## 5 Conclusions  
As part of the heat generated by an electric arc is used to melt the electrode material, which in the form of droplets falls into the weld pool, it is necessary to take into consideration the heat of the molten metal in the temperature field descriptions in arc weld surfacing processes. In this work, the analytical solution of the temperature field of multi-pass arc weld surfacing for a semi-infinite model of body  
Figure 19: Maximum temperatures (°C) in the middle part area of cross-section during surfacing with alternate sequence of the weld padding.  
Figure 20: Heat-affected zone after surfacing with alternate sequence of the weld padding.  
Figure 18: The scheme of GMAW surfaced area on the top surface of the plate with alternate sequence of the weld padding.  
is presented. The solution is obtained by adding together the temperature increments caused by the application of liquid metal and thermal radiation from the electrode as well as from the areas already heated up. The analytical model also considered a weld overlap and auxiliary time connected with the idle movement of electrode (welding head) or other activity resulting from the needs of technological processing (e.g., correction or change of technological parameters).  
For the applied metal, the heat source of parabolic shape in the cross-section of a weld is assumed. For the electric arc, the source with Gaussian surface distribution of power density is assumed. The dimensions of the weld and technological parameters of the process were adopted from the experience of other authors. The amount of heat transmitted by the applied padding weld was determined on the basis of the heat cumulated in the electrode melted material. Calculations of the temperature field during multi-pass arc weld surfacing are conducted on a steel plate.  
Analysis of the temperature fields in the control cross-section showed a slight increase in the depth of the heat-affected zone when performing successive beads. This is due to the relatively short times between successive passages of the heat source in a sectional view. Also noticeable is the influence of heat of applied padding welds on those previously imposed causing an increase in temperature in the areas of reinforcements (reinforcements). This effect can be reduced by (often used in practice) alternate padding welds application, increasing the time between the passages of the weld heat source over particular areas of the surfaced element.  
The presented model has a significant meaning especially in temperature field computations during the application of high (a few millimeters) and wide (a dozen or so millimeters) welds, because the expected dimensions of the welds are also the geometrical parameters of the volumetric model of the weld heat source.  
The adoption of a bimodal heat source allowed the reconstruction of the irregular shape of the fusion line, often found in welding practice and impossible to obtain using a single-distributed heat source. In the description of the temperature field, the heat of the molten electrode has been taken into account. This approach brings the model closer to the real phenomena occurring in the welding process. The description of the temperature field is obtained by the analytical solution for multi-pass weld surfacing, unprecedented in the literature with the use of something other than a point heat source. The adopted algorithm allows one to analyze the influence of the surfacing sequence on the shape and dimensions of the heat-affected zone.  
The advantage of an analytical model of the temperature field is the possibility of quick analysis of welding thermal cycle at any point of the surfaced object without determining temperatures in the whole object, as well as the possibility to easily track temperature changes for selected cross-sections of an object in the selected time of the process.