test by ASTM standards can be used to measure the resistance of a given material to temperature rise fires. The time required for the average temperature of a steel column insulated with the material being tested to exceed 1000 F.

In the time the flame spreads non-Fourier heat conduction cannot be ignored. The damped wave conduction and relaxation equation is used to model the transient heat conduction in a cylindrical naval warhead coated with the thermal barrier coating. In the asymptotic limit of infinite heat velocity the hyperbolic PDE reduces to a parabolic PDE. In the asymptotic limit of infinite relaxation time the hyperbolic governing equation reduces to a wave equation in cylindrical coordinates. The time time taken for the average temperatuer in a finite slab subject to convective boundary condition is obtained. An analytical solution to the time averaged hyperbolic PDE is obtained. For Biot modulus greater than 1/8 the average temperature is found to be subcritical damped oscillatory. The Biot modulus is given by h/SR where S is the storage coefficient, R is the half-width of the slab and h is the heat transfer coefficient of the surroundings. The storage modulus, S is given by the product of density and heat capacity divided by the relaxation time. Thus for materials with large relaxation times the temperature will begin to pulsate although they are subcritical damped in nature. The exact solution for the temperature in the naval warhead is obtained by the separation of variables. A transient part and steady state is solved for the cylindrical assembly. The thickness of the insulation below which the temperature will undergo subcritical damped oscillations was found to be when,

R < 4.8096 SQRT(alpha*tou(r))

The exact solution for the transient temperature in a thin film and warhead in cartesian coordinates was obtained. For thickness of the film, delta < (12/h*)^1/3 SQRT(alpha*tou(r)) subcritical damped oscillations will occur.