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Thermal energy storage plays an important role in correcting the disparity between energy supply and demand as well as improving the energy efficiency. The present work numerically investigates the conjugate heat transfer between PCM and heat transfer fluid within the novel and efficient frustum-shaped thermal storage units. A two-dimensional control volume-based numerical model is developed employing the CFD software Fluent. Five units of equal volume but different dimensions are compared to illustrate impacts of geometry on melting, and the optimal geometric design is determined. Then, the multiple PCMs technology is employed to the optimal unit to further enhance the melting heat transfer. Effects of the multiple PCMs arrangement, multiple PCMs' melting temperature distribution, and type on the melting behavior and heat transfer are investigated. Compared with the frustum-shaped and traditional shell-and-tube unit with a single PCM, predicted results indicate that the five PCMs arrangement in frustum-shaped unit can make the thermal storage time reduced by 21.5 % and 47.5 %, respectively. The great improvement may be of great significance to the optimal design of latent heat storage. [ABSTRACT FROM AUTHOR]