Premixed hydrogen/air micro-flame stabilizations in a narrow channel confined by two parallel plates with thermally isotropic and orthotropic wall materials are numerically studied using a OpenFOAM-based, reacting flow code. For a range of simulated equivalence ratios and inflow velocities, two modes of flame shapes (convex-shaped and concave- shaped) are observed, accompanying with variations of the number of heat release rate peaks in flame structures, which can be attributed to the appearance of some critical O-participating and H-participating elementary reactions. Flame stability limits are studied for three sets of wall thermal conductivities of k = 16 W/m K, k = 128 W/m K (isotropic) and k(xx) = 128 W/m K & k(yy) = 16 W/m K (orthotropic). The low velocity limits show invariant with wall thermal conductivities, while the high velocity limits in descending order are found to be: "k = 128 W/m K" > "k(xx) = 128 W/m K & k(yy) = 16 W/m K" > "k = 16 W/m K". The logic behind is the competition between two mechanisms: the wall pre-heating effects and the transverse heat losses to the ambient. The critical convective heat transfer coefficients that reflect the combustor's ability to resist heat losses are also investigated among the three cases. The reduction of the transverse thermal conductivity can have a high critical coefficient value in the low-inflow velocity regime while makes negligible impacts on extending the critical coefficient in the high-inflow velocity regime. In summary, the use of thermally orthotropic wall materials leads to a slightly decreased high velocity limit ((similar to)3% lower) but a considerably increased critical convective heat transfer coefficient in the high-inflow velocity-regime ((similar to)25% higher), as compared to the thermally isotropic combustor of k = 128 W/m K. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.