The current study develops a transient combustion model formulated in oblate ellipsoidal coordinates to analyze the behavior of non-buoyant burner-generated diffusion flames. The combustion model is axially symmetric and considers a porous gas-fueled burner called the Burning Rate Emulator (BRE), which is idealized as an ellipsoidal disk. An approximate analytical transient solution for the flame shape and heat transfer to the surface of the burner is generated as a product of the exact steady-state result and the asymptotic transient result that becomes exact far from the burner. Microgravity BRE experiments conducted at NASA Glenn's 5.18-s Zero Gravity Research Facility indicated the evolution of an approximately ellipsoidal flame moving away from the burner with steady state not achieved during the 5-second test period. The microgravity experimental results are shown to be in good agreement with the mathematical model, which can help predict the flame behavior beyond the duration of the test. Published by Elsevier Inc. on behalf of The Combustion Institute.