Exact and analytic-numerical solutions of bidimensional lagging models of heat conduction

Lagging models of heat conduction, such as the Dual-Phase-Lag or the Single-Phase-Lag models, lead to heat conduction equations in the form of partial differential equations with delays or to partial differential equations of hyperbolic type, and have been considered to model microscale heat transfer in engineering problems or bio-heat transfer in medical treatments.In this work we obtain explicit solutions for bidimensional lagging models of heat conduction, with different types of boundary conditions, in the form of infinite series solutions, allowing the construction of analytic-numerical solutions with bounded errors. Numerical examples, showing differences between models and the influence of parameters, are discussed.