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Purpose -- The purpose of this paper is to conduct a numerical study to analyze the melting process along a vertical wavy surface with uniform surface temperature. Design/methodology/approach -- The cavity horizontal walls are insulated while the left hot wavy wall and the right cold wall are maintained at temperatures, TH = 38.3°C and TC = 28.3°C, respectively. The enclosure was filled by solid Gallium initially at temperature TC. A numerical code is developed using an unstructured finite-volume method and an enthalpy porosity technique to solve for natural convection coupled to solid-liquid phase change. The validity of the numerical code used is ascertained by comparing the results with previously published results. Findings -- The effect of number of wavy surface undulation and amplitude of the wavy surface on the flow structure and heat transfer characteristics is investigated in detail. The numerical results show that the enhanced total heat transfer rate seems to depend on the amplitude of the wavy surface. Originality/value -- Flow and heat transfer from irregular surfaces are often encountered in many engineering applications to enhance heat transfer such as micro-electronic devices, flat plate solar collectors and flat-plate condensers in refrigerators, etc. Roughened surfaces could be used in latent storage systems where the wall heat flux is known. One of the reasons why a roughened surface is more efficient in heat transfer is its capability to promote fluid motion near the surface; in this way a complex wavy surface is expected to promote a larger heat transfer rate than a flat plate. This complex geometry will promote a correspondingly complicated motion in the fluid near the surface; this motion is described by the nonlinear boundary-layer equations. [ABSTRACT FROM AUTHOR]