A versatile numerical tool based on the open-source framework OpenFOAM has been developed in this paper for modeling time-accurate, low-Mach number reacting flows, with a particular interest in small-scale flames. This tool consists of a gas-phase Navier-Stokes solver and a solid-wall heat conduction solver which can be implemented alone, or used together in a coupled means to reveal the small-scale combustion’s characteristics of significantly enhanced flame-wall thermal coupling. Validation works has proved that the tool is capable of reproducing experimental flames at various scales (from conventional to small scales), including well-recognized micro-flame features in literature such as three modes of premixed flame dynamics (weak flames, flames with repetitive extinction and ignition, and stable flames). Then, an experimentally-already-found but rarely-simulated unique phenomenon of diffusion flame street is successfully reproduced with well-captured flame structures. Moreover, the conjugate heat transfer model with the specific formulation of solid-wall heat conduction enables an attempt to simulate a novel, thermally-orthotropic combustor with its axial thermal conductivities superior to the transverse ones. Finally, computational performance of the developed OpenFOAM solver is compared to that of the previously-used compressible flow solver Eilmer. The OpenFOAM solver is found to show better wave-damping abilities for overcoming acoustic wave effects at the initial stage of simulations, and is much more efficient in terms of the computational cost.