In this work, experimental measurements of flame heat flux and sample mass loss rate are obtained as a diffusion flame spreads vertically upward (in the direction opposed to the vector of gravity) over the surface of seven commonly used polymeric materials, two of which are glass reinforced composites. Using these measurements, a previously developed empirical flame model specific to poly(methyl methacrylate) is generalized such that it can predict (flame to material surface) heat feedback from 3 to 20 cm tall flames supported by a wide range of materials. Model generalization is accomplished through scaling on the basis of a material's gaseous pyrolyzate heat of combustion, which can be measured using mg-sized material samples in a microscale combustion calorimeter. For all seven materials tested in this work, which represent diverse chemical compositions and burning behaviors including polymer melt flow, sample burnout, and heavy soot and solid residue formation, model-predicted flame heat flux (to a water-cooled heat flux gauge) is shown to match experimental measurements taken across the full length of the flame with an average absolute error of 3.8 kW m(-2) (approximately 10-15% of peak measured flame heat flux). Coupled with a numerical pyrolysis solver, this generalized wall flame model provides the framework to quantitatively study material propensity to ignite and support early fire growth in a range of common scenarios with a level of accuracy and reduced computational cost unmatched by other currently available modeling tools. (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.