The purpose of this paper is to establish the detailed parametric study for compressible natural convection flow of two-phase dusty fluid along a vertical wavy cone. Typical sinusoidal surface is used to elucidate the heat transport phenomena for the compressible dusty fluid. The governing equations are transformed into parabolic coordinates and the singularity of the leading edge is removed. The resulting equations are then solved straightforwardly by implicit finite difference method. The influence of compressibility, dusty fluid and the transverse curvature of the surface are discussed in detail in terms of local heat transfer rate, skin friction coefficient, velocity and temperature distributions. In order to ensure the accuracy, comparison with some special cases are also presented and the agreement is found to be very good. The key observation from the present study is that the half-cone angle, 0, and mass concentration parameter, D rho, extensively promote the rate of heat transfer into the compressible boundary layer region. (C) 2016 Elsevier Ltd. All rights reserved.