The latent thermal energy storage (LTES) using phase change material (PCM) is able to improve the efficiency of power plants. However, the convectional TES using constant heat flux will reduce the ratio latent heat, leading to the higher temperature at the end of energy storage and more cost of heat preservation (more expensive material and thicker wall of enclosure). Consequently, the LIES with two energy storage tanks are proposed. The heating method is simplified as time-dependent heat flux boundary and the effects of periods, Rayleigh numbers and amplifications are studied numerically. The results show that the time-dependent scheme can reduce the final average temperature of PCM. However, the total melting time is nearly twice as much as that of constant scheme when the amplification is 1.0. In order to enhance the heat transfer, the heat flux applied to the TES is enlarged with amplification factor. When the amplification is 2.0, the latent heat gets energy from sensible heat and the temperature difference between wall and adjacent PCM is larger. As a result, the total melting time is decreased compared with the constant scheme. (C) 2019 Elsevier Ltd. All rights reserved.