Today heat pipes are widely used by the designers in industries such as air conditioning and heat transformers for optimizing energy consumption. Existence of a permeable cylinder at the beginning and ending part of the heat pipe was considered on the basis of two assumptions for surface temperature of the cylinder and the mainstream velocity at the outer edge of the boundary layer vary linearly with the axial distance x from the leading edge. In this paper solution has been presented analytically with introduction of mixed convection parameter and coefficient of porosity . Various forms of flow were examined and the optimum state for minimum entropy generation was suggested. Manuscript profile