This study establishes forward closed-form and inverse analyses of wet fins of various profiles involving all modes of heat transfer. Existing limitations in the literature are addressed here by choosing the appropriate nonlinear variation of thermal conductivity and radiation effects. The error between linear and nonlinear methodologies is found to be within 60%. Furthermore, the maximum error between the closed-form solution based on the differential transformation method (DTM), and the numerical solution is observed as 0.5%. After necessary validations, optimization of various fin profiles is carried out by the maximization of the net fin heat transmission rate under a defined fin volume and thermogeometrical constraints. For the optimum criterion, the suitability of the artificial bee colony (ABC)-based metaheuristic technique is established. The identification of thermogeometrical parameters is realized by analyzing combinations obtained from 100 runs of ABC and the decision-making criterion is adopted on the basis of the maximum thermal performance. Among the studied profiles, concave parabolic geometry yields the maximum heat transport rate, which is followed by triangular, convex, and rectangular geometries for the same fin volume. The present combination of DTM and ABC techniques is proposed to be useful in practical applications toward design and the selection of evaporator fins for air-conditioning and refrigeration appliances operating under wet conditions in a more accurate and optimized manner.