is laser beam heat flux. Unlike CW (Continuous Wave) laser welding which involves one moving thermal cycle, pulsed laser involves repetitively impinging on the same spot, thus creating multiple overlapping thermal cycles. A method of addressing this is to add a step function that multiplies the heat flux by one when the beam is on but multiplies the heat flux by zero when the beam is off. One way to achieve this is by using a Kronecker delta which modifies q as follows: , where δ= the Kronecker delta, qe=experimentally determined heat flux. The problem with this method, is it does not allow you to see the effect of pulse duration. One way of solving this is to a use a modifier that is time-dependent function such as: where v= pulse frequency, n=0,1, 2,...,v-1), τ= pulse duration. Next, you would apply this boundary condition and solve for Fourier's 2nd Law to obtain the internal temperature distribution. Assuming no internal heat generation, the solution is , where k=thermal conductivity, ρ=density, Cp=specific heat capacity, =fluid velocity vector. Step 5 Incrementing is done by discretizing the governing equations presented in the previous steps and applying the next time and length steps. Step 6 Results can be validated by specific experimental observations or trends from generic experiments. These experiments have involved metallographic verification of the depth of fusion. Consequences of simplifying assumptions The physics of pulsed laser can be very complex and therefore, some simplifying assumptions need to be made to either speed up calculation or compensate for a lack of materials properties. The temperature-dependence of material properties such as specific heat are ignored to minimize computing time. The liquid temperature can be overestimated if the amount of heat loss due to mass loss from vapor leaving the liquid-metal interface is not accounted for. References Bibliography Cary, Howard B. and Scott C. Helzer (2005). Modern Welding Technology. Upper Saddle River, New Jersey: Pearson Education. . Weman, Klas (2003). Welding processes handbook. New York: CRC Press LLC. . Kalpakjian, Serope and Schmid,Steven R.(2006). Manufacturing Engineering and Technology5th ed. Upper Saddle River, New Jersey: Pearson Education. External links Dual beam laser welding; research article from the 2002 Welding Journal Weld morphology and thermal modeling in dual-beam laser welding; research article from the 2002 Welding Journal Laser welding articles from the Industrial Laser Solutions Magazine Robotic laser welding Welding Welding Welding Articles containing video clips