On the role of axial wall conduction in mini/micro counterflow heat exchangers

•Multidimensional wall conduction effects in counterflow parallel plate heat exchangers are studied.•The eigencondition exhibits singularities that hinder the computation of the eigenvalues.•A parametric study is presented showing the existence of four wall conduction regimes.•The optimum wall conductivity leads to wall axial and normal heat fluxes of similar magnitude.•The optimum wall conductivity does not exists for heat exchangers with moderately thick walls.