Calcium carbonate is wildly used in cementitious composites at different scales and can affect the properties of cementitious composites through physical effects (such as the filler effect, dilution effect and nucleation effect) and chemical effects. The effects of macro (>1 mm)-, micro (1 μm–1 mm)- and nano (<1 μm)-sizes of calcium carbonate on the hydration process, workability, mechanical properties and durability are reviewed. Macro-calcium carbonate mainly acts as an inert filler and can be involved in building the skeletons of hardened cementitious composites to provide part of the strength. Micro-calcium carbonate not only fills the voids between cement grains, but also accelerates the hydration process and affects the workability, mechanical properties and durability through the dilution, nucleation and even chemical effects. Nano-calcium carbonate also has both physical and chemical effects on the properties of cementitious composites, and these effects behave even more effectively than those of micro-calcium carbonate. However, agglomeration of nano-calcium carbonate reduces its enhancement effects remarkably.

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Purpose The main purpose of this paper is to calculate the analytical solution or a closed-form solution for the temperature distribution in the heterogeneous casting-mould system. Design/methodology/approach First, the authors formulate and analyze the mathematical formulation of heat conduction equation in the heterogeneous casting-mould system, with an arbitrary assumption of the ideal contact at the cast-mould contact point. Then, He-Laplace method, based on variational iteration method (VIM), Laplace transform and homotopy perturbation method (HPM), is used to elaborate the analytical solution of this system. The main focus of He-Laplace method is to find the Lagrange multiplier with an easy approach which enables the implementation of HPM very smoothly and provides the series solution very close to the exact solution. Findings An example is considered to show that He-Laplace method provides the efficient results for calculating the temperature distribution in the casting-mould heterogeneous system. Graphical representation and error distribution represents that He-Laplace method is very simple to implement and effective for casting-mould heterogeneous system. Originality/value The work in this paper is original and advanced. Specially, calculation of Lagrange multiplier for casting-mould system has not been reported in the literature for this work.