Mathematical modelling of heat transmission in the temperature history apparatus by using inverse method to evaluate the latent heat of high temperature PCMs.

• Inverse method used to improve original T-history method equations to determine PCMs latent heat. • The method shown to be suitable method to calculate latent heat of low thermal conductivity bulk PCMs. • New transient modelling is more suitable for calculating latent heat with cooling rates than using original equations. High temperature phase change materials (PCMs) are being proposed as thermal energy storage media in concentrated solar power plants. The thermophysical properties of PCMs, such as the latent heat of fusion/solidification need to be defined to enable system design and evaluate system performance and cost analysis. Several methods have been used to measure the latent heat of fusion/solidification of PCMs including the T-history method. The original assumption of the T-history method is the Biot number should be less than 0.1 where the lumped capacitance method is applicable. However, when the Biot number is more than 0.1 then the original equations are not applicable to estimate the latent heat of PCM. This paper demonstrates how a one-dimensional heat transfer mathematical model can be used by applying an inverse method to overcome the limitation of the lumped capacitance method in the original T-history method to determine the latent heat of PCMs. The mathematical model demonstrates that variation of the temperature distributions inside the samples for the discharge curves. Furthermore, this model shows the errors in the latent heat values if the T-history method is used. It is evident from the discharge curves of low thermal conductivity PCMs that the original simplified equations used for interpreting the T-history test results are not applicable for calculating the latent heat at different ambient temperature. [ABSTRACT FROM AUTHOR]