In the mathematical modeling of solid fuel combustion, thermal losses are commonly neglected to allow a rigorous analysis. In this work, different choice of simplifications was made, making the model more physically realistic. Besides the analysis of the solutions including existence and uniqueness, a classification in the combustion regimes as a function of thermal losses was obtained. Some examples were analyzed, evidencing the validity of the proposed classification. Numerical simulations with more realistic models show the validity of the proposed formulas and applications for filtration combustion. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.