# Electro-Thermal Properties of Carbon-Fiber-Reinforced Mortar Prisms
## 4 Experimental Results
For estimation, the average temperature of the surface area defined by the rectangle with 320 pixels in horizontal and 222 pixels in vertical direction are found. These pixels correspond to 57.66 mm \(\times\) 40 mm of the surface area. This rectangle is specified by the four corner pixels having the positions of (156, 122), (476, 122), (156, 344) and (476, 344), as shown in Figure 4. It is expected that the 57.66 mm dimension covers most of the prism lengths because the prism pieces are not of the same size, and their broken faces have very bumpy profiles. Along with the averaged surface temperature, observed are the temperature distributions of the horizontal line that bisects the prism piece into two horizontal parts and another horizontal line at 3 mm distance from the bottom edge of the piece. The former represents the lowest temperature and the latter represents the highest temperature zone of the heated prism. The bisecting horizontal line will pass the pixels (156, 233) and (156, 327), and the other line will pass the pixels at (156, 233) and (156, 327) in Figure 4. These temperature distributions are used to show the heat diffusion pattern of the prism. The relative positions of the lines and sizes of the rectangles in other percentage prisms are also the same. Apart from these lines and rectangle, the average temperatures of the broken rectangle in the middle part of the piece, which corresponds to the surface areas of the minimum volume, and the vertical bisect line of this rectangle are also found to identify the heat deposition pattern with time. In fact, the vertical bisect line represents the line connecting the centers of two electrodes, where the wires from the power supply are in contact. This line will be one of the normal lines to two electrodes. In Figure 5, the thermal images of the electrical heating for the 0.5%, 1.0%, 1.5% and 2.0% prism pieces are shown. These images show the temperature distribution pattern for the heating time specified at each image. However, it is expected that this distribution pattern may not be the same as those of different cross-sections of the volume underneath the surface because of inhomogeneity of the prisms. The temperature range of each thermal image is normalized from 22.8\({}^{\circ}\) to 80\({}^{\circ}\) to compare the temperature variations of different percentage prisms with heating time. The color bar on the right side of the images informs about the temperature corresponding to each color. The numbers in the bar represent the temperature of each color. The dotted rectangle in each image represents the surface area corresponding to the minimum volume. When a voltage is applied through the electrodes, a current loop is formed by the wires connected to the \"+\" terminal of the power supply, electrode, fibers in the minimum volume, opposite side electrode and wires connected to the \"\(-\)\"/ground terminal of the power supply. In this loop, the overall resistance is the sum of the resistances from the contacting parts of (1) the wires and the electrodes, (2) the electrodes and fibers in the volume, and (3) the fibers themselves. Among these three, the highest resistance will be that from the contacting part of the electrodes and fibers. Due to this resistance, the heat contribution from the fiber heating will not be significant. The temperature distribution pattern indicates that the heat is mostly generated at the surface of the piece, where the wires, the electrodes and the fibers near the electrodes meet. The applied electric power is mostly deposited at the interfaces between the electrodes and the fibers. That is why the heat distribution pattern has the shape of a half circle. The heat from the interfaces is diffused radially to the inside of the prisms. However, since the interfaces are not completely parallel to the electrode's long sides and they are different for different electrodes, the two circles do not have the same radius and they are somewhat distorted.