For Newtonian concentric annular flows analytical solutions are obtained under imposed asymmetric constant wall heat fluxes as well as under imposed asymmetric constant wall temperatures, taking into account viscous dissipation and for fluid dynamic and thermally fully-developed conditions. Results for the special case of the heat flux ratio for identical wall temperatures and the critical Brinkman numbers marking changes of sign in wall heat fluxes are also derived. Equations are presented for the Nusselt numbers at the inner and outer walls, bulk temperature and normalised temperature distribution as a function of all relevant non-dimensional numbers. Given the complexity of the derived equations, simpler exact expressions are presented for the Nusselt numbers for ease of use, with their coefficients given in tables as a function of the radius ratio. (c) 2006 Elsevier Ltd. All rights reserved.