A 2D Model for Heat Transport in a Hele–Shaw Geometry

This paper is devoted to the theoretical and numerical analysis of the heat transport problem through a viscous and incompressible fluid in a Hele–Shaw geometry. This model corresponds to a bi-dimensional system derived from the 3D-Navier–Stokes equations coupled with an advection-diffusion equation for the heat transport. We analyze the existence of global solutions and construct a numerical scheme, based on finite element approximations in...