Thermal energy transport in a two-dimensional horizontal and vertical channel with an isothermal rectangular beam attached to one adiabatic wall is investigated from the numerical solution of Navier-Stokes and energy equations. The solutions have been obtained for dimensionless aspect equations. The solutions have been obtained for dimensionless aspect ratios of beam, H/B=$0.25{sim}4$, Reynolds numbers, Re=$50{sim}500$ and Grashof numbers, Gr=$0{sim}5{ imes}10^4$. The mean Nusselt number, $overline{Nu}$ for horizontal and vertical channels shows same value at Gr=0 and increases as Gr increases and decreases as H/B increases at Re=100. $overline{Nu}$ of vertical channel shows higher in $0.25{leq}H/B<1.1$ and lower in $1.1{leq}H/B{leq}4.0$ than that of horizontal channel at $Gr=10^4$, Re=100. $overline{Nu}$ of vertical channel shows higher in $0.25{leq}H/B<1.1$ and lower in $1.1{leq}H/B=1.0$ than that of horizontal channel at Re=100, $0