A mathematical/empirical model compatible with the jet mixing theory for predicting the flow field properties, flame envelope, temperature distribution, and flame heights around a free vertical axi-symmetric turbulent diffusion flame has been developed. The model considers the effects of buoyancy force and the relative angle between the reactant jets. The flames are issued from a burner which consists of a central air jet and an annular fuel (commercial butane) jet. The annular jet is issued either vertically or at an angle to the flame axis. Experiments were performed earlier to measure the temperature distribution and concentration of carbon dioxide and oxygen in such flames. Three angular positions of the annular fuel jet and nine burner geometries were investigated. The model predictions in similar configurations are found to be in fair agreement with the experimental data.