Journal of Theoretical
and Applied Mechanics
0, 0, pp. , Warsaw 0

Theoritical simulation of temperature distribution in gun barrel based on DPL model

Mohammad Reza Talaee, Seyed Ali Hosseinli
In this paper, an exact closed form solution is introduced for heat conduction equation in cylindrical coordinates under consecutive inner time dependent surface heat flux by both Fourier and dual-phase-lag (DPL) model. The solution is used to calculate the temperature distribution in gun barrel subjected to single and consecutive shoots and result is compared with literature. The parametrical study is done using the analytical solution, to show the effect of shooting frequency which lead to different heat power from each fire shoot and temperature distribution. Result shows good ability of analytical solution for estimation of temperature distribution in gun barrel, especially under consecutive shoots in which unexpected incidents such as barrel melting is so probable. The closed form solution can be applied for verification of other numerical works in this area.
Keywords: DPL heat conduction model; Cylindrical coordinates; Gun barrel; Exponential Decaying heat flux; Pure analytical solution.

References


Cattaneo, C., A form of heat-conduction equations which eliminates the paradox of instantaneous propagation. Comptes Rendus, 1958. 247: p. 431.

Vernotte, P., Some possible complications in the phenomena of thermal conduction. Compte Rendus, 1961. 252: p. 2190-2191.

Tzou, D.Y., The generalized lagging response in small-scale and high-rate heating. International Journal of Heat and Mass Transfer, 1995. 38(17): p. 3231-3240.

Tzou, D.Y., Macro- to Microscale Heat Transfer: The Lagging Behavior. Taylor and Francis, Washington, DC, 1997.

Afrin, N., Y. Zhang, and J. Chen, Dual-phase lag behavior of a gas-saturated porous-medium heated by a short-pulsed laser. International Journal of Thermal Sciences, 2014. 75: p. 21-27.

Ghazanfarian, J. and A. Abbassi, Effect of boundary phonon scattering on Dual-Phase-Lag model to simulate micro-and nano-scale heat conduction. International Journal of Heat and Mass Transfer, 2009. 52(15-16): p. 3706-3711.

Ghazanfarian, J. and A. Abbassi, Investigation of 2D transient heat transfer under the effect of dual-phase-lag model in a nanoscale geometry. International Journal of Thermophysics, 2012. 33(3): p. 552-566.

Ghazanfarian, J. and Z. Shomali, Investigation of dual-phase-lag heat conduction model in a nanoscale metal-oxide-semiconductor field-effect transistor. International Journal of Heat and Mass Transfer, 2012. 55(21-22): p. 6231-6237.

Han, P., D. Tang, and L. Zhou, Numerical analysis of two-dimensional lagging thermal behavior under short-pulse-laser heating on surface. International journal of engineering science, 2006. 44(20): p. 1510-1519.

Liu, K.-C. and H.-T. Chen, Investigation for the dual phase lag behavior of bio-heat transfer. International Journal of Thermal Sciences, 2010. 49(7): p. 1138-1146.

Chandrasekharaiah, D., Hyperbolic thermoelasticity: a review of recent literature. Applied Mechanics Reviews, 1998. 51(12): p. 705-729.

Torabi, M. and S. Saedodin, Analytical and numerical solutions of hyperbolic heat conduction in cylindrical coordinates. Journal of Thermophysics and Heat Transfer, 2011. 25(2): p. 239-253.

Mishra, S.C. and H. Sahai, Analyses of non-Fourier heat conduction in 1-D cylindrical and spherical geometry–An application of the lattice Boltzmann method. International Journal of Heat and Mass Transfer, 2012. 55(23-24): p. 7015-7023.

Gheitaghy, A. and M. Talaee, Solving hyperbolic heat conduction using electrical simulation. Journal of Mechanical Science and Technology, 2013. 27(12): p. 3885-3891.

Talaee, M., M. Alizadeh, and S. Bakhshandeh, An exact analytical solution of non-Fourier thermal stress in cylindrical shell under periodic boundary condition. Engineering Solid Mechanics, 2014. 2(4): p. 293-302.

Saedodin, S. and M. Barforoush, An exact solution for thermal analysis of a cylindrical object using hyperbolic thermal conduction model. Thermophysics and Aeromechanics, 2017. 24(6): p. 909-920.

Akbarzadeh, A. and Z. Chen, Transient heat conduction in a functionally graded cylindrical panel based on the dual phase lag theory. International Journal of Thermophysics, 2012. 33(6): p. 1100-1125.

Torabi, M. and K. Zhang, Multi-dimensional dual-phase-lag heat conduction in cylindrical coordinates: Analytical and numerical solutions. International Journal of Heat and Mass Transfer, 2014. 78: p. 960-966.

Chen, T.-C., et al., Inverse estimation of heat flux and temperature in multi-layer gun barrel. International journal of heat and mass transfer, 2007. 50(11-12): p. 2060-2068.

Wu, B., G. Chen, and W. Xia, Heat transfer in a 155 mm compound gun barrel with full length integral midwall cooling channels. Applied Thermal Engineering, 2008. 28(8-9): p. 881-888.

Chen, T.-C. and C.-C. Liu, Inverse Estimation of Time-varied Heat Flux and Temperature on 2-D GunBarrel using Input Estimation Method with Finite-element Scheme. Defence Science Journal, 2008. 58(1): p. 57.

Lee, H.-L., et al., Estimation of heat flux and thermal stresses in multilayer gun barrel with thermal contact resistance. Applied Mathematics and Computation, 2009. 209(2): p. 211-221.

Mishra, A., A. Hameed, and B. Lawton, A novel scheme for computing gun barrel temperature history and its experimental validation. Journal of Pressure Vessel Technology, 2010. 132(6): p. 061202.

Hill, R.D. and J.M. Conner, Transient heat transfer model of machine gun barrels. Materials and Manufacturing Processes, 2012. 27(8): p. 840-845.

Lawton, B., Thermo-chemical erosion in gun barrels. Wear, 2001. 251(1-12): p. 827-838.

Seiler, F., et al., Experimental and numerical estimation of gun barrel heating for rapid fire. WIT Transactions on Modelling and Simulation, 2003. 33.

Dębski, A., et al., Analysis of Heat Transfer in a 35 mm Barrel of an Anti-Aircraft Cannon. Problemy Mechatroniki: uzbrojenie, lotnictwo, inżynieria bezpieczeństwa, 2016. 7.

Atefi, G. and M.R. Talaee, Non-fourier temperature field in a solid homogeneous finite hollow cylinder. Archive of Applied Mechanics, 2011. 81(5): p. 569-583.

Talaee, M. and V. Sarafrazi, Analytical Solution for Three-Dimensional Hyperbolic Heat Conduction Equation with Time-Dependent and Distributed Heat Source. Journal of Mechanics, 2017. 33(1): p. 65-75.

Talaee, M., V. Sarafrazi, and S. Bakhshandeh, Exact Analytical Hyperbolic Temperature Profile in a Three-Dimensional Media Under Pulse Surface Heat Flux. Journal of Mechanics, 2016. 32(3): p. 339-347.

Talaee, M.R. and G. Atefi, Non-Fourier heat conduction in a finite hollow cylinder with periodic surface heat flux. Archive of Applied Mechanics, 2011. 81(12): p. 1793-1806.

Talaee, M.R. and A. Kabiri, Exact Analytical Solution of Bioheat Equation Subjected to Intensive Moving Heat Source. Journal of Mechanics in Medicine and Biology, 2017. 17(05): p. 1750081.

Talaee, M.R. and A. Kabiri, Analytical Solution of Hyperbolic Bioheat Equation in Spherical Coordinates Applied in Radiofrequency Heating. Journal of Mechanics in Medicine and Biology, 2017. 17(04): p. 1750072.

Talaee, M.R., A. Kabiri, and R. Khodarahmi, Analytical Solution of Hyperbolic Heat Conduction Equation in a Finite Medium Under Pulsatile Heat Source. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2017: p. 1-9.

Underwood, J., G. Vigilante, and C. Mulligan, Review of thermo-mechanical cracking and wear mechanisms in large caliber guns. Wear, 2007. 263(7-12): p. 1616-1621.

Malter, L. and D. Langmuir, Resistance, emissivities and melting point of tantalum. Physical Review, 1939. 55(8): p. 743