Radiative heat transfer plays a crucial role in most fire hazard related combustion processes. The existing classic and modified mass transfer B-Numbers have deficiencies for some burning cases of fires because they do not involve external radiation and/or assume flame transparent to thermal radiation. This study extended the concept of the mass transfer B-Number using the one-dimensional steady-state diffusion flame model. An analytical expression of the universal mass transfer B-Number B-R was derived, which applies to semi-transparent flames with external radiation. Compared with the classic mass transfer B-Number, in the numerator denoting the net heat generated and held by the combustion system, B-R has an additional term that represents radiative heat which is being held and transferred within the semi-transparent flame; as well as in the denominator denoting the convective heat needing for maintaining the combustion, the contribution from the radiative heat is deducted from the total heat required for vaporizing a unit mass of fuel at the fuel surface. B-R increases as external radiation and/or ambient oxygen concentration raise. In order to examine its physical significance, new parameters were defined and illustrated, such as the mass transfer equivalent absorption coefficient, specific radiant heat feedback and radiation factor, that demonstrate interactions of heat and mass transfers and radiative absorption and emission within inhomogeneous flames. Effects of the external radiation and ambient oxygen concentration on these parameters were also evaluated. Increases in the radiation factor as the ambient oxygen concentration rises theoretically validated enhanced radiative heat transfer in rich oxygen combustion. (C) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.