Gas Turbine blade cooling is an important topic of research, as a high turbine inlet temperature (TIT) essentially means an increase in efficiency of gas turbine cycles. Internal cooling channels in gas turbine blades are key to the cooling and prevention of thermal failure of the material. Serpentine channels are a common feature in internal blade cooling. Optimization methods are often employed in the design of blade internal cooling channels to improve heat-transfer and reduce pressure drop. Topology optimization uses a variable porosity approach to manipulate flow geometries by adding or removing material. Such a method has been employed in the current work to modify the geometric configuration of a serpentine channel to improve total heat transferred and reduce the pressure drop. An in-house OpenFOAM solver has been used to create non-traditional geometries from two generic designs. Geometry-1 is a 2-D serpentine passage with an inlet and 4 bleeding holes as outlets for ejection into the trailing edge. Geometry-2 is a 3-D serpentine passage with an aspect ratio of 3:1 and consists of two 180-degree bends. The inlet velocity for both the geometries was used as 20 m/s. The governing equations employ a “Brinkman porosity parameter” to account for the porous cells in the flow domain. Results have shown a change in shape of the channel walls to enhance heat-transfer in the passage. Additive manufacturing can be employed to make such unconventional shapes.