## Materials and Methods
### Experimental Design  
A series of experiments were designed to investigate the respective effects of wall height, heat input, and heat dissipation on the bead geometry, as given in Table 1. These experiments were divided into three groups according to their heat dissipation conditions. Each experiment was repeated three times.  
In Group I, the depositions were performed on a flat substrate with dimensions 150 mm (length) \(\times\) 150 mm (width) \(\times\) 6 mm (height) (just like Figure 1a). This could reflect the heat dissipation condition of lower layers. In Group II, the depositions were performed on an existing wall with dimensions 150 mm (length) \(\times\) 12 mm (width) \(\times\) 150 mm (height) (just like Figure 1b). The two side surfaces of the wall were exposed to the ambient air to reflect the heat dissipation condition of upper layers. In Group III, the depositions were also performed on an existing wall but the two side surfaces of the wall were attached to the thermoelectric coolers (just like Figure 1c). Groups III-1 and III-2 employed different cooling powers (nominal value) by adjusting the input voltage of the coolers. Within each group, three deposition experiments were conducted with different process parameters. Four main process parameters that affect the heat input, i.e., wire feed rate (_WFR_), travel speed (_TS_), arc voltage (_U_), and arc current (_I_), were considered. The selection of _WFR_ covers a wide range. For lower  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Run No.**} & \multirow{2}{*}{**Group No.**} & \multirow{2}{*}{**Heat Dissipation Conditions**} & \multicolumn{6}{c}{**Process Parameters**} \\ \cline{3-8}  & & & **WFR (m/min)** & _TS (m/min)_ & _U (V)_ & _I (A)_ & **Cooling Power** \\ \hline
1 & & & & 3 & 0.3 & 130 & 17.9 & - \\
2 & 1 & Flat substrate + conduction & 4 & 0.4 & 176 & 18.6 & - \\
3 & & & & 5 & 0.5 & 222 & 19.5 & - \\ \hline
4 & & & & 3 & 0.3 & 130 & 17.9 & - \\
5 & II & Wall + convection \& radiation & 4 & 0.4 & 176 & 18.6 & - \\
6 & & & & 5 & 0.5 & 222 & 19.5 & - \\ \hline
7 & & & & 3 & 0.3 & 130 & 17.9 & 240 W \\
8 & III-1 & & & 4 & 0.4 & 176 & 18.6 & 240 W \\
9 & & & & 5 & 0.5 & 222 & 19.5 & 240 W \\ \hline
10 & & & & 3 & 0.3 & 130 & 17.9 & 360 W \\
11 & III-2 & & & 4 & 0.4 & 176 & 18.6 & 360 W \\
12 & & & & 5 & 0.5 & 222 & 19.5 & 360 W \\ \hline \hline \end{tabular}
\end{table}
Table 1: Heat dissipation conditions and parameter sets in the experiments.  
_WFR_, the welding arc is not quite stable and incomplete melting occurs, while for higher _WFR_, pool overflowing occurs due to excessive heat input as well as the large arc force and strong droplet impingement. Note that the ratio of _WFR_ to _TS_ is fixed at 10 herein in order to maintain the same area of the bead cross section (i.e., the metal deposition rate per unit length) which is in direct proportion to _WFR_/_TS_[23]. It is difficult to compare different bead geometries if their cross-sectional areas are not the same. \(U\) and \(I\) were obtained from the power supplies once _WFR_ and _TS_ were determined.  
From these experiments, we can analyze (1) the effect of heat input on the bead geometry by comparing the three experiments within each group; (2) the effect of wall height on the bead geometry by comparing Groups I and II; and (3) the effect of heat dissipation on the bead geometry by comparing Groups II and III.