Rayleigh-Benard convection in normal fluids shows interesting variation when a boundary is temperature modulated. As granular fluids show quite good resemblance to normal fluids, it is expected that they exhibit similar variation in convective dynamics under such a condition. A study of convection in granular fluids by injecting spatially non-uniform energy through a boundary is done in this paper. Emphasis is made on the dependence of onset and strength of granular convection on the relevant dimensionless parameters characterizing the convective state. The non-uniform energy injection is modelled by spatially periodic modulation of the lower boundary. It is seen that the amplitude and the wavelength of the periodic modulation are two new important parameters characterizing the dynamics. (C) 2017 Elsevier B.V. All rights reserved.