International Scientific Journal

Thermal Science - Online First

Authors of this Paper

External Links

online first only

Heat transfer on simplified pre-period stage of tunnel fire

Tunnel fire is a part of applied thermal problems. With increase of transient temperature of the tunnel fire on the structure surface (i.e. tunnel lining), the heat transfer from the surface is possibly varying transient temperature distribution within the structure. The transient temperature distribution is also possibly damaging the composition of structure (micro-crack) because of critical damage temperature. Therefore, the transient temperature distribution has a significantly important role on defining mechanical and physical properties of structure and determining thermal-induced damaged region. The damage at pre-period stage of tunnel fire is perhaps more significant than that at the other period stages because of thermal gradient. Consequently, a theoretical model was developed for simplifying complicated thermal engineering during pre-period stage of tunnel fire. A hollow solid model (HSM) in a combination of dimensional analysis and heat transfer theory with Bessel’s Function and Duhamel’s Theorem were employed to verify a theoretical equation for dimensionless transient temperature distribution (DTTD) under linear transient thermal loading (LTTL). Experimental and numerical methods were also adopted to approve the results from this theoretical equation. The heating rate (M) is a primary variable for discussing DTTD on three means. The heating rate of 10.191, 10 and 240°C/min were applied to experimental and numerical studies. The experimental and numerical results are consistent with the theoretical solution, successfully verifying that the theoretical solution can predict the DTTD well in field. This equation can be used for thermal/tunnel engineers to evaluate the damaged region and to obtain the parameters related to DTTD.
PAPER REVISED: 2018-08-29
PAPER ACCEPTED: 2018-12-10
  1. Enomoto, Y., Furuhama, S., Study on Thin Film Thermocouple for Measuring Instantaneous Temperature on Surface of Combustion Chamber Wall in Internal Combustion Engine, Bulletin of JSME, 28 (1985), 235, pp. 108-116
  2. Malekan, M., et al., Thermo-Mechanical Analysis of a Cylindrical Tube under Internal Shock Loading Using Numerical Solution, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38 (2016), 8, pp. 2635-2649
  3. Menezes, P. L., Influence of Cutter Velocity, Friction Coefficient and Rake Angle on the Formation of Discontinuous Rock Fragments During Rock Cutting Process, The International Journal of Advanced Manufacturing Technology, 90 (2017), 9, pp. 3811-3827
  4. Cao, P., et al., Experimental Investigation of Cutting Temperature in Ice Drilling, Cold Regions Science and Technology, 116 (2015), pp. 78-85
  5. Fox, D. B., et al., Sustainable Heat Farming: Modeling Extraction and Recovery in Discretely Fractured Geothermal Reservoirs, Geothermics, 46 (2013), pp. 42-54
  6. Vilarrasa, V., et al., Hydromechanical Characterization of Co2 Injection Sites, International Journal of Greenhouse Gas Control, 19 (2013), pp. 665-677
  7. Gor, G. Y., et al., Effects of Thermal Stresses on Caprock Integrity During Co2 Storage, International Journal of Greenhouse Gas Control, 12 (2013), pp. 300-309
  8. Lönnermark, A., Ingason, H., Gas Temperatures in Heavy Goods Vehicle Fires in Tunnels, Fire Safety Journal, 40 (2005), 6, pp. 506-527
  9. Pichler, C., et al., Safety Assessment of Concrete Tunnel Linings under Fire Load, Journal of Structural Engineering, 132 (2006), 6, pp. 961-969
  10. Brito Filho, J. P., Heat Transfer in Bare and Insulated Electrical Wires with Linear Temperature-Dependent Resistivity, Applied Thermal Engineering, 112 (2017), pp. 881-887
  11. Liu, H., et al., Suggested Continued Heat-Treatment Method for Investigating Static and Dynamic Mechanical Properties of Cement-Based Materials, Construction and Building Materials, 69 (2014), pp. 91-100
  12. Yu, J., et al., Residual Fracture Properties of Concrete Subjected to Elevated Temperatures, Materials and Structures, 45 (2012), 8, pp. 1155-1165
  13. He, Z. J., Song, Y. P., Triaxial Strength and Failure Criterion of Plain High-Strength and High-Performance Concrete before and after High Temperatures, Cement and Concrete Research, 40 (2010), 1, pp. 171-178
  14. Peng, G. F., et al., Explosive Spalling and Residual Mechanical Properties of Fiber-Toughened High-Performance Concrete Subjected to High Temperatures, Cement and Concrete Research, 36 (2006), 4, pp. 723-727
  15. Yu, K., Lu, Z., Determining Residual Double-K Fracture Toughness of Post-Fire Concrete Using Analytical and Weight Function Method, Materials and Structures, 47 (2014), 5, pp. 839-852
  16. Zhang, Z. Z., et al., Effect of Thermal Treatment on Fractals in Acoustic Emission of Rock Material, Advances in Materials Science and Engineering, 2016 (2016), pp. 1-9
  17. Zhang, Y., et al., An Experimental Investigation of Transient Heat Transfer in Surrounding Rock Mass of High Geothermal Roadway, Thermal Science, 20 (2016), 6, pp. 2149-2158
  18. Segall, A. E., Transient Analysis of Thick-Walled Piping under Polynomial Thermal Loading, Nuclear Engineering and Design, 226 (2003), 3, pp. 183-191
  19. Shahani, A. R., Nabavi, S. M., Analytical Solution of the Quasi-Static Thermoelasticity Problem in a Pressurized Thick-Walled Cylinder Subjected to Transient Thermal Loading, Applied Mathematical Modelling, 31 (2007), 9, pp. 1807-1818
  20. Radu, V., et al., Development of New Analytical Solutions for Elastic Thermal Stress Components in a Hollow Cylinder under Sinusoidal Transient Thermal Loading, International Journal of Pressure Vessels and Piping, 85 (2008), 12, pp. 885-893
  21. Marie, S., Analytical Expression of the Thermal Stresses in a Vessel or Pipe with Cladding Submitted to Any Thermal Transient, International Journal of Pressure Vessels and Piping, 81 (2004), 4, pp. 303-312
  22. Eraslan, A. N., Apatay, T., Analytical Solution to Thermal Loading and Unloading of a Cylinder Subjected to Periodic Surface Heating, Journal of Thermal Stresses, 39 (2016), 8, pp. 928-941
  23. Özișik, M. N., Heat Conduction, Wiley, New York, USA, 1993
  24. Zhang, J. G., The Fourier-Yang Integral Transform for Solving the 1-D Heat Diffusion Equation, Thermal Science, 21 (2017), 1, pp. S63-S69
  25. Barenblatt, G. I., Dimensional Analysis, CRC Press, Boca Raton, USA, 1987
  26. Chen, L. H., Failure of Rock under Normal Wedge Indentation: Civil & Mineral Engineering, Ph. D. thesis, University of Minnesota, Minneapolis, USA, 2001
  27. Krishnamurthy, H., Application of Duhamel's Theorem to Problems Involving Oscillating Heat Source, M. SC. thesis, Bangalore University, Bengaluru, India, 2002
  28. Haddag, B., et al., Finite Element Formulation Effect in Three-Dimensional Modeling of a Chip Formation During Machining, International Journal of Material Forming, 3 (2010), 1, pp. 527-530
  29. Yao, W., et al., Quantification of Thermally Induced Damage and Its Effect on Dynamic Fracture Toughness of Two Mortars, Engineering Fracture Mechanics, 169 (2017), pp. 74-88
  30. Mahanta, B., et al., Influence of Thermal Treatment on Mode I Fracture Toughness of Certain Indian Rocks, Engineering Geology, 210 (2016), pp. 103-114
  31. Yin, T., et al., Effect of Thermal Treatment on the Dynamic Fracture Toughness of Laurentian Granite, Rock Mechanics and Rock Engineering, 45 (2012), 6, pp. 1087-1094
  32. Chaki, S., et al., Influence of Thermal Damage on Physical Properties of a Granite Rock: Porosity, Permeability and Ultrasonic Wave Evolutions, Construction and Building Materials, 22 (2008), 7, pp. 1456-1461