The problem of laminar-flow heat transfer in tubes of rectangular and triangular cross section is considered. A numerical relaxation method is used to obtain minimum limiting Nusselt-number magnitudes to supplement the presently available data. Boundary conditions of both constant heat input per unit of length, and constant wall temperature are included. For the case of rectangular tubes sufficient points have been calculated so that interpolation of the limiting Nusselt numbers for any aspect ratio can be accomplished. Experimental data are presented for a square tube for both constant wall temperature and constant heat input, and for a rectangular tube, aspect ratio 2.62, for constant wall temperature. These data, together with the limiting Nusselt-number theory, provide a rational basis for estimation of entrance-length effects for rectangular tubes, and result in a correlation in the form, NNu = ϕ[NRNPr/(l/4rh)], applicable to the design of gas-flow heat exchangers.