Study of iterative characteristics of convective-diffusive and conjugate heat transfer problems

Iterative characteristics of convective-diffusive equations can be substantially different from the results obtained from analyzing diffusive equations. This study investigates the convergence characteristics of both a single-phase convective-diffusive equation and a conjugate heat transfer problem represented by a combined pair of convective-diffusive and purely diffusive equations. A diagonal enhancement technique has been devised that improves the stability for both problems while substantially broadening the range of relaxation factors allowable by the iterative algorithm. An illustration is also presented on how nonlinear thermal conductivities can destabilize a line iterative procedure, with the usefulness of the diagonal enhancement method demonstrated. Furthermore, poor convergence rates can arise from constant heat flux boundary conditions if the ratio of thermal conductivities between the solid and fluid is greater than 0(l). In such cases a method employing nonuniform grid spacing is shown to partially offset the adverse effect of disparate conductivities by improving convergence.