Heat transfer analysis of a semi-infinite solid heated by a laser beam Bekir S. Yilbas, M. Sami Abstract Laser heating of semi-infinite solid substance is introduced and analytical solution appropriate to the laser machining power intensities is obtained. Both conduction limited and non-conduction limited cases are considered. The limiting cases in non-conduction limited equation are investigated and the equation governing the conduction limited heating is deduced. In the case of non-conduction limited heating process, the location of maximum tem- perature and its functional relation with the substance and laser properties are developed. Steady state analysis of the heating process is taken into account and limiting laser power intensity is concluded. In addition, the applicability of Fourier heat conduction equation in laser heating is discussed. Untersuchung des Wa ¨ rmeu ¨ bertragungs- vorgangs beim Aufheizen eines halbunendlichen Festko ¨ rpers durch einen Laserstrahl Zusammenfassung Als physikalisches Modell wird ein durch einen Laserstrahl aufgeheizter halbunendlicher Korper vorgegeben, und eine der Laserschnittleistung an- gepaßte analytische Losung entwickelt. Sowohl der lei- tungs-, wie der nicht-leitungslimitierte Fall finden Berucksichtigung. Fur den ersten Fall wird die Gleichung abgeleitet; beim zweiten Fall werden dessen Grenzfalle naher untersucht, wobei sich der Ort maximaler Temper- atur und dessen funktionelle Beziehung zu den Ei- genschaften des Festkorpers und des Lasers bestimmen lassen. Auch der Stationarfall des Heizprozesses wird un- tersucht, woraus sich auf die limitierende Laserleistung schließen la ¨ßt. Abschließend wird die Anwendbarkeit der Fourierschen Warmeleitungstheorie bei Aufheizprozessen mittels Laser diskutiert. List of Symbols C p Specific heat capacity (J/kgK) I Power intensity (W m 2 ) k Thermal conductivity (W mK) k B Boltzmann’s constant L Enthalpy of evaporation (kJ/kg) m Atomic weight (kg) t Time (s) Z Equilibrium time (s) T Temperature (K) T s Surface temperature (K) T max Maximum temperature (K) T c Critical temperature (K) T sup Superheat temperature (K) V Instantaneous velocity (m/s) x Distance from the surface (m) X max Depth at which temperature is maximum (m)  Thermal diffusivity (m 2 s)  Absorption depth (1/m)  Density (kg m 3 ) 1 Introduction Laser machining, including drilling, cutting, welding and surface heating, is widely spread in industry due to its low cost and precision operation. In order to improve the machining process, the physical process involved in laser- workpiece interaction should be investigated in detail. In this regard, there have been a number of analytical solu- tions presented in the literature for both conduction and non-conduction limited processes [1, 2, 3, 4]. The term conduction limited process applies when the machining involves solid phase heating only while non-conduction limited process applies when phase change phenomenon occurs. In general, laser spot welding is a conduction limited process whilst continuous welding can be con- sidered as being at the border between the two processes since it involves the production and propagation of a deep cavity through the molten material. As the temperature of the irradiated surface starts to rise, particle emission begins to take place. This can in- volve the following: (i) thermionic emission of electrons and ions, i.e. of charged particles, (ii) emission of vapor- ized material and (iii) formation of plasma. However, it has been demonstrated that the thermionic emission was negligible at temperatures around 3500 K and the plasma formation was possible at high intensity laser pulses, in this case, the power intensities ( 10 12 Wm 2 ) are re- quired. However, for machining power intensities Heat and Mass Transfer 32 (1997) 245–253  Springer-Verlag 1997 245 Received on 13 May 1996 Bekir S. Yilbas, M. Sami Department of Mechanical Engineering King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia The authors acknowledge the support of King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for this work. Correspondence to: B. S. Yilbas