3-D thermoacoustic instability analysis based on Green's function approach

•Tailored Green's function approach has been presented in time and frequency domain.•Green's function approach provides stability information with low numerical effort.•Stability behaviour of a flame in a box depends on the orientation of the flame.•Passive control can be achieved by careful choice of flame position and orientation.•Thermoacoustic modes with similar frequencies can cause acoustic beating.•Study is fundamental, yet gives guidelines for furnace design.