Analytical Solution of Heat Transfer in LaserIrradiated Skin Tissue with Surface Heat Convection Using Dual Phase Lag Model

Document Type : Research Article

Authors

Mechanical Engineering Department, Golpayegan University of Technology, Isfahan, Iran

Abstract

The temperature distribution in the laser-irradiated biological tissue is investigated considering heat convection. The first- and the second-degree burn times are predicted using estimation of thermal damage. A non-Fourier equation of bio-heat transfer based on dual phase lag model is employed. The transport behavior of laser light in the tissue is regarded as highly absorbed and effects of the phase lag times on thermal response and thermal damage are explored considering different heat convection coefficients. The Laplace transform with discretization technique and also using boundary conditions, a set of algebraic equations in Laplace domain is generated which are solved by numerical Laplace inverse transform. The results show that the highly absorbed laser light in the tissue plays an important role in the burned skin time. Also, convective heat transfer boundary condition on the surface provides different results, even by considering the natural convection on the surface, and the first- and the second-degree burns are postponed at least 0.02 second.

Keywords

Main Subjects

References

[1] H.H. Pennes, Analysis of tissue and arterial blood temperatures in the resting human forearm, Journal of applied physiology, 1(2) (1948) 93-122.
[2] C. Cattaneo, A form of heat-conduction equations which eliminates the paradox of instantaneous propagation, Comptes Rendus, 247 (1958) 431.
[3] P. Vernotte, Les paradoxes de la theorie continue de l'equation de la chaleur, Compt. Rendu, 246 (1958) 3154-3155.
[4] J. Liu, R. Zepei, W. Cuncheng, Interpretation of living tissue's temperature oscillations by thermal wave theory, Chinese Science Bulletin, 17 (1995) 021.
[5] S. Brorson, J. Fujimoto, E. Ippen, Femtosecond electronic heat-transport dynamics in thin gold films, Physical Review Letters, 59(17) (1987) 1962.
[6] Y. Taitel, On the parabolic, hyperbolic and discrete formulation of the heat conduction equation, International Journal of Heat and Mass Transfer, 15(2) (1972) 369-371.
[7] C. Bai, A. Lavine, On hyperbolic heat conduction and the second law of thermodynamics, Journal of Heat Transfer, 117(2) (1995) 256-263.
[8] C. Körner, H. Bergmann, The physical defects of the hyperbolic heat conduction equation, Applied Physics A, 67(4) (1998) 397-401.
[9] D.Y. Tzou, Macro-to microscale heat transfer: the lagging behavior, John Wiley & Sons, 2014.
[10] Y. Zhang, Generalized dual-phase lag bioheat equations based on nonequilibrium heat transfer in living biological tissues, International Journal of Heat and Mass Transfer, 52(21-22) (2009) 4829-4834.
[11] H. Ahmadikia, R. Fazlali, A. Moradi, Analytical solution of the parabolic and hyperbolic heat transfer equations with constant and transient heat flux conditions on skin tissue, International communications in heat and mass transfer, 39(1) (2012) 121-130.
[12] H. Ahmadikia, A. Moradi, R. Fazlali, A.B. Parsa, Analytical solution of non-Fourier and Fourier bioheat transfer analysis during laser irradiation of skin tissue, Journal of Mechanical Science and Technology, 26(6)(2012) 1937-1947.
[13] S.-M. Lin, Analytical solutions of bio-heat conduction on skin in Fourier and non-Fourier models, Journal of Mechanics in Medicine and Biology, 13(04) (2013) 1350063.
[14] K.-C. Liu, C.-C. Wang, P.-J. Cheng, Nonlinear Behavior of Thermal Lagging in Laser-Irradiated Layered Tissue, Advances in Mechanical Engineering, 5 (2013) 732575.
[15] K.-C. Liu, J.-C. Wang, Analysis of thermal damage to laser irradiated tissue based on the dual-phase-lag model, International Journal of Heat and Mass Transfer, 70 (2014) 621-628.
[16] H. Askarizadeh, H. Ahmadikia, Analytical analysis of the dual-phase-lag model of bioheat transfer equation during transient heating of skin tissue, Heat and Mass Transfer, 50(12) (2014) 1673-1684.
[17] J. Valsa, L. Brančik, Approximate formulae for numerical inversion of Laplace transforms, International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 11(3) (1998) 153-166.
[18] A. Welch, The thermal response of laser irradiated tissue, IEEE journal of quantum electronics, 20(12) (1984) 1471-1481.
[19] A. Moradi, H.Z. Poor, H. Moosavi, Analysis of the DPL bio-heat transfer equation with constant and timedependent heat flux conditions on skin surface, (2014).
[20] J. Liu, X. Chen, L.X. Xu, New thermal wave aspects on burn evaluation of skin subjected to instantaneous heating, IEEE transactions on biomedical engineering, 46(4) (1999) 420-428.
[21] T.-C. Shih, P. Yuan, W.-L. Lin, H.-S. Kou, Analytical analysis of the Pennes bioheat transfer equation with sinusoidal heat flux condition on skin surface, Medical Engineering & Physics, 29(9) (2007) 946-953.
[22] F. Xu, K. Seffen, T. Lu, Non-Fourier analysis of skin biothermomechanics, International Journal of Heat and Mass Transfer, 51(9-10) (2008) 2237-2259.
[23] W. Kaminski, Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure, Journal of Heat Transfer, 112(3) (1990) 555-560.
[24] K. Mitra, S. Kumar, A. Vedevarz, M. Moallemi, Experimental evidence of hyperbolic heat conduction in processed meat, Journal of Heat Transfer, 117(3) (1995) 568-573.
[25] P.J. Antaki, New interpretation of non-Fourier heat conduction in processed meat, Journal of Heat Transfer, 127(2) (2005) 189-193.
[26] A. Mehta, F. Wong, Measurement of Flammability and Burn Potential of Fabrics. Project DSR 73884,[CNTIS: COM-73-10960], in, MIT, 1973.
Amirkabir Journal of Mechanical Engineering
Volume 50, Issue 2
July and August 2018
Pages 285-294

Files

Share

How to cite

Statistics