**3. Results and discussion**

The heating profile characteristic of hematite ore mixed with coal was modeled using simulation parameters of **Table 3**. Variations of thermal conductivity, heat capacity and thermal diffusivity as a function of temperature are shown in **Figure 3**.

#### **3.1 Temperature estimation**

When solving the 1D heat equation, convection and radiation conditions were also considered. It is observed that there is an increase in temperature till 100 s, and beyond this time, the increase in temperature is negligible. The temperature of the slab at the center (x = 0 m) is considered to be 30°C. After heating for 100 s, it gave an indication that the thermal runaway may occur during the microwave heating.

#### *Numerical Simulation – Advanced Techniques for Science and Engineering*


*\*Value calculated based on the data reported in Refs. [19, 22]*

*\*\*Value calculated based on the data reported in Ref. [16].*

*\*\*\*\*Value calculated based on the data reported in Ref. [19, 22].*

*\*\*\*Value calculated based on the data reported in Ref. [16].*

*\*\*\*\*\*Value calculated based on the data reported in Ref. [19, 22–24].*

#### **Table 3.**

*Thermophysical properties and modeling parameters were used in the simulation, and k, ρ, Cp, and Dp calculation processes are shown in Appendices.*

*Simulation Study of Microwave Heating of Hematite and Coal Mixture DOI: http://dx.doi.org/10.5772/intechopen.106312*

**Figure 4.**

*Temperature distribution in a 20 cm 20 cm slab for different heating periods, viz., 1 s, 30 s, 60 s, 100 s, 200 s, 300 s, and 400 s, respectively, at a constant power.*

Temperature profiles for different heating time periods 1s, 30 s, 60 s, 100 s, 200 s, 300 s, and 400 s (at 915 MHz and 1 MW) are shown in **Figure 4**. The highest temperatures inside the object are around 33°C, 220°C, 415°C, 719°C, 912°C, 1016°C, and 1042°C for 1 s, 10 s, 30 s, 60 s, 100 s, 200 s, 300 s, and 400 s respectively. Within the first 100 s of heating, the temperature in the 1D slab increases rapidly from 25 to 912°C. The reason for this rapid increase is due to the increase in thermal energy supplied by microwave radiation [8]. From 100 s to 400 s, the temperature increases from 912 to 1042°C. This increase is slower as compared to heating from 0 s to 100 s. It is mainly attributed to the initial heating (0–100 s). The thermal contribution from microwave heat generation dominates the temperature rise in the sample due to the weak thermal radiation effect and the relatively low temperature of the object. As the heating continues, the temperature of the object increases, which leads to a high radiation effect. At higher temperatures, thermal conductivity reduces, and heat capacity increases. The heat diffusivity is found in **Figure 3c** to be in the order of 4 x 10–<sup>6</sup> m<sup>2</sup> /s and decreases with increasing temperature. Heat capacity is found in **Figure 3b** to be 200 J/kg/K and increases with increasing temperature.

#### **3.2 Temperature distribution across length for different powers of microwave**

The 1D heat equation was solved by considering different values of power flux. Convection and radiation conditions were also considered. It was observed that there was an increase in temperature till a power flux of 2.5 MW/m<sup>2</sup> , and beyond this power flux, the increase in temperature was negligible. Temperature profiles are plotted for a 1D slab with dimensions 0.20 m x 0.20 m. In this slab, different microwave powers (P0) of 0.5, 1.5, 2.5, and 3.5 MW/m<sup>2</sup> were considered as shown in **Figure 5**. The temperature of the object increases with increasing microwave power. The highest temperatures attained in microwave heating for 60 s using different microwave powers of 0.5 MW/m<sup>2</sup> , 1.5 MW/m<sup>2</sup> , 2.5 MW/m<sup>2</sup> , and 3.5 MW/m<sup>2</sup> are 370°C, 723.6°C, 1062°C, and 1112°C, respectively. Similarly, for times of 1 s, 120 s, and 180 s, temperatures attained are shown in **Table 4**. It is clear that if the source power increases, the microwave heating rate increases rapidly within 60 s. However, after 60 s, the temperature does not increase rapidly, even for higher microwave powers because of radiation and convection losses at high temperatures. It demonstrates that an appropriate power applied in microwave heating is influential in obtaining a high heating

#### **Figure 5.**

*Temperature distribution in a 20 cm 20 cm slab by varying power flux, viz., 0.5 MW/m<sup>2</sup> , 1.5 MW/m2 , 2.5 MW/m2 , and 3.5 MW/m2 , respectively, at a constant time of 50 s.*


**Table 4.**

*Temperature distribution at various times and various power flux.*

rate in a short time. On account of more radiation and convection heat losses to the environment at high temperatures, the peak migrates inward to keep heat balance between the object and surroundings.
