A physical process of transient heat transfer during charging and discharging of the latent heat storage unit has been analysed in this paper. A mathematical model has been set by observing heat phenomena of the conjugate problem of transient forced convection between heat transfer fluid and the wall, heat conduction through the wall and the heat exchange of the phase change material in the elementary storage section. Differential equations of flow and heat transfer of the heat transfer fluid, differential equation of heat conduction through the wall and differential enthalpy equation of the phase change material, with initial and boundary conditions, have been discretised by a control volume approach. The obtained set of algebraic equations has been solved by Fortran software using the iterative procedure. Numerical analysis has been applied to the model of latent heat storage unit, used in experimental investigations, to validate the defined numerical model. Mutual agreement has been established between numerically and experimentally obtained timewise temperature variations. An exergy analysis, based on the second law of thermodynamics, has been applied for determining the efficiency of the storage unit. Temperature fields and melting i.e. solidification fronts in different time periods have been obtained by numerical calculation of transient heat transfer in the storage unit and thermal behaviour of the heat storage unit has been simulated. A series of numerical procedures has been performed in order to analyse the influence of different operating conditions and construction parameters on the amount of charged i.e. discharged energy and exergy efficiency of the latent heat storage unit.