Convection of energy in partially ionised vapour in laser keyhole welding

Laser power is absorbed in laser keyhole welding by several mechanisms. In CW CO₂ welding absorption into the partially ionised vapour in the keyhole by the processes of inverse bremsstrahlung and thermal conduction can be important. The energy is then transferred to the work piece by thermal conduction through the vapour. This process has recently been partially modelled mathematically. Experimental observations give a wide range of values for the possible vapour temperatures and as a result, widely varying estimates for the power absorbed can be obtained. The recent theoretical models have tended to give too high a value when compared to expectations. Most models ignore convection in the vapour, but a recent example [1] presents a theoretical form that allows for the effect in a simple manner. However, it does not attempt to find any solutions and goes no further than showing by order of magnitude arguments, that the convection effect is likely to matter. It probably has the consequence that temperature estimates obtained theoretically which ignore convection, almost certainly give values that are a good deal too high. In this paper, the model derived there is solved and the consequences studied, confirming this expectation.