High aspect ratio channels are a common internal cooling feature in Gas Turbine blades, mostly suitable for the trailing edge region or mid-chord regions. Traditionally such channels are fitted with rib-turbulators and/or pin-fin turbulators to augment heat transfer and prevent material failure. Highly efficient internal cooling of blades can improve the efficiency of a real Gas Turbine power cycle by tolerating higher Turbine Inlet Temperatures (TIT). Multi-physics Topology optimization (TO) has been employed in the current study to find optimized shape of these ducts, with an aim to increase heat transfer, while constraining the pressure drop across the channel. This method, commonly used in structural problems, is a novel topic of research when applied to fluid-thermal studies. Material distribution in the computational domain is varied by changing porosity value in each cell and thereby altering the fluid path and creating a conjugate heat transfer problem. Each cell has a value of Brinkmann porosity factor which either simulates a blockage, or a fluid region depending on a low or high value of this design variable. Hence the degree of freedom is high in this method, and there is no manual bias introduced, unlike in parametric shape optimization which is limited to a few design parameters. The unconventional geometries obtained as an end product of this optimization process can thus be an alternative to existing rib/pin-fin type of cooling geometries. The recent progress in additive manufacturing can now facilitate the manufacturing of complicated shapes. An in-house Open-FOAM solver has been used to carry out the process in only twice the amount of time compared to a regular RANS-CFD. 3-Dimensional rectangular channels with inlet aspect ratios of 4:1 and 8:1 have been considered as baselines with a constant inlet velocity. Resulting optimum geometries were found to have organic tree like branching arrangements of rib-like wall roughness and v-shaped structures.