A new mathematical method to solve highly coupled equations of heat and mass transfer in porous media

Abstract

Heat and mass conservation equations in porous media are coupled and, in general, solved, iteratively, by using the values of temperature and moisture content from previous iteration to calculate source terms. This is the traditional mathematical method and numerical stability is only ensured for small time steps, depending on the source term's magnitudes. This is specially important, when material properties have strong variations with moisture content. This paper presents an unconditionally stable numerical method, conceived accordingly to a new methodology, which considers: (i) linearization of the term giving the vapor exchanged at the boundaries in terms of temperature and moisture content and (ii) introduction of a new generic algorithm to solve, simultaneously, the governing equations, for each time step. Numerical stability of these two methods are compared and it is shown that, in addition to avoid numerical unstability for arbitrary time steps and material properties, convergence is always quickly reached, in the presently proposed calculation method.