A general boundary-layer coordinate transformation was proposed in order to find the necessary conditions under which similarity solutions exist for free, forced and mixed convective Darcian flows subject to local thermal non-equilibrium. The aim of this study is to present the effects of local thermal non-equilibrium on the boundary-layer heat transfer in porous media, identifying each of the parameters controlling the thermal boundary-layer development. The findings of this systematic study are quite beneficial to those dealing with thermal applications using porous media. Similarity solutions are found to exist for such local thermal non-equilibrium cases as forced convection around the stagnation regions of horizontal cylinder and sphere heated according to a power function of the distance from the stagnation point, free convection over a vertical plate with its temperature increasing linearly, and free and mixed convection around the stagnation regions of isothermally heated horizontal cylinder and sphere. The study clearly indicates that the local thermal equilibrium assumption results in substantial overestimation of heat transfer rates. The local non-equilibrium effects must be considered when the modified interstitial Stanton number is less than its criterion value around 10.