Modelling of heat transfer with bulk transport requires methods that are efficient and accurate. This is of paramount importance for the efficient simulation of many industrial processes including semi-solid forming and casting. This paper presents a new control volume capacitance method (CVCM) to cater for bulk transport. The governing equations utilised are described on a moving reference frame and are transformable into a finite element system that is similar to that used to model transient heat conduction. Any enthalpy discontinuities present are precisely accounted for with the application of an analytical integration procedure. Numerical tests on a 1-D semi-infinite problem are compared against analytical solutions; the approach is shown to be accurate, stable and computationally competitive.

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