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Experiments have been carried out to observe fire plume interactions of free-standing equi-distant identical fires in 3x3 and 5x5 square arrays in terms of plume dynamics and fire whirls at various inter-fuel pan distances, and also to measure and record the corresponding burn-out times of individual fires in the arrays from ignition relative to that of a single free-standing fire which is used as a reference. The difference in the burn-out times of any fire in a given array from the reference fire is an indication of how fire plume interaction affects the average burn rate of that fire. It is observed that flame interactions depend strongly on the fuel-pan spacings. An analysis of the empirical data on the burn-out times of individual fires, expressed in terms of an interaction index, shows different extents of interactions at various fire locations in the array and also at different distances between adjacent fuel pans. Similarities and differences in interactions between the 3x3 and 5x5 fire arrays have also been noted.