In this paper a numerical and asymptotic analysis to the Graetz problem with viscous dissipation is carried out, based on a series expansion of the temperature field, the Nusselt number is reported for different values of the Brinkman number. The range of Brinkman numbers considered has been extended to larger values. Numerical results are compared with an asymptotic analysis to larger values of Brinkman number. (C) 2021 The Author(s). Published by Elsevier B.V.