The present work is concerned with the computational analysis of flow and heat transfer from the circular pin fin channels in the trailing edge region of a gas turbine vane. Combined effects of channel shape, conjugate boundary condition and flow orientation are studied. Four different channel shapes: Straight Rectangular, Straight Converged, Cambered Rectangular and Cambered Converged are considered. Both straight and lateral coolant entry are investigated at a nominal Reynolds number of 20,000. Numerical simulations are performed for the steady, incompressible, turbulent flow with the help of a computational fluid dynamics code. A structured hexahedral mesh having about 5 million cells is generated in the domain. The computational methodology is validated against the data from a standard ERCOFTAC bench mark test case. Flow and heat transfer characteristics at various locations in the channel and the axial temperature variation for a chosen pin are reported.