Solar power microturbines are required to produce steady power despite the fluctuating solar radiation, with concerns on the dispatchability of such plants where thermal energy storage may offer a solution to address the issue. This paper presents a mathematical model for performance prediction of a honeycomb sensible-heat thermal energy storage designed for application of concentrated solar power microturbine. The focus in the model is to consider the laminar developing boundary layers at the entry of the flow channels, which could have a profound effect on the heat-transfer coefficient due to large velocity and temperature gradients, an effect which has not been considered in the modelling of such storage systems. Analysing the thermal and hydrodynamic boundary layer development, the Nusselt number and the friction factor were evaluated using a validated conjugate heat-transfer method. The simulations results were used to develop accurate regression functions for Nusselt number and friction factor. These formulations have been adopted within a one-dimensional model to evaluate the performance of the storage under different operating conditions. The model was in good agreement with conjugate heat transfer results with maximum relative error below 2%. Two case studies are presented to demonstrate the applicability of the proposed methodology.