The study of interaction between microwave radiation and minerals is gaining increasing interest in the field of minerals and material processing. Further studies are, however, still required to deepen the understanding of such microwave heating mechanisms in order to develop innovative techniques for mineral treatment using microwave heating. In this paper, effects of sample shapes and thickness on the distribution of temperature inside the mineral ilmenite (FeTiO₃) due to microwave heating were numerically studied using the finite element (FE) method. The analysis was carried out in such a way that the flux of microwave energy was converted into an equivalent amount of heat generation in the mineral through the Poynting theorem of conservation of energy for the electromagnetic field. In this study, as a first attempt, the cylinder and slab of ilmenite were modeled to be irradiated from top and bottom surfaces with the variation of cylinder and slab thicknesses. Temperature-dependent material properties of ilmenite were taken into account in the FE simulation. Corresponding boundary conditions were then applied accordingly to the cylinder and slab of ilmenite with comparable characteristic length. Numerical results showed that, in terms of temperature differences between locations having maximum and minimum temperatures, slab geometries tended to produce higher values in comparison to those of cylinder geometries with the thickness variation, while the profiles of temperature inside the ilmenite samples were similar for both geometries. For the same duration of microwave heating, the slab geometry, hence, induced greater non-uniformity of temperature inside the ilmenite. It was also observed that, for the ilmenite samples with thickness value greater than 1.5 cm, the hotspot locations were not in the center of the sample, but on the surface of sample. Moreover, from several thickness values considered in this study, the ilmenite sample with thickness value of 3 cm gave a good trade-off between the maximum temperature value attained and temperature differences inside the sample, for both geometries. Thus, the shape and thickness of ilmenite samples affect the effectiveness of microwave heating of ilmenite, in terms of maximum temperature attained, temperature differences, and uniformity of temperature.

Purpose: – The purpose of this paper is to present a new approach of meshless local B-spline based finite difference (FD) method for solving two dimensional transient heat conduction problems. Design/methodology/approach: – In the present method, any governing equations are discretized by B-spline approximation which is implemented in the spirit of FD technique using a local B-spline collocation scheme. The key aspect of the method is that any derivative is stated as neighbouring nodal values based on B-spline interpolants. The set of neighbouring nodes are allowed to be randomly distributed thus enhanced flexibility in the numerical simulation can be obtained. The method requires no mesh connectivity at all for either field variable approximation or integration. Time integration is performed by using the Crank-Nicolson implicit time stepping technique. Findings: – Several heat conduction problems in complex domains which represent for extended surfaces in industrial applications are examined to demonstrate the effectiveness of the present approach. Comparison of the obtained results with solutions from other numerical method available in literature is given. Excellent agreement with reference numerical method has been found. Research limitations/implications: – The method is presented for 2D problems. Nevertheless, it would be also applicable for 3D problems. Practical implications: – A transient two dimensional heat conduction in complex domains which represent for extended surfaces in industrial applications is presented. Originality/value: – The presented new meshless local method is simple and accurate, while it is also suitable for analysis in domains of arbitrary geometries.