This study analyses the influence of axial conduction and Biot number on the forced convective heat transfer characteristics in a duct filled with porous material that is thermally developing under local thermal non-equilibrium (LTNE). Channel walls are subjected to heat flux. The unidirectional flow in the porous region corresponds to the Darcy Brinkman model. A successive accelerated replacement (SAR) approach has been used to obtain numerical solutions. The investigations further quantify the impact of the Biot number on heat transfer enhancement. For fluid-solid phases, dimensionless temperatures, and local Nusselt number (<i>Nu_&xi;</i>), profiles are given in the present investigation. Validation of fully developed conditions for LTNE is done. The axial conduction effect is more at the low Peclet number <i>Pe_H</i> for all the Biot numbers Bi. For large <i>Pe_H</i>, the axial conduction effect is negligible. The <i>Nu_&xi;</i> decreases as the ratio of thermal conductivities, <i>&kappa;</i> and <i>Bi</i>, increases. LTNE is equivalent to local thermal equilibrium (LTE) for a large Bi.