Difference schemes for time-dependent heat conduction models with delay

Abstract

Different non-Fourier models of heat conduction, that incorporate time lags in the heat flux and/or the temperature gradient, have been increasingly considered in the last years to model microscale heat transfer problems in engineering. Numerical schemes to obtain approximate solutions of constant coefficients lagging models of heat conduction have already been proposed. In this work, an explicit finite difference scheme for a model with coefficients variable in time is developed, and their properties of convergence and stability are studied. Numerical computations showing examples of applications of the scheme are presented.

Keywords:

• non-Fourier heat conduction
• finite differences
• convergence and stability

2010 AMS Subject Classifications:

• 65M06
• 65M12
• 65Q20
• 35R10
• 80M20