We examine the attachment of diffusion flames (DFs) near cold, chemically inert surfaces. A two-dimensional model based on the examination of the diffusion flame leading edge is constructed. Two matching procedures give separate models, the simplified model and the detailed model. A quench-distance formula is produced by the simplified model, which correlates the numerical results in terms of the reduced Damkohler number. The detailed model predicts quench distances in good agreement with numerical solutions for the stoichiometrics chosen herein. Heat fluxes to the cold adjacent surface from the flame tip are evaluated from the model. A formula is derived which predicts the flame heat flux to the surface beneath the flame leading edge. The final form of this formula contains a coefficient function of stoichiometry, which was derived by matching the theoretical and numerical predictions.