As a small scale, two-phase, passive thermal device, micro heat pipe (MHP) has promising applications to transfer high heat flux from dissipating components & mitigate the formation of hot spots while minimizing the thermal stress on avionic packages used in spacecraft applications. With water as the working fluid, the current work presents a comparative thermal analysis of a silicon MHP having triangular & square cross- sections with a generalised constant temperature mathematical model. Based on the mass, momentum & energy equations for respective phases (liquid & vapor), the numerical model has considered interfacial mass & energy transfer, wall shear stresses & lastly, interfacial shear stress between liquid & vapor phase. Young-Laplace equation is utilized to address the interfacial pressure change & estimate the thickness of the liquid film. It is observed that, for a given hydraulic diameter, formation of dry-out is prolonged in a triangular channel ensuring higher heat transfer capability. Restricted capillary pumping at the end portion & higher relative velocity between liquid and vapor phase at the inlet portion results in lower thermal performance of a square channel, instead of having more number of corners than the triangular one. A parametric analysis with respect to hydraulic diameter, effective length & temperature of operation is conducted for both the channels & estimation of maximum heat transfer capability is duly presented with appropriate curve fitting.