The present work is a numerical investigation of the combustion instability arising in a duct having non-premixed flame. The combustion occurs in a small zone inside the duct which acts as source of energy to the longitudinal acoustic waves in the duct. The presence of acoustics in duct causes the time variation in the pressure and velocity fields in the combustion zone. A two dimensional thermo-diffusive model is adopted for the combustion simulation. In the acoustic zone, the inhomogeneous wave equation is solved using the Galerkln technique. The growth of oscillations is compared with the exponential growth obtained using the linearised response function theory. In the present work, inhomogeneitys due to the sharp change in the temperature across the combustion zone is considered. The temperature gradient causes the change in the natural frequency of the duct acoustic modes and modification in the spatial distribution of the acoustic field. In order to show the effect of temperature gradient due to the presence of the flame, the computations are performed with and without considering the temperature gradient in duct.