针对有较长热驰豫时间的材料在表面受到激光脉冲照射时的非Fourier热传导问题,利用Laplace、Hankel变换及其逆变换,给出了一个半解析解.数值仿真表明,该半解析解能够清晰显示非Fourier热传导问题中的热波现象.
The non-Fourier model of heat transfer as a laser pulse irritating on surface of material with large thermal relaxation time is considered.A new semi-analytic solution is derived by using Laplace,Hankel and their inverse transforms.By numerically simulating the solution,the wave form behavior of temperature can be seen clearly.
[1] KUANG Z,LI J,EDW AR DSON S,et al.Ultrafast laser beam shaping for material processing at imaging plane by geometric masks using a spatial light modulator[J].Opt Laser Eng,2015,70: 1-5.DOI:10.1016/j.optlaseng.2015.02.004.
[2] FARAYIBI P K,ABIOYE T E,MVRRAY J W,et al.Surface improvement of laser clad Ti–6Al–4V using plain waterjet and pulsed electron beam irradiation[J].Journal of Materials Processing Technology,2015,218: 1-11.DOI:10.1016/j.jmatprotec.2014.11.035.
[3] SHEN Y,YUE W,XIE A,et al.Influence of HSA on the properties of OA/OAM monolayers and the growth of calcium oxalate[J].Colloids & Surfaces A Physicochemical & Engineering Aspects,2004,234(1-3):35-41.DOI:10.1016/j.colsurfa.2003.12.004.
[4] CATTANEO C.A form of heat conduction equation which eliminates the paradox of instantaneous propagation[J].Compte Rendus,1958,247: 431-433.
[5] VERNOTTE P.Les paradoxes de la theorie continue de l'equation de la chaleur[J].Compte Rendus,1958,246: 3154-3155.
[6] ZHANG M K,CAO B Y,CUO Y C.Numerical studies on dispersion of thermal waves[J].International Journal of Heat and Mass Transfer,2013,67: 1072-1082.DOI:10.1016/j.ijheatmasstransfer.2013.08.102.
[7] STR HER G R,STRÖHER G L.Numerical thermal analysis of skin tissue using parabolic and hyperbolic approaches[J].International Communications in Heat and Mass Transfer,2014,57: 193-199.DOI:10.1016/j.icheatmasstransfer.2014.07.026.
[8] ZHANG M K,CAO B Y,CUO Y C.Numerical studies on damping of thermal waves[J].International Journal of Thermal Sciences,2014,84: 9-20.DOI:10.1016/j.ijthermalsci.2014.04.014.
[9] TZOU D Y,GUO Z Y.Nonlocal behavior in thermal lagging[J].International Journal of Thermal Sciences,2010,49(7): 1133-1137.DOI:10.1016/j.ijthermalsci.2010.01.022.
[10] LAM T T.A unified solution of several heat conduction models[J].International Journal of Heat and Mass Transfer,2013,56(1-2): 653-666.DOI:10.1016/j.ijheatmasstransfer.2012.08.055.
[11] YILBAS B S,KALYON M.Analytical solution for pulsed laser heating process: convective boundary condition case[J].International Journal of Heat and Mass Transfer,2002,45(7): 1571-1582.DOI:10.1016/S0017-9310(01)00239-3.
[12] JING L,XU C,XU L X.New thermal wave aspects on burn evaluation of skin subjected to instantaneous heating[J].IEEE Transactions on Biomedical Engineering,1999,46(4): 420-428.
