Finite Volume Solution of a 1-D Hyperbolic Conduction Equation

A one-dimensional hyperbolic conduction equation written in primitive variables is solved by a numerical method based on a finite volume formulation. Accuracy of the proposed formulation is verified by exact solutions for homogeneous medium and then applied to composite materials with different conductivity, specific heat, and heat flux lagging constant. Results show quite distinct wave penetration through and reflection at interfaces of dissimilar materials even though the wave speed in the second medium remains identical in all cases. Effect of non-uniform cross-sectional area on wave propagation is also examined. The formulation is straightforward and can be easily extended to multidimensional problems for heterogeneous media with temperature-dependent properties since no special treatments are needed at the interfaces.