In this study, an algorithm is proposed which takes into account the manufacturing (EDM and extrusion) constraints as well as container design, temperature drop criterion between the evaporator and condenser together the with the vapor and liquid pressure losses for axially grooved heat pipes. The algorithm was executed for rectangular, triangular, trapezoidal and reentrant grooved heat pipes for a fixed outer diameter with and without manufacturing constraints. It was seen that for all groove types, the maximum heat transport capacity was found to be higher for the case in which manufacturing constraints are neglected. Results also show that for trapezoidal and reentrant grooves, the width and depth combinations yielding the maximum heat transport cannot be actually manufactured. On the other hand, the maximum heat transport occurs in the range where the heat pipe can actually be manufactured for rectangular and triangular grooves.