On the paradox of heat conduction in porous media subject to lack of local thermal equilibrium

An apparent paradox that appears in problems of heat conduction in porous media subject to lack of local thermal equilibrium (LaLotheq) that was introduced by Vadasz [Transport in Porous Media 59 (2005) 341–355] is reformulated and resolved. This apparent paradox relates to a combination of Dirichlet and insulation boundary conditions and leads the solution towards local thermal equilibrium (Lotheq).