Abordagem introdutória da equação de condução do calor linear e não linear

Abstract

The heat conduction equation is a Partial Differential Equation (PDE) that deduces the behavior of the heat propagation phenomenon in the process of diffusion in solids, so that, through it, it is possible to measure the temperature variation in different positions of the solid, depending on the variation of the heat diffusion time. In addition to the objectivity of modeling the phenomenon of heat diffusion, this equation also has a lot of influence in other fields of science, being also used in mathematics, statistics, mechanics, civil engineering, etc. The present work seeks to approach the equation of homogeneous heat conduction and to deduce from the studies synthesized initially by Jean Baptiste Joseph Fourier. In addition to the appropriate deductions from the equation and exemplification of its application, the method of obtaining the classic solution of the one dimensional homogeneous heat conduction equation through the Variable Separation method will also be demonstrated for the Dirichlet boundary conditions, with fixed temperatures at the ends and for the Neumann boundary conditions, with heat flow derivatives fixed at the ends.