# The Law and Mechanism of the Effect of Surface Roughness on Microwave-Assisted Rock Breaking
## 4 Analysis and Discussion
Heat flux in the \(x\)-direction of [PERSON]'s law in heat conduction, \(q_{x}\), can be calculated as follows:  
\[q_{x}=\kappa\cdot A\cdot\frac{\mathrm{d}T}{\mathrm{d}x} \tag{2}\]  
where \(\kappa\) is the thermal conductivity coefficient, W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\); \(A\) is the heat transfer area, m\({}^{2}\), for temperature K; and \(x\) is the coordinates on the thermal conduction surface, m. As shown in Figure 17, during the microwave-irradiation process, the heat conduction of the flat surface specimen was not limited to just the \(x\) and \(z\) directions, and the conduction range was hemispherical. Heat conduction at the contour convex position of the rough surface specimen was limited to the \(x\)-direction, which led to a reduction in the local heat transfer area, a decrease in the heat flux, and an observed heat accumulation effect. This caused the local temperature to be too high, and the large thermal stress destroyed the rock, thereby increasing the microwave-irradiation effect. The shear stress distribution contour of the cross-section of the sample in the irradiation center area is shown in Figure 18. The maximum shear stress point of the 1.5 roughness sample appeared at the highest point of the contour convex position in the irradiation center area, whereas that of the sample with a flat surface appeared in the center of the surface: The temperature of the maximum stress point was 100 \({}^{\circ}\)C; the maximum shear stress of the flat surface sample was 22.23 MPa; and the roughness of the 1.5 sample was 37.43 MPa. Therefore, rough surface specimen contour fluctuations are prone to stress concentrations; if the stress is large and coupled with the propagation of existing cracks, the specimen is more likely to be damaged, thereby increasing the effect of microwave irradiation rock breakage. Analysis of the physical and numerical test results showed that the electric field strength, average temperature, and plastic zone volume of the rock surface had basically the same trend with roughness, which first increased and then decreased with the increase in roughness. A threshold between roughness values of approximately 1.4 and 1.6 was demonstrated to maximize the surface temperature, electric field strength, and plastic zone volume of the sample. Combined with the test conclusion and the influencing mechanism, there are three main reasons for the occurrence of this threshold. First, when the degree of roughness is larger, the undulating profile is larger, and the maximum difference is larger, which leads to an increase in the distance from the microwave irradiation to some positions  
Figure 17: Heat conduction direction of different samples during microwave irradiation (Arrows are the main direction of heat transfer, and different colored lines represent different temperature gradients). (**a**) Flat surface. (**b**) Non-flat surface. of the sample, and the microwave intensity decreases with the increase in irradiation distance. Therefore, when the weakening irradiation effect caused by the increase in distance increases, the influence of the rough surface on the microwave-irradiation effect is weakened. Moreover, the larger the roughness value, the larger the surface area of the sample, and thus, the area of heat conduction on the surface of the whole sample will increase, resulting in weakening of the microwave-heating effect of the entire surface. Third, with the increase in roughness, undulations of the rock surface contour will be greater, more stress concentrations are likely to occur, and the volume of the plastic zone after microwave irradiation will also be larger. However, when the roughness reaches a value of 1.5, the rock surface contour is even more undulating, and there are more convex fragments; the rock surface is thus \"divided\" into multiple parts by these larger contour protrusions, resulting in a reduction in the main temperature distribution area and a decrease in the plastic zone expansion area.