Phase change materials (PCMs) are used to store thermal energy. They possess high specific energy at nearly constant temperatures. The usage of the PCMs is limited due to their very low thermal conductivity, which results in poor heat transfer. To overcome this problem usage of fins is a potential technique. In the current analysis, the surface area of the heat transfer fluid (HTF) tube is increased by radial (R-type), spiral (S-type), and longitudinal (L-type) fins. A 3D numerical analysis of melting and solidification is carried out on R-type, S-type, and L-type shell and tube (S&T) PCM heat exchanger (HX) by considering the inclination effects. Lauric acid is used as PCM. Phase change time, energy ratio, and exergy efficiency are considered to analyze the performance of HXs. MOORA analysis is carried out to select the best HX. It is observed that R-type HX at the vertical position has shown better performance among the selected HXs. Among the considered geometries, the maximum average exergy efficiency is obtained for 45° inclination with R-type HX and minimum for horizontally positioned L-type HX during both melting and solidification. The charging time of the vertically positioned HX, when compared to 45o oriented HX with R type, S type, and L type HX is observed to decrease by 47.5%, 45.7%, and 23%, respectively.