The Influence of Axial Conduction on the Thermal Entry-Region Heat Transfer in Magnetohydrodynamic Channel Flow

The influence of axial conduction on thermal entry-region temperature distribution and heat transfer in Hartmann's flow through a magnetohydrodynamic channel is analytically investigated. Viscous dissipation and Joule heating are also considered in the analysis. The temperature solutions, which are found to be Peclet number dependent, reduce to those corresponding to negligible axial conduction as the Peclet number approaches infinity. The appropriate first 12 eigenvalues and the corresponding eigenfunctions have been determined for Hartmann numbers of 1, 4, and 10 and for a wide range of Peclet numbers. The series expansion coefficients, applicable to an arbitrary value of the heat-generation parameter, have been evaluated for a few electric-field magnitude factors of practical importance. By employing the computed constants, the effect of the electric-field magnitude factor and the heat-generation parameter as well as axial conduction on the local temperature profiles and Nusselt numbers are examined and reported.