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Non-Fourier temperature field in a solid homogeneous finite hollow cylinder. (English) Zbl 1271.80001

Summary: Analytical solution of the non-Fourier axisymmetric temperature field within a finite hollow cylinder is investigated considering the Cattaneo-Vernotte constitutive heat flux relation. The solution is found for the most general linear time-independent boundary conditions. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method of separation of variables is used. The present solution can be reduced to special problems of interest by choosing appropriate boundary condition parameters. The solution is applied for two special cases including constant heat flux and the Gaussian distribution heating of a cylinder, and their respective non-Fourier thermal behavior is studied.

MSC:

80A20 Heat and mass transfer, heat flow (MSC2010)
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[1] Cattaneo C.: A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Compute. Rendus 247, 431–433 (1958) · Zbl 1339.35135
[2] Vernotte P.: Les paradoxes de la théorie continue de I’equation de la chaleur. Compute. Rendus 246, 3154–3155 (1958) · Zbl 1341.35086
[3] Gembarovic J., Majernik V.: Non-Fourier propagation of heat pulses in finite medium. Int J Heat Mass Transf. 31, 1073–1080 (1988) · Zbl 0664.73013 · doi:10.1016/0017-9310(88)90095-6
[4] Tang D.W., Araki N.: Non-Fourier heat conduction in a finite medium under periodic surface thermal disturbance. Int. J. Heat Mass Transf. 39, 1585–1590 (1996) · Zbl 0964.74501 · doi:10.1016/0017-9310(95)00261-8
[5] Tang D.W., Araki N.: Non-Fourier heat conduction in a finite medium under periodic surface thermal disturbance-II. Another form of solution. Int. J. Heat Mass Transf. 39, 3305–3308 (1996) · doi:10.1016/0017-9310(95)00411-4
[6] Tang D.W., Araki N.: Analytical solution of non-Fourier temperature response in a finite medium under laser-pulse heating. Heat Mass Transf. 31, 359–363 (1996) · doi:10.1007/BF02184051
[7] Tang D.W., Araki N.: Non-Fourier heat conduction behavior in finite mediums under pulse surface heating. Mater. Sci. Eng. A. 292, 173–178 (2000) · doi:10.1016/S0921-5093(00)01000-5
[8] Lewandowska M., Malinowski L.: Hyperbolic heat conduction in the semi-infinite body with the heat source which capacity linearly depends on temperature. Heat Mass Transf. 33, 389–393 (1998) · doi:10.1007/s002310050206
[9] Lewandowska M., Malinowski L.: 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, 61–69 (2006) · doi:10.1016/j.icheatmasstransfer.2005.08.004
[10] Abdel-Hamid B.: Modeling non-Fourier heat conduction with periodic thermal oscillation using the finite integral transform. Appl. Math. Model. 23, 899–914 (1999) · Zbl 0934.35083 · doi:10.1016/S0307-904X(99)00017-7
[11] Moosaie A.: Non-Fourier heat conduction in a finite medium subjected to arbitrary periodic surface disturbance. Int. Commun. Heat mass Transf. 34, 996–1002 (2007) · doi:10.1016/j.icheatmasstransfer.2007.05.002
[12] Moosaie A.: Non-Fourier heat conduction in a finite medium subjected to arbitrary non-periodic surface disturbance. Int. Commun. Heat mass Transf. 35, 376–383 (2008) · doi:10.1016/j.icheatmasstransfer.2007.08.007
[13] Babaei M.H., chen Z.T.: Hyperbolic heat conduction problem in a functionally graded hollow sphere. Int J Thermophys. 29, 1457–1469 (2008) · doi:10.1007/s10765-008-0502-1
[14] Zhang, Z; Liu, D.: Hyperbolic heat propagation in a spherical solid medium under extremely high heating rates. In: Armaly, B.F. et al. (eds.) AIAA/ASME joint thermophysics and heat transfer conference, New York, vol. 3, pp. 275–283 (1998)
[15] Jiang F.: Solution and analysis of hyperbolic heat propagation in hollow spherical objects. Heat Mass Transf. 42, 1083–1091 (2006) · doi:10.1007/s00231-005-0066-6
[16] Moosaie A.: Axisymetric non-Fourier temperature field in a hollow sphere. Arch. Appl. Mech. 79, 679–694 (2009) · Zbl 1264.80014 · doi:10.1007/s00419-008-0245-2
[17] Liu K.C., Chang P.C.: Analysis of dual-phase lag heat conduction in cylindrical system with a hybrid method. Appl. Math. Model. 31, 369–380 (2007) · Zbl 1158.80004 · doi:10.1016/j.apm.2005.11.006
[18] Barletta A., Pulvirenti B.: Hyperbolic thermal waves in a solid cylinder with a non-stationary boundary heat flux. Int. J. Heat Mass Transf. 41, 107–116 (1998) · Zbl 0932.74018 · doi:10.1016/S0017-9310(97)00098-7
[19] Barletta A., Zanchini E.: Thermal-wave heat conduction in a solid cylinder which undergoes a change of boundary temperature. Heat Mass Transf. 32, 285–291 (1997) · doi:10.1007/s002310050123
[20] Barletta A., Zanchini E.: Hyperbolic heat conduction and thermal resonance in a cylindrical solid carrying a steady-periodic electric field. Int. J. Heat Mass Transf. 39, 1307–1315 (1996) · doi:10.1016/0017-9310(95)00202-2
[21] Sadd N.H., Cha C.Y.: Axisimetric non-Fourier temperatures in cylindrically bounded domains. Int. J. Non-Linear Mech. 17, 129–136 (1982) · Zbl 0491.73130 · doi:10.1016/0020-7462(82)90012-9
[22] Trostel R.: Instationäre Wärmespannungen in Hohlzylindern mit Kreisringquerschnitt. Ingenieur-Archiv 24, 1–26 (1956) · Zbl 0074.19805 · doi:10.1007/BF00536952
[23] Leung M.: Phase-Change Heat transfer in laser transformation hardening by moving Gaussian rectangular heat source. J Phys. D: Appl. Phys. 34, 3434–3441 (2001) · doi:10.1088/0022-3727/34/24/303
[24] Bennacer R., Mohamad A.A., Leonardi E.: The effect of heat flux distribution on thermocapillary convection in a side-heated liquid bridge. Numerical Heat Transfer, Part A 41, 657–671 (2002) · doi:10.1080/104077802317418278
[25] Rivas D., Vasquez-Espi C.: An analysis of Lamp Irradiation in Ellipsoidal Mirror Furnaces. J. Crystal Growth 223, 433–445 (2001) · doi:10.1016/S0022-0248(01)00676-5
[26] Ozisik M.N.: Boundary value problems of heat conduction. Dover Publication Inc, New York (1989)
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