An Analysis of Heat Explosion for Thermally Insulated and Conducting Systems

Affiliation(s)

Department of Mathematical Sciences, Clemson University, Clemson, USA.

Department of Mechanical Engineering, Clemson University, Clemson, USA.

Department of Materials Science and Engineering, Clemson University, Clemson, USA.

Department of Mathematical Sciences, Clemson University, Clemson, USA.

Department of Mechanical Engineering, Clemson University, Clemson, USA.

Department of Materials Science and Engineering, Clemson University, Clemson, USA.

ABSTRACT

In the scope of material science, it is well understood that mechanical behavior of a material is temperature dependent. The converse is also true and for specific loading cases contributes to a unique thermal failure mechanism known as “heat explosion”. The goal for this paper is to improve the mathematical models for predicting heat explosion by using a specific case of the Fourier heat transfer system that focuses on thermoviscoelastic properties of materials. This is done by using a computational analysis to solve for an internal heat parameter that determines thermal failure at a critical value. This critical value is calculated under conditions either accounting for or negating the effect of heat dissipated by the material. This model is an improvement on existing models because it accounts for material specific properties and in doing so limits mathematical assumptions of the system. By limiting the assumptions in the conditions of the model, the model becomes more accurate and useful in regards to material design.

In the scope of material science, it is well understood that mechanical behavior of a material is temperature dependent. The converse is also true and for specific loading cases contributes to a unique thermal failure mechanism known as “heat explosion”. The goal for this paper is to improve the mathematical models for predicting heat explosion by using a specific case of the Fourier heat transfer system that focuses on thermoviscoelastic properties of materials. This is done by using a computational analysis to solve for an internal heat parameter that determines thermal failure at a critical value. This critical value is calculated under conditions either accounting for or negating the effect of heat dissipated by the material. This model is an improvement on existing models because it accounts for material specific properties and in doing so limits mathematical assumptions of the system. By limiting the assumptions in the conditions of the model, the model becomes more accurate and useful in regards to material design.

Cite this paper

I. Viktorova, M. Scruggs, I. Zeller and K. Fairchild, "An Analysis of Heat Explosion for Thermally Insulated and Conducting Systems,"*Applied Mathematics*, Vol. 3 No. 6, 2012, pp. 535-540. doi: 10.4236/am.2012.36081.

I. Viktorova, M. Scruggs, I. Zeller and K. Fairchild, "An Analysis of Heat Explosion for Thermally Insulated and Conducting Systems,"

References

[1] P. P. Oldyrev, “Heating-Up Temperature and Failure of Plastics under Cyclic Deformation,” Mechanics of Polymers, Vol. 3, 1967, pp. 483-492.

[2] P. P. Oldyrev and V. P. Tamuz, “Change in Properties of Glass-Reinforced Plastic under Cyclic Tension-Compression,” Mechanics of Polymers, Vol. 5, 1967, pp. 864-872.

[3] P. H. Francis, “Thermo-Mechanical Effects in Elastic Wave Propagation: A Survey,” Journal of Sound and Vibration, Vol. 21, No. 2, 1972, pp. 181-192. doi:10.1016/0022-460X(72)90905-4

[4] D. Meinkohn, “Heat Explosion Theory and Vibrational Heating of Polymers,” International Journal of Heat and Mass Transfer, Vol. 25, No. 4, 1981, pp. 645-648. doi:10.1016/0017-9310(81)90008-9

[5] I. Viktorova, J. V. Suvorova and A. E. Osokin, “SelfHeating of Inelastic Composites under Cyclic Deformation,” Izvestiya AN USSR Mechanics of Solids, Vol. 19, No. 1, 1984, pp. 99-105.

[6] I. Viktorova, “The Dependence of Heat Evaluation on Parameters of Cyclic Deformation Process,” Izvestiya AN USSR Mechanics of Solids, No. 4, 1981, pp. 110-114.

[1] P. P. Oldyrev, “Heating-Up Temperature and Failure of Plastics under Cyclic Deformation,” Mechanics of Polymers, Vol. 3, 1967, pp. 483-492.

[2] P. P. Oldyrev and V. P. Tamuz, “Change in Properties of Glass-Reinforced Plastic under Cyclic Tension-Compression,” Mechanics of Polymers, Vol. 5, 1967, pp. 864-872.

[3] P. H. Francis, “Thermo-Mechanical Effects in Elastic Wave Propagation: A Survey,” Journal of Sound and Vibration, Vol. 21, No. 2, 1972, pp. 181-192. doi:10.1016/0022-460X(72)90905-4

[4] D. Meinkohn, “Heat Explosion Theory and Vibrational Heating of Polymers,” International Journal of Heat and Mass Transfer, Vol. 25, No. 4, 1981, pp. 645-648. doi:10.1016/0017-9310(81)90008-9

[5] I. Viktorova, J. V. Suvorova and A. E. Osokin, “SelfHeating of Inelastic Composites under Cyclic Deformation,” Izvestiya AN USSR Mechanics of Solids, Vol. 19, No. 1, 1984, pp. 99-105.

[6] I. Viktorova, “The Dependence of Heat Evaluation on Parameters of Cyclic Deformation Process,” Izvestiya AN USSR Mechanics of Solids, No. 4, 1981, pp. 110-114.