Employing fin parameter and tip temperature, a new concept with Lagrange’s multiplier method is proposed to obtain the optimum width, height, heat dissipation, and efficiency of longitudinal fins for boiling heat transfer. A power-law type heat transfer coefficient is assumed in this analysis. Longitudinal fins of rectangular, convex parabolic, triangular, and concave parabolic profiles are first investigated. It is found that the optimum dimensions of a fin depends upon fin profile area, heat transfer coefficient at the fin base, and the thermal conductivity of the fin. Then, the least material fin profile is derived for each single heat transfer mode. To facilitate the thermal design of heat transfer components, simple mathematical expressions far the optimum dimensions of fins are presented in this study.