Computational fluid dynamic analysis of a phase change material (PCM) based heat sink has been carried out in the present study. The PCM used is RT44HC. Longitudinal fins made of aluminum have been considered. The influence of pertinent parameters viz., fin number, fin thickness, orientation and base thickness on melt fraction and operational time have been analyzed. The critical temperature considered for the study is 54.8 °C. The melting behavior of the PCM is simulated by using the volume of fluid (VOF) method. The design of the experiment has been performed using the Taguchi method. By using gray relational multicriteria optimization technique and multi-objective optimization on the basis of ratio analysis (MOORA) method, the best thermally performing configuration has been attained through the optimum values of operational time and melt fraction. In addition to the above, analysis of variance (ANOVA) is performed to find the most significant parameter. Based on the investigation, fin thickness and number of fins are observed to significantly influence the thermal transport.