Giải pháp phân tích cho phương trình dẫn nhiệt siêu bậc trong môi trường hữu hạn dưới nguồn nhiệt xung động

Abdel-Hamid B (1999) Modelling non-Fourier heat conduction with periodic thermal oscillation using the finite integral transform. Appl Math Model 23(12):899–914 Ahmadikia H, Moradi A, Fazlali R, Parsa AB (2012) Analytical solution of non-Fourier and Fourier bioheat transfer analysis during laser irradiation of skin tissue. J Mech Sci Technol 26(6):1937–1947 Antaki PJ (1997) Analysis of hyperbolic heat conduction in a semi-infinite slab with surface convection. Int J Heat Mass Transf 40(13):3247–3250 Asmar NH (2005) Partial differential equations with Fourier series and boundary value problems. Prentice Hall, Upper Saddle River Barletta A, Pulvirenti B (1998) Hyperbolic thermal waves in a solid cylinder with a non-stationary boundary heat flux. Int J Heat Mass Transf 41(1):107–116 Blackwell BF (1990) Temperature profile in semi-infinite body with exponential source and convective boundary condition. J Heat Transf 112(3):567–571 Cattaneo C (1958) A form of heat conduction equation which eliminates the paradox of instantaneous propagation. C R 247(4):431–433 Lewandowska M (2001) Hyperbolic heat conduction in the semi-infinite body with a time-dependent laser heat source. Heat Mass Transf 37(4–5):333–342 Lewandowska M, Malinowski L (1998) Hyperbolic heat conduction in the semi-infinite body with the heat source which capacity linearly depends on temperature. Heat Mass Transf 33(5–6):389–393 Lewandowska M, Malinowski L (2006) An analytical solution of the hyperbolic heat conduction equation for the case of a finite medium symmetrically heated on both sides. Int Commun Heat Mass Transf 33(1):61–69 López-Molina JA, Rivera MJ, Trujillo M, Burdío F, Lequerica JL, Hornero F, Berjano EJ (2008) Assessment of hyperbolic heat transfer equation in theoretical modeling for radiofrequency heating techniques. Open Biomed Eng J 2:22 Manns F, Borja D, Parel JM, Smiddy W, Culbertson W (2003) Semianalytical thermal model for sub ablative laser heating of homogeneous nonperfused biological tissue: application to laser thermokeratoplasty. J Biomed Opt 8(2):288–297 Moosaie A (2007) Non-Fourier heat conduction in a finite medium subjected to arbitrary periodic surface disturbance. Int Commun Heat Mass Transf 34(8):996–1002 Moosaie A (2008a) Non-Fourier heat conduction in a finite medium subjected to arbitrary non-periodic surface disturbance. Int Commun Heat Mass Transf 35(3):376–383 Moosaie A (2008b) Non-Fourier heat conduction in a finite medium with insulated boundaries and arbitrary initial conditions. Int Commun Heat Mass Transf 35(1):103–111 O’Neil P (2011) Advanced engineering mathematics. Cengage Learning, Boston Rasteaar S (1989, August) Hyperbolic heat conduction in pulsed laser irradiation of tissue. In: OE/LASE’89, 15–20 Jan 1989. International Society for Optics and Photonics, Los Angeles, pp 114–117 Tang DW, Araki N (1996a) Non-Fourier heat conduction in a finite medium under periodic surface thermal disturbance. Int J Heat Mass Transf 39(8):1585–1590 Tang DW, Araki N (1996b) Non-Fourier heat conduction in a finite medium under periodic surface thermal disturbance—II. Another form of solution. Int J Heat Mass Transf 39(15):3305–3308 Tang DW, Araki N (1996c) Analytical solution of non-Fourier temperature response in a finite medium under laser-pulse heating. Heat Mass Transf 31(5):359–363 Tang DW, Araki N (2000) Non-fourier heat condution behavior in finite mediums under pulse surface heating. Mater Sci Eng A 292(2):173–178 Tang DS, Hua YC, Nie BD, Cao BY (2016a) Phonon wave propagation in ballistic-diffusive regime. J Appl Phys 119(12):124301 Tang DS, Hua YC, Cao BY (2016b) Thermal wave propagation through nanofilms in ballistic-diffusive regime by Monte Carlo simulations. Int J Therm Sci 109:81–89 Trujillo M, Rivera MJ, López Molina JA, Berjano EJ (2009) Analytical thermal–optic model for laser heating of biological tissue using the hyperbolic heat transfer equation. Math Med Biol 26(3):187–200 Vernotte P (1958) Les paradoxes de la théorie continue de léquation de la chaleur. C R Hebd Seances Acad Sci 246(22):3154–3155 Zhang MK, Cao BY, Guo YC (2014) Numerical studies on damping of thermal waves. Int J Therm Sci 84:9–20 Zhou J, Chen JK, Zhang Y (2007) Theoretical analysis of thermal damage in biological tissues caused by laser irradiation. Mol Cell Biomech 4(1):27 Zubair SM, Chaudhry MA (1996) Heat conduction in a semi-infinite solid due to time-dependent laser source. Int J Heat Mass Transf 39(14):3067–3074