Analytical prediction of Nusselt number in a simultaneously developing laminar flow between parallel plates

A simultaneously developing laminar flow between parallel plates was studied. The wall temperatures were uniform and equal. A linear profile was used for the axial component of the velocity and then the energy equation was solved by the method of similarity. The expression obtained for the Nusselt number in this manner contained terms involving wall shear stress. In order to eliminate these terms, the velocity profile was approximated by a second-degree polynomial, which finally led to a closed form expression for the Nusselt number in terms of x ∗ and Pr. The prediction was compared with more exact existing results, which indicated the accuracy of the present analysis.