The control volume formulation to model the convective–diffusive unsteady heat transfer over the 1-D semi-infinite domain

The aim of this work is to develop a formulation called the control volume capacitance method which can provide stabilized numerical results for convective–diffusive problems. The formulation employs the control volume approach to derive an artificial capacitance by equating heat and energy flow unsteady equations. The formulation is designed for materials that exhibit combined unsteady heat transfer and mass transport. Here, energy and in particular thermal capacitance are related to physical (real/material) and non-physical (non-real/mesh) quantities, respectively. The use of the control volume approach ensures that predicted temperature fields correspond exactly with the unsteady flow energy equation and so providing an extremely stable formulation. Unsteady convective–diffusive heat transfer is performed in the 1-D semi-infinite domain to demonstrate the applicability of the method. To validate the method, predictions are compared against exact and popular numerical schemes.