A Linearized Analytical Solution Of PDE Heat Transfer In A Solid Material Excited By Light With Radiant Thermal Losses


  • Raúl González-García
  • Rumen I. Tsonchev
  • Miguel A. Ruiz-Cabrera
  • Alicia Grajales-Lagunes
  • José J. Villa-Hernández
  • Daniel Alaniz-Lumbreras




Heat transfer, PDE, Radiant losses, Analytical solution.


A method to linearize partial differential equations (PDEs) of heat diffusion and its initial with boundary conditions in a wide interval of temperature is presented. Thus, an analytical solution of the heat conduction problem was achieved in a virtual experiment performed in a lead wall with an ideally established configuration. For other arrangements where an analytical solution is not possible, simple standard programs can be used as an alternative to solve the linearized partial differential equations obtained with the proposed method. A sophisticated computer program as the standard gold method of COMSOL Multiphysics® was used for the evaluation of error of procedure. It was validated that the relative error of the analytical solution, in comparison to the digital simulation with COMSOL Multiphysics, can be found without the need to own and use the COMSOL Multiphysics program. For our configuration, the error is 1.16 % and focuses on the initial part of the process.