An Asymptotic Study of the Nusselt-Graetz Problem—Part I: Large x Behavior

A method is given for determining the large x behavior of the Nusselt number for a variety of Nusselt-Graetz problems. Exploitation of properties of the Laplace transform of the temperature yields analytic expressions for Nu as explicit functions of the other parameters of the problem. Accurate results (<1 percent error) are deduced for problems involving the laminar flow of a Newtonian flow between parallel plates and in a circular pipe (valid for all values of the wall Nusselt number).