**Abstract**

Temperature distribution in hematite ore mixed with 7.5% coal was predicted by solving a 1-D heat conduction equation using an implicit finite difference approach. In this work, a square slab of 20 cm x 20 cm was considered, which assumed the coal to be uniformly mixed with hematite ore. MATLAB 2018a software was used to solve the equations. Heat transfer effects in this one dimensional slab having convective and radiative boundary conditions are also considered in this study. Temperature distribution is obtained inside the hematite slab by considering microwave heating time, thermal conductivity, heat capacity, carbon percentage, sample dimensions, and many other factors, such as penetration depth, permittivity, and permeability of coal and hematite ore mixtures. The resulting temperature profile used as a guiding tool for optimizing the microwave-assisted carbothermal reduction process of hematite slab which was extended to other dimensions as well, viz., 1 cm x 1 cm, 5 cm x 5 cm, 10 cm x 10 cm, and 20 cm x 20 cm. The model predictions are in good agreement with experimental results.

**Keywords:** Hematite ore, coal, microwave processing, heat transfer, implicit method, temperature distribution
