In a recent article by Barletta and Nield (Transport in Porous Media, DOI 10.1007/s11242-008-9320-y, 2009), the title problem for the fully developed parallel flow regime was considered assuming isoflux/isothermal wall conditions. For the limiting cases of the forced and the free convection, analytical solutions were reported; for the general case, numerical solutions were reported. The aim of the present note is (i) to give an analytical solution for the full problem in terms of the Weierstrass elliptic P-function, (ii) to illustrate this general approach by two easily manageable examples, and (iii) to rise a couple of questions of basic physical interest concerning the interplay between the viscous dissipation and the pressure work. In this context, the concept of "eigenflow" introduced by Barletta and Nield is discussed in some detail.